Machine Learning Toolbox

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Introduction

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• Course notes from the Machine Learning Toolbox course on DataCamp
  • Taught by Max Kuhn, author of the caret package. Has been working on it over a decade
  • And Zachary Deane-Mayer, contribbutor to caret and working data scientist at data robot.

Whats Covered

• Regression models: fitting them and evaluating their performance
• Classification models: fitting them and evaluating their performance
• Tuning model parameters to improve performance
• Preprocessing your data
• Selecting models: a case study in churn prediction

Additional Resources

• caret package documentation on github
• Zach on kaggle
  • who, he has been in the top 10 in multiple competitions
• A brief introduction to caretEnsemble by Zach Mayer
• caret Models for train function

Libraries and Data

library(dplyr)
library(ggplot2)
library(mlbench) # sonar data
library(caret)
library(caTools)

source('create_datasets.R')

   

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Regression models: fitting them and evaluating their performance

---

Welcome to the course

• We will use the caret package in the course
• Supervised learning is machine learning when you have a target variable (aka predictive modeling)
  • Classic example is picking what species an iris belongs to based on its pedal measurements, or predicting which customers will churn
• Two types of predictive models
  • Classification - Qualitative (species of iris, churn yes or no)
  • Regression - Quantitative (price of a diamond)
• Need to use a metric to evaluate the models
  • This lets say how well the model fits the data in a quantifiable nad objective way
  • Root Mean Squarred Error (RMSE) is the most common metric for regression models
  • RMSE is what is minimized in the lm funciton in R
• Evaluating model performance
  • Its common to calculate in-sample RMSE.
  • However, in-sample error is too optimistic and leads to overfitting
  • Its much better to cacluate out-of-sample error
  • This simulates real world model usage and helps avoid overfitting

In-sample error example:

# Fit a model to the mtcars data
data(mtcars)
model <- lm(mpg ~ hp, mtcars[1:20, ])
model

## 
## Call:
## lm(formula = mpg ~ hp, data = mtcars[1:20, ])
## 
## Coefficients:
## (Intercept)           hp  
##    32.79788     -0.09301

# Predict in-sample
predicted <- predict(model, mtcars[1:20, ], type = "response")

# Calculate RMSE
actual <- mtcars[1:20,"mpg"]

as.numeric(predicted)

##  [1] 22.56685 22.56685 24.14800 22.56685 16.52124 23.03189 10.01058
##  [8] 27.03129 23.96199 21.35772 21.35772 16.05619 16.05619 16.05619
## [15] 13.73096 12.80086 11.40572 26.65926 27.96139 26.75227

actual

##  [1] 21.0 21.0 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 17.8 16.4 17.3 15.2
## [15] 10.4 10.4 14.7 32.4 30.4 33.9

sqrt(mean((predicted - actual)^2))

## [1] 3.172132

– In-sample RMSE for linear regression on diamonds

• errors = predicted − actual

data(diamonds)
glimpse(diamonds)

## Observations: 53,940
## Variables: 10
## $ carat   <dbl> 0.23, 0.21, 0.23, 0.29, 0.31, 0.24, 0.24, 0.26, 0.22, ...
## $ cut     <ord> Ideal, Premium, Good, Premium, Good, Very Good, Very G...
## $ color   <ord> E, E, E, I, J, J, I, H, E, H, J, J, F, J, E, E, I, J, ...
## $ clarity <ord> SI2, SI1, VS1, VS2, SI2, VVS2, VVS1, SI1, VS2, VS1, SI...
## $ depth   <dbl> 61.5, 59.8, 56.9, 62.4, 63.3, 62.8, 62.3, 61.9, 65.1, ...
## $ table   <dbl> 55, 61, 65, 58, 58, 57, 57, 55, 61, 61, 55, 56, 61, 54...
## $ price   <int> 326, 326, 327, 334, 335, 336, 336, 337, 337, 338, 339,...
## $ x       <dbl> 3.95, 3.89, 4.05, 4.20, 4.34, 3.94, 3.95, 4.07, 3.87, ...
## $ y       <dbl> 3.98, 3.84, 4.07, 4.23, 4.35, 3.96, 3.98, 4.11, 3.78, ...
## $ z       <dbl> 2.43, 2.31, 2.31, 2.63, 2.75, 2.48, 2.47, 2.53, 2.49, ...

# Fit lm model: model
model <- lm(price ~ ., diamonds)

# Predict on full data: p
p <- predict(model, diamonds)

# Compute errors: error
error <- p - diamonds$price

# Calculate RMSE
sqrt(mean(error^2))

## [1] 1129.843

Introducing out-of-sample error measures

• We want models that don’t overfit and generalize well
• We need to make sure the models perform well on new data
• We will test our models on new data (or test data) to simulate this real world usage.
• This is a key insight of machine learning. Its how we stay honest as a modeler.
• Using in-sample validation (testing on your training data) will give better model fits but it essentially garuntees that you overfit.
• The goal of the caret package and this course: don’t overfit.

Example of out-of-sample RMSE:

• Here we manually split the data
• in caret we can use createResamples() or createFolds() functions

# Fit model to the mtcars data (first 20 rows)
model <- lm(mpg ~ hp, mtcars[1:20, ])

# Predict out-of-sample
predicted <- predict(model, mtcars[21:32, ], type = "response")

# Evaluate error
actual <- mtcars[21:32, "mpg"]
sqrt(mean((predicted - actual)^2))

## [1] 5.507236

• RMSE has the same units as the test set so our model is off by 5-6 mpg on average.
• The in-sample was just 3.7 mpg off but its fooling us into thinking our model is better than it really is.
• With new data our model will work like the out-of-sample prediction

– Randomly order the data frame

• We set a seed so that our work is reproducible
• We randomly shuffle the rows so sorting does not affect our model, like being sorted by price.

# Set seed
set.seed(42)

# Shuffle row indices: rows
rows <- sample(nrow(diamonds))
head(rows)

## [1] 49345 50545 15434 44792 34614 27998

# Randomly order data
diamonds <- diamonds[rows, ]

– Try an 80/20 split

# Determine row to split on: split
split <- round(nrow(diamonds) * .80)
split

## [1] 43152

# Create train
train <- diamonds[1:split,]

# Create test
test <- diamonds[(split + 1):nrow(diamonds),]

dim(diamonds)

## [1] 53940    10

dim(train)

## [1] 43152    10

dim(test)

## [1] 10788    10

– Predict on test set

• the new data set in the predict model must have all the columns from the training data
• but they can be in a different order with different values

# Fit lm model on train: model
model <- lm(price ~ ., train)
model

## 
## Call:
## lm(formula = price ~ ., data = train)
## 
## Coefficients:
## (Intercept)        carat        cut.L        cut.Q        cut.C  
##    5179.769    11237.590      602.695     -307.809      151.088  
##       cut^4      color.L      color.Q      color.C      color^4  
##     -25.812    -1941.427     -660.511     -160.640       43.022  
##     color^5      color^6    clarity.L    clarity.Q    clarity.C  
##     -96.375      -47.526     4087.131    -1937.609      977.749  
##   clarity^4    clarity^5    clarity^6    clarity^7        depth  
##    -383.520      231.186        7.064       94.505      -56.218  
##       table            x            y            z  
##     -24.767     -967.581        9.207     -110.286

# Predict on test: p
p <- predict(model, test)

– Calculate test set RMSE by hand

# Compute errors: error
error <- p - test$price

# Calculate RMSE
sqrt(mean(error^2))

## [1] 1136.596

• This is just a little bit higher than the 1129.8 when training and test on the full dataset, but its less overfit.

Cross-validation

• In our last example we only used one split and train test cycle to get our expected RMSE
  • This is a little fragile as one outlier can really skew the fit
  • Its better to do this multiple times and average the out-of-sample error
• Cross validation is a common way to test our data multiple times
  • We create 10 folds (10 is common)
  • Each point in the data set occurs in exactly 1 of the folds and is assigned randomly
  • Only used to estimated out-of-sample error
  • After doing cross validation you throw away all of the re-sampled models and fit the final model on the full dataset
  • This takes 11 times longer than just doing one train test cycle. Its pretty expensive.
  • You can do this in the caret package or a very similar method of bootstrapping.

Cross Validation Example:

• the train function formula interface is exactly like the lm function in R
  • But it supports 100s of models in the method argument.
  • Here we use ‘lm’ but we could just as easily use ‘rf’ for random forest.
  • this is the second most useful feature of the caret package behind the cross validation of models.
• the trControl arugment controls the parameters used for cross validation
  • we will usually use 10 folds in the number argument
  • we use verboseIter so we can see the progress of each model and know if we have time to get coffee.

# the caret library is loaded
set.seed(42)

# Fit linear regression model using caret
model <- train(mpg ~ hp, mtcars,
               method = "lm",
               trControl = trainControl(
                 method = "cv",
                 number = 10,
                 verboseIter = T
               ))

## + Fold01: intercept=TRUE 
## - Fold01: intercept=TRUE 
## + Fold02: intercept=TRUE 
## - Fold02: intercept=TRUE 
## + Fold03: intercept=TRUE 
## - Fold03: intercept=TRUE 
## + Fold04: intercept=TRUE 
## - Fold04: intercept=TRUE 
## + Fold05: intercept=TRUE 
## - Fold05: intercept=TRUE 
## + Fold06: intercept=TRUE 
## - Fold06: intercept=TRUE 
## + Fold07: intercept=TRUE 
## - Fold07: intercept=TRUE 
## + Fold08: intercept=TRUE 
## - Fold08: intercept=TRUE 
## + Fold09: intercept=TRUE 
## - Fold09: intercept=TRUE 
## + Fold10: intercept=TRUE 
## - Fold10: intercept=TRUE 
## Aggregating results
## Fitting final model on full training set

model

## Linear Regression 
## 
## 32 samples
##  1 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 30, 29, 29, 28, 29, 28, ... 
## Resampling results:
## 
##   RMSE      Rsquared   MAE     
##   3.957996  0.9252153  3.349958
## 
## Tuning parameter 'intercept' was held constant at a value of TRUE

– 10-fold cross-validation

# Fit lm model using 10-fold CV: model
model <- train(
  price ~ ., diamonds,
  method = "lm",
  trControl = trainControl(
    method = "cv", number = 10,
    verboseIter = TRUE
  )
)

## + Fold01: intercept=TRUE 
## - Fold01: intercept=TRUE 
## + Fold02: intercept=TRUE 
## - Fold02: intercept=TRUE 
## + Fold03: intercept=TRUE 
## - Fold03: intercept=TRUE 
## + Fold04: intercept=TRUE 
## - Fold04: intercept=TRUE 
## + Fold05: intercept=TRUE 
## - Fold05: intercept=TRUE 
## + Fold06: intercept=TRUE 
## - Fold06: intercept=TRUE 
## + Fold07: intercept=TRUE 
## - Fold07: intercept=TRUE 
## + Fold08: intercept=TRUE 
## - Fold08: intercept=TRUE 
## + Fold09: intercept=TRUE 
## - Fold09: intercept=TRUE 
## + Fold10: intercept=TRUE 
## - Fold10: intercept=TRUE 
## Aggregating results
## Fitting final model on full training set

# Print model to console
model

## Linear Regression 
## 
## 53940 samples
##     9 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 48546, 48546, 48545, 48547, 48547, 48546, ... 
## Resampling results:
## 
##   RMSE      Rsquared   MAE     
##   1130.765  0.9196636  740.4743
## 
## Tuning parameter 'intercept' was held constant at a value of TRUE

– 5-fold cross-validation

# Fit lm model using 5-fold CV: model
model <- train(
  medv ~ . , Boston,
  method = "lm",
  trControl = trainControl(
    method = "cv", number = 5,
    verboseIter = TRUE
  )
)

## + Fold1: intercept=TRUE 
## - Fold1: intercept=TRUE 
## + Fold2: intercept=TRUE 
## - Fold2: intercept=TRUE 
## + Fold3: intercept=TRUE 
## - Fold3: intercept=TRUE 
## + Fold4: intercept=TRUE 
## - Fold4: intercept=TRUE 
## + Fold5: intercept=TRUE 
## - Fold5: intercept=TRUE 
## Aggregating results
## Fitting final model on full training set

# Print model to console
model

## Linear Regression 
## 
## 506 samples
##  13 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 404, 405, 405, 405, 405 
## Resampling results:
## 
##   RMSE      Rsquared   MAE     
##   4.816486  0.7249456  3.404306
## 
## Tuning parameter 'intercept' was held constant at a value of TRUE

– 5 x 5-fold cross-validation

# Fit lm model using 5 x 5-fold CV: model
model <- train(
  medv ~ ., Boston,
  method = "lm",
  trControl = trainControl(
    method = "cv", 
    number = 5,
    repeats = 5, 
    verboseIter = TRUE
  )
)

## + Fold1: intercept=TRUE 
## - Fold1: intercept=TRUE 
## + Fold2: intercept=TRUE 
## - Fold2: intercept=TRUE 
## + Fold3: intercept=TRUE 
## - Fold3: intercept=TRUE 
## + Fold4: intercept=TRUE 
## - Fold4: intercept=TRUE 
## + Fold5: intercept=TRUE 
## - Fold5: intercept=TRUE 
## Aggregating results
## Fitting final model on full training set

# Print model to console
model

## Linear Regression 
## 
## 506 samples
##  13 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 404, 405, 405, 405, 405 
## Resampling results:
## 
##   RMSE      Rsquared   MAE     
##   4.896398  0.7254017  3.423548
## 
## Tuning parameter 'intercept' was held constant at a value of TRUE

– Making predictions on new data

# Predict on full Boston dataset
p <- predict(model, Boston)
head(p)

##        1        2        3        4        5        6 
## 30.00384 25.02556 30.56760 28.60704 27.94352 25.25628

   

---

Classification models: fitting them and evaluating their performance

---

Logistic regression on sonar

– Try a 60/40 split

• The 60/40 split gives us a little more reliable test set since the dataset is small
• It would be even better to do a k-fold split as we did before

data(Sonar)

# Shuffle row indices: rows
rows <- sample(nrow(Sonar))

# Randomly order data: Sonar
Sonar <- Sonar[rows,]

# Identify row to split on: split
split <- round(nrow(Sonar) * .60)

# Create train
train <- Sonar[1:split,]

# Create test
test <- Sonar[(split + 1):nrow(Sonar), ]

nrow(train)/nrow(Sonar)

## [1] 0.6009615

– Fit a logistic regression model

• Don’t worry about warnings like:
  • glm.fit: algorithm did not converge or
  • glm.fit: fitted probabilities numerically 0 or 1 occurred
• These are common on smaller datasets and usually don’t cause any issues. They typically mean your dataset is perfectly seperable, which can cause problems for the math behind the model, but R’s glm() function is almost always robust enough to handle this case with no problems.
  • I think this means that we can perfectly figure out the Class based on the vairbles. Its probably becasue we have lots of data to use in the model and not many observations to predict.

glimpse(Sonar)

## Observations: 208
## Variables: 61
## $ V1    <dbl> 0.0086, 0.0209, 0.0491, 0.0131, 0.0201, 0.0187, 0.0664, ...
## $ V2    <dbl> 0.0215, 0.0261, 0.0279, 0.0068, 0.0116, 0.0346, 0.0575, ...
## $ V3    <dbl> 0.0242, 0.0120, 0.0592, 0.0308, 0.0123, 0.0168, 0.0842, ...
## $ V4    <dbl> 0.0445, 0.0768, 0.1270, 0.0311, 0.0245, 0.0177, 0.0372, ...
## $ V5    <dbl> 0.0667, 0.1064, 0.1772, 0.0085, 0.0547, 0.0393, 0.0458, ...
## $ V6    <dbl> 0.0771, 0.1680, 0.1908, 0.0767, 0.0208, 0.1630, 0.0771, ...
## $ V7    <dbl> 0.0499, 0.3016, 0.2217, 0.0771, 0.0891, 0.2028, 0.0771, ...
## $ V8    <dbl> 0.0906, 0.3460, 0.0768, 0.0640, 0.0836, 0.1694, 0.1130, ...
## $ V9    <dbl> 0.1229, 0.3314, 0.1246, 0.0726, 0.1335, 0.2328, 0.2353, ...
## $ V10   <dbl> 0.1185, 0.4125, 0.2028, 0.0901, 0.1199, 0.2684, 0.1838, ...
## $ V11   <dbl> 0.0775, 0.3943, 0.0947, 0.0750, 0.1742, 0.3108, 0.2869, ...
## $ V12   <dbl> 0.1101, 0.1334, 0.2497, 0.0844, 0.1387, 0.2933, 0.4129, ...
## $ V13   <dbl> 0.1042, 0.4622, 0.2209, 0.1226, 0.2042, 0.2275, 0.3647, ...
## $ V14   <dbl> 0.0853, 0.9970, 0.3195, 0.1619, 0.2580, 0.0994, 0.1984, ...
## $ V15   <dbl> 0.0456, 0.9137, 0.3340, 0.2317, 0.2616, 0.1801, 0.2840, ...
## $ V16   <dbl> 0.1304, 0.8292, 0.3323, 0.2934, 0.2097, 0.2200, 0.4039, ...
## $ V17   <dbl> 0.2690, 0.6994, 0.2780, 0.3526, 0.2532, 0.2732, 0.5837, ...
## $ V18   <dbl> 0.2947, 0.7825, 0.2975, 0.3657, 0.3213, 0.2862, 0.6792, ...
## $ V19   <dbl> 0.3669, 0.8789, 0.2948, 0.3221, 0.4327, 0.2034, 0.6086, ...
## $ V20   <dbl> 0.4948, 0.8501, 0.1729, 0.3093, 0.4760, 0.1740, 0.4858, ...
## $ V21   <dbl> 0.6275, 0.8920, 0.3264, 0.4084, 0.5328, 0.4130, 0.3246, ...
## $ V22   <dbl> 0.8162, 0.9473, 0.3834, 0.4285, 0.6057, 0.6879, 0.2013, ...
## $ V23   <dbl> 0.9237, 1.0000, 0.3523, 0.4663, 0.6696, 0.8120, 0.2082, ...
## $ V24   <dbl> 0.8710, 0.8975, 0.5410, 0.5956, 0.7476, 0.8453, 0.1686, ...
## $ V25   <dbl> 0.8052, 0.7806, 0.5228, 0.6948, 0.8930, 0.8919, 0.2484, ...
## $ V26   <dbl> 0.8756, 0.8321, 0.4475, 0.8386, 0.9405, 0.9300, 0.2736, ...
## $ V27   <dbl> 1.0000, 0.6502, 0.5340, 0.8875, 1.0000, 0.9987, 0.2984, ...
## $ V28   <dbl> 0.9858, 0.4548, 0.5323, 0.6404, 0.9785, 1.0000, 0.4655, ...
## $ V29   <dbl> 0.9427, 0.4732, 0.3907, 0.3308, 0.8473, 0.8104, 0.6990, ...
## $ V30   <dbl> 0.8114, 0.3391, 0.3456, 0.3425, 0.7639, 0.6199, 0.7474, ...
## $ V31   <dbl> 0.6987, 0.2747, 0.4091, 0.4920, 0.6701, 0.6041, 0.7956, ...
## $ V32   <dbl> 0.6810, 0.0978, 0.4639, 0.4592, 0.4989, 0.5547, 0.7981, ...
## $ V33   <dbl> 0.6591, 0.0477, 0.5580, 0.3034, 0.3718, 0.4160, 0.6715, ...
## $ V34   <dbl> 0.6954, 0.1403, 0.5727, 0.4366, 0.2196, 0.1472, 0.6942, ...
## $ V35   <dbl> 0.7290, 0.1834, 0.6355, 0.5175, 0.1416, 0.0849, 0.7440, ...
## $ V36   <dbl> 0.6680, 0.2148, 0.7563, 0.5122, 0.2680, 0.0608, 0.8169, ...
## $ V37   <dbl> 0.5917, 0.1271, 0.6903, 0.4746, 0.2630, 0.0969, 0.8912, ...
## $ V38   <dbl> 0.4899, 0.1912, 0.6176, 0.4902, 0.3104, 0.1411, 1.0000, ...
## $ V39   <dbl> 0.3439, 0.3391, 0.5379, 0.4603, 0.3392, 0.1676, 0.8753, ...
## $ V40   <dbl> 0.2366, 0.3444, 0.5622, 0.4460, 0.2123, 0.1200, 0.7061, ...
## $ V41   <dbl> 0.1716, 0.2369, 0.6508, 0.4196, 0.1170, 0.1201, 0.6803, ...
## $ V42   <dbl> 0.1013, 0.1195, 0.4797, 0.2873, 0.2655, 0.1036, 0.5898, ...
## $ V43   <dbl> 0.0766, 0.2665, 0.3736, 0.2296, 0.2203, 0.1977, 0.4618, ...
## $ V44   <dbl> 0.0845, 0.2587, 0.2804, 0.0949, 0.1541, 0.1339, 0.3639, ...
## $ V45   <dbl> 0.0260, 0.1393, 0.1982, 0.0095, 0.1464, 0.0902, 0.1492, ...
## $ V46   <dbl> 0.0333, 0.1083, 0.2438, 0.0527, 0.1044, 0.1085, 0.1216, ...
## $ V47   <dbl> 0.0205, 0.1383, 0.1789, 0.0383, 0.1225, 0.1521, 0.1306, ...
## $ V48   <dbl> 0.0309, 0.1321, 0.1706, 0.0107, 0.0745, 0.1363, 0.1198, ...
## $ V49   <dbl> 0.0101, 0.1069, 0.0762, 0.0108, 0.0490, 0.0858, 0.0578, ...
## $ V50   <dbl> 0.0095, 0.0325, 0.0238, 0.0077, 0.0224, 0.0290, 0.0235, ...
## $ V51   <dbl> 0.0047, 0.0316, 0.0268, 0.0109, 0.0032, 0.0203, 0.0135, ...
## $ V52   <dbl> 0.0072, 0.0057, 0.0081, 0.0062, 0.0076, 0.0116, 0.0141, ...
## $ V53   <dbl> 0.0054, 0.0159, 0.0129, 0.0028, 0.0045, 0.0098, 0.0190, ...
## $ V54   <dbl> 0.0022, 0.0085, 0.0161, 0.0040, 0.0056, 0.0199, 0.0043, ...
## $ V55   <dbl> 0.0016, 0.0372, 0.0063, 0.0075, 0.0075, 0.0033, 0.0036, ...
## $ V56   <dbl> 0.0029, 0.0101, 0.0119, 0.0039, 0.0037, 0.0101, 0.0026, ...
## $ V57   <dbl> 0.0058, 0.0127, 0.0194, 0.0053, 0.0045, 0.0065, 0.0024, ...
## $ V58   <dbl> 0.0050, 0.0288, 0.0140, 0.0013, 0.0029, 0.0115, 0.0162, ...
## $ V59   <dbl> 0.0024, 0.0129, 0.0332, 0.0052, 0.0008, 0.0193, 0.0109, ...
## $ V60   <dbl> 0.0030, 0.0023, 0.0439, 0.0023, 0.0018, 0.0157, 0.0079, ...
## $ Class <fctr> R, M, M, R, R, M, R, R, R, R, M, R, M, R, M, M, M, R, M...

# Fit glm model: model
model <- glm(Class ~ ., family = "binomial", train)
model

## 
## Call:  glm(formula = Class ~ ., family = "binomial", data = train)
## 
## Coefficients:
## (Intercept)           V1           V2           V3           V4  
##      145.95       351.31      -456.22       359.50      -524.19  
##          V5           V6           V7           V8           V9  
##       84.67        39.10      -158.13       440.59      -512.82  
##         V10          V11          V12          V13          V14  
##      -18.64       315.68      -295.58        39.11      -198.35  
##         V15          V16          V17          V18          V19  
##      137.16       -16.54       186.89      -165.70       -10.90  
##         V20          V21          V22          V23          V24  
##      -77.54       227.15      -320.07       202.39      -176.36  
##         V25          V26          V27          V28          V29  
##     -100.99       101.45        31.31       -10.64        37.27  
##         V30          V31          V32          V33          V34  
##     -171.07       234.99      -181.58        67.45       258.65  
##         V35          V36          V37          V38          V39  
##     -417.93       376.45      -191.05       241.65      -456.91  
##         V40          V41          V42          V43          V44  
##      383.27      -153.17       113.53      -267.66        85.57  
##         V45          V46          V47          V48          V49  
##      -40.81       231.24      -398.87       616.56     -1509.64  
##         V50          V51          V52          V53          V54  
##     2067.74     -1443.52      -618.43       185.89      1874.93  
##         V55          V56          V57          V58          V59  
##     2674.37     -1592.68      -514.08      1475.45       208.12  
##         V60  
##       -6.22  
## 
## Degrees of Freedom: 124 Total (i.e. Null);  64 Residual
## Null Deviance:       172.3 
## Residual Deviance: 3.997e-09     AIC: 122

# Predict on test: p
p <- predict(model, test, type = "response")

Confusion matrix

– Calculate a confusion matrix

• Using the confusionMatix function from caret gives you the contigency table as well as important statistics
  • install.packages(‘caret’, dependencies = TRUE) or you will get a error about needing package e1071
  • No information rate = what you would get if you always predicted yes
  • Sensitivity = True positive rate
  • Specificity = True negative rate

# Calculate class probabilities: p_class
p_class <- ifelse(p > .50, "M", "R")

# Create confusion matrix
confusionMatrix(p_class, test$Class)

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  M  R
##          M 17 29
##          R 26 11
##                                           
##                Accuracy : 0.3373          
##                  95% CI : (0.2372, 0.4495)
##     No Information Rate : 0.5181          
##     P-Value [Acc > NIR] : 0.9997          
##                                           
##                   Kappa : -0.3305         
##  Mcnemar's Test P-Value : 0.7874          
##                                           
##             Sensitivity : 0.3953          
##             Specificity : 0.2750          
##          Pos Pred Value : 0.3696          
##          Neg Pred Value : 0.2973          
##              Prevalence : 0.5181          
##          Detection Rate : 0.2048          
##    Detection Prevalence : 0.5542          
##       Balanced Accuracy : 0.3352          
##                                           
##        'Positive' Class : M               
## 

• The accuracy is 0.337
  • this is less than the no info rate of .5181.
  • so we would have done better just guessing yes to every rock being a mine
• Our sensitivity is .395 and our specificity is .275

Class probabilities and class predictions

• Different thresholds
  • We don’t have to use 50% as the threshold
  • We could set it to .10 and we would get more mines but have less certainty we have a mine
  • Or we could set it to .90 and we would get less mines but be more certian what we have are mines
• Choosing a threshold is an exercise in balanceing the true positive and false positive rate
  • Which way you lean depends on the cost benefit of the problem

– Try another threshold

# Apply threshold of 0.9: p_class
p_class <- ifelse(p > .9, "M", "R")

# Create confusion matrix
confusionMatrix(p_class, test[["Class"]])

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  M  R
##          M 16 29
##          R 27 11
##                                          
##                Accuracy : 0.3253         
##                  95% CI : (0.2265, 0.437)
##     No Information Rate : 0.5181         
##     P-Value [Acc > NIR] : 0.9999         
##                                          
##                   Kappa : -0.3535        
##  Mcnemar's Test P-Value : 0.8937         
##                                          
##             Sensitivity : 0.3721         
##             Specificity : 0.2750         
##          Pos Pred Value : 0.3556         
##          Neg Pred Value : 0.2895         
##              Prevalence : 0.5181         
##          Detection Rate : 0.1928         
##    Detection Prevalence : 0.5422         
##       Balanced Accuracy : 0.3235         
##                                          
##        'Positive' Class : M              
## 

– From probabilites to confusion matrix

# Apply threshold of 0.10: p_class
p_class <- ifelse(p > .10, "M", "R")

# Create confusion matrix
confusionMatrix(p_class, test[["Class"]])

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  M  R
##          M 18 32
##          R 25  8
##                                           
##                Accuracy : 0.3133          
##                  95% CI : (0.2159, 0.4244)
##     No Information Rate : 0.5181          
##     P-Value [Acc > NIR] : 0.9999          
##                                           
##                   Kappa : -0.3837         
##  Mcnemar's Test P-Value : 0.4268          
##                                           
##             Sensitivity : 0.4186          
##             Specificity : 0.2000          
##          Pos Pred Value : 0.3600          
##          Neg Pred Value : 0.2424          
##              Prevalence : 0.5181          
##          Detection Rate : 0.2169          
##    Detection Prevalence : 0.6024          
##       Balanced Accuracy : 0.3093          
##                                           
##        'Positive' Class : M               
## 

Introducing the ROC curve

• Doing this by hand is cumbersome
• We can simply use a computer to calcualte the true/false positive rate at every possible threshold
• Then plot the tradeoffs between the two extremes (100% true positive vs 0% false positive rate)
• This is called a receiver operating characteric (ROC) curve
  • It was developed during world war II to analyze radar signals. No one remembers the acronym.

– Plot an ROC curve

• This is a nice tool for summarizing the performance of a classifier over all possible thresholds.
• The teacher likes the caTools package and colAUC function.
  • It can actually calculate ROC curves for multple predictors at once

# the caTools library is loaded

# Predict on test: p
p <- predict(model, test, type = "response")

# Make ROC curve
colAUC(p, test$Class, plotROC = T)

##              [,1]
## M vs. R 0.7148256

Area under the curve

• AUC (area under curve) is a single number summary of the model performance across all classification thresholds
  • a completely random model will create a diagonal line with an AUC of .5
  • a perfect separation models creates a box with an AUC of 1
• The AUG lets us compare models easily
  • 1 = model always right
  • 0.5 random guessing
  • think of it as a letter grade with .9 = ‘A’ and .8 = ‘B’ and so on
• this is much more useful than simple ranking models by their accuracy at a set threshold

– Customizing trainControl

• You can use the trainControl() function in caret to use AUC (instead of accuracy) to tune the parameters of your models.
• twoClassSummary() convience function lets us do this easily
  • always include classprobs = TRUE or the model will throw an error
  • you have to have the probbilities, not just the predictions of the model
  • put this in place of defaultSummary for the summaryFunction argument

myControl <- trainControl(
  method = "cv",
  number = 10,
  summaryFunction = twoClassSummary,
  classProbs = T, # IMPORTANT!
  verboseIter = TRUE
)

– Using custom trainControl

# Train glm with custom trainControl: model
model <- train(Class ~., Sonar,
  method = "glm",
  trControl = myControl)

## + Fold01: parameter=none 
## - Fold01: parameter=none 
## + Fold02: parameter=none 
## - Fold02: parameter=none 
## + Fold03: parameter=none 
## - Fold03: parameter=none 
## + Fold04: parameter=none 
## - Fold04: parameter=none 
## + Fold05: parameter=none 
## - Fold05: parameter=none 
## + Fold06: parameter=none 
## - Fold06: parameter=none 
## + Fold07: parameter=none 
## - Fold07: parameter=none 
## + Fold08: parameter=none 
## - Fold08: parameter=none 
## + Fold09: parameter=none 
## - Fold09: parameter=none 
## + Fold10: parameter=none 
## - Fold10: parameter=none 
## Aggregating results
## Fitting final model on full training set

# Print model to console
model

## Generalized Linear Model 
## 
## 208 samples
##  60 predictor
##   2 classes: 'M', 'R' 
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 187, 187, 187, 187, 188, 187, ... 
## Resampling results:
## 
##   ROC        Sens       Spec     
##   0.7473737  0.7575758  0.6711111

   

---

Tuning model parameters to improve performance

---

Random forests and wine

• Very popular type of machine learning model
• Good for beginners becuse robust to overfitting
• Yield very accurate, non linear models with little extra work on the part of the data scientist
• Draw back is that they have hyperparameters which require manual specification
  • The default values are usually fine but occasionally need adjustment.
• A decision tree is fast but not necesarrily very accurate
• Random forest improves on this by running many decision trees on bootstrap samples of the data
  • This is called bootstrap aggregation or bagging
  • Random forest go a step further by randomling sampling the columns at each split (whatever that means)

Quick random forest example:

data(Sonar)
set.seed(42)
model <- train(Class~., data = Sonar, method = "ranger")
plot(model)

I’ll learn what this plot means later I think.

– Random forests vs. linear models

• All of these are true but the third one is technically the correct answer. : )
• What is the primary advantage of random forests over linear models?
  • They make you sound cooler during job interviews
  • You can’t understand what’s going on inside of a random forest model, so you don’t have to explain it to anyone.
  • A random forest is a more flexible model than a linear model, but just as easy to fit.

– Fit a random forest

• So random forest are apparently much more flexible than linear models. Makes sense as linear models are pretty straight forward. ; )
• They can model complicated nonlinear effects as well as autoatically capture interactions between variables.
• They tend to give good results on real world data.
  • This set of data on wine quality is a good example. The goal is to predict human-evaluated quality of a batch of wine. Not a very linear thing, I imagine.
• the ‘ranger’ method is pretty much the same as th classic randomForest method in R but much faster. It is strongly suggest by the instructors to use this.

glimpse(wine)

## Observations: 100
## Variables: 13
## $ fixed.acidity        <dbl> 6.7, 6.7, 5.8, 6.3, 6.6, 7.8, 5.5, 9.1, 6...
## $ volatile.acidity     <dbl> 0.270, 0.480, 0.360, 0.320, 0.240, 0.390,...
## $ citric.acid          <dbl> 0.69, 0.49, 0.38, 0.26, 0.28, 0.26, 0.33,...
## $ residual.sugar       <dbl> 1.2, 2.9, 0.9, 12.0, 1.8, 9.9, 1.0, 1.6, ...
## $ chlorides            <dbl> 0.176, 0.030, 0.037, 0.049, 0.028, 0.059,...
## $ free.sulfur.dioxide  <dbl> 36.0, 28.0, 3.0, 63.0, 39.0, 33.0, 23.0, ...
## $ total.sulfur.dioxide <dbl> 106.0, 122.0, 75.0, 170.0, 132.0, 181.0, ...
## $ density              <dbl> 0.99288, 0.98926, 0.99040, 0.99610, 0.991...
## $ pH                   <dbl> 2.96, 3.13, 3.28, 3.14, 3.34, 3.04, 3.25,...
## $ sulphates            <dbl> 0.43, 0.40, 0.34, 0.55, 0.46, 0.42, 0.45,...
## $ alcohol              <dbl> 9.20, 13.00, 11.40, 9.90, 11.40, 10.90, 9...
## $ quality              <int> 6, 6, 4, 6, 5, 6, 5, 7, 7, 6, 6, 6, 6, 6,...
## $ color                <fctr> white, white, white, white, white, white...

# Fit random forest: model
model <- train(
  quality ~ .,
  data = wine,
  method = "ranger",
  tuneLength = 1,
  trControl = trainControl(
    method = "cv", 
    number = 5, 
    verboseIter = TRUE
    )
)

## + Fold1: mtry=3, splitrule=variance 
## - Fold1: mtry=3, splitrule=variance 
## + Fold1: mtry=3, splitrule=extratrees 
## - Fold1: mtry=3, splitrule=extratrees 
## + Fold2: mtry=3, splitrule=variance 
## - Fold2: mtry=3, splitrule=variance 
## + Fold2: mtry=3, splitrule=extratrees 
## - Fold2: mtry=3, splitrule=extratrees 
## + Fold3: mtry=3, splitrule=variance 
## - Fold3: mtry=3, splitrule=variance 
## + Fold3: mtry=3, splitrule=extratrees 
## - Fold3: mtry=3, splitrule=extratrees 
## + Fold4: mtry=3, splitrule=variance 
## - Fold4: mtry=3, splitrule=variance 
## + Fold4: mtry=3, splitrule=extratrees 
## - Fold4: mtry=3, splitrule=extratrees 
## + Fold5: mtry=3, splitrule=variance 
## - Fold5: mtry=3, splitrule=variance 
## + Fold5: mtry=3, splitrule=extratrees 
## - Fold5: mtry=3, splitrule=extratrees 
## Aggregating results
## Selecting tuning parameters
## Fitting mtry = 3, splitrule = variance on full training set

# Print model to console
model

## Random Forest 
## 
## 100 samples
##  12 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 80, 80, 80, 80, 80 
## Resampling results across tuning parameters:
## 
##   splitrule   RMSE       Rsquared   MAE      
##   variance    0.6494058  0.3317282  0.4912203
##   extratrees  0.6916759  0.2631151  0.5162687
## 
## Tuning parameter 'mtry' was held constant at a value of 3
## RMSE was used to select the optimal model using  the smallest value.
## The final values used for the model were mtry = 3 and splitrule = variance.

Explore a wider model space

• You have to prune, I mean tune, your forest.
• There are hyperparameters that control how the model is fit.
• these have to be picked by hand before fitting the model
  • the mtry parameter is one of the key ones
  • Its is the number of randomly selected variables used at each split
  • it could be 2 (more random) or 100 (less random)
  • you really just have to try these out to see how the model works with that parameter
  • caret automates this process in something called grid search
  • grid search is a process of selecting hyperparameters based on out-of-sample error

– Try a longer tune length

• A longer tunelength allows us to explore more potential models and can potentially find a better model
  • But it does take longer

# Fit random forest: model
model <- train(
  quality ~ .,
  tuneLength = 3,
  data = wine, 
  method = "ranger",
  trControl = trainControl(
    method = "cv", 
    number = 5, 
    verboseIter = TRUE)
)

## + Fold1: mtry= 2, splitrule=variance 
## - Fold1: mtry= 2, splitrule=variance 
## + Fold1: mtry= 7, splitrule=variance 
## - Fold1: mtry= 7, splitrule=variance 
## + Fold1: mtry=12, splitrule=variance 
## - Fold1: mtry=12, splitrule=variance 
## + Fold1: mtry= 2, splitrule=extratrees 
## - Fold1: mtry= 2, splitrule=extratrees 
## + Fold1: mtry= 7, splitrule=extratrees 
## - Fold1: mtry= 7, splitrule=extratrees 
## + Fold1: mtry=12, splitrule=extratrees 
## - Fold1: mtry=12, splitrule=extratrees 
## + Fold2: mtry= 2, splitrule=variance 
## - Fold2: mtry= 2, splitrule=variance 
## + Fold2: mtry= 7, splitrule=variance 
## - Fold2: mtry= 7, splitrule=variance 
## + Fold2: mtry=12, splitrule=variance 
## - Fold2: mtry=12, splitrule=variance 
## + Fold2: mtry= 2, splitrule=extratrees 
## - Fold2: mtry= 2, splitrule=extratrees 
## + Fold2: mtry= 7, splitrule=extratrees 
## - Fold2: mtry= 7, splitrule=extratrees 
## + Fold2: mtry=12, splitrule=extratrees 
## - Fold2: mtry=12, splitrule=extratrees 
## + Fold3: mtry= 2, splitrule=variance 
## - Fold3: mtry= 2, splitrule=variance 
## + Fold3: mtry= 7, splitrule=variance 
## - Fold3: mtry= 7, splitrule=variance 
## + Fold3: mtry=12, splitrule=variance 
## - Fold3: mtry=12, splitrule=variance 
## + Fold3: mtry= 2, splitrule=extratrees 
## - Fold3: mtry= 2, splitrule=extratrees 
## + Fold3: mtry= 7, splitrule=extratrees 
## - Fold3: mtry= 7, splitrule=extratrees 
## + Fold3: mtry=12, splitrule=extratrees 
## - Fold3: mtry=12, splitrule=extratrees 
## + Fold4: mtry= 2, splitrule=variance 
## - Fold4: mtry= 2, splitrule=variance 
## + Fold4: mtry= 7, splitrule=variance 
## - Fold4: mtry= 7, splitrule=variance 
## + Fold4: mtry=12, splitrule=variance 
## - Fold4: mtry=12, splitrule=variance 
## + Fold4: mtry= 2, splitrule=extratrees 
## - Fold4: mtry= 2, splitrule=extratrees 
## + Fold4: mtry= 7, splitrule=extratrees 
## - Fold4: mtry= 7, splitrule=extratrees 
## + Fold4: mtry=12, splitrule=extratrees 
## - Fold4: mtry=12, splitrule=extratrees 
## + Fold5: mtry= 2, splitrule=variance 
## - Fold5: mtry= 2, splitrule=variance 
## + Fold5: mtry= 7, splitrule=variance 
## - Fold5: mtry= 7, splitrule=variance 
## + Fold5: mtry=12, splitrule=variance 
## - Fold5: mtry=12, splitrule=variance 
## + Fold5: mtry= 2, splitrule=extratrees 
## - Fold5: mtry= 2, splitrule=extratrees 
## + Fold5: mtry= 7, splitrule=extratrees 
## - Fold5: mtry= 7, splitrule=extratrees 
## + Fold5: mtry=12, splitrule=extratrees 
## - Fold5: mtry=12, splitrule=extratrees 
## Aggregating results
## Selecting tuning parameters
## Fitting mtry = 12, splitrule = variance on full training set

# Print model to console
model

## Random Forest 
## 
## 100 samples
##  12 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 80, 80, 80, 80, 80 
## Resampling results across tuning parameters:
## 
##   mtry  splitrule   RMSE       Rsquared   MAE      
##    2    variance    0.6509389  0.3520433  0.4895340
##    2    extratrees  0.6894546  0.2800724  0.5150384
##    7    variance    0.6237783  0.3952847  0.4768267
##    7    extratrees  0.6841207  0.2475494  0.5174830
##   12    variance    0.6189958  0.3965301  0.4781017
##   12    extratrees  0.6742885  0.2692004  0.5121810
## 
## RMSE was used to select the optimal model using  the smallest value.
## The final values used for the model were mtry = 12 and splitrule
##  = variance.

# Plot model
plot(model)

Custom tuning grids

• We can pass our own df to the tuneGrid argument
  • This helps us be more flexible fitting caret models and gives us control over how the model is fit
  • But it requires some knowledge of the model and can dramatically increase run time.

# Define a custome tuning grid
myGrid <- data.frame(mtry = c(2,3,4,5,10,20,30,40),
                     splitrule = rep("extratrees",8))

# fit a model with a custom tuning grid
set.seed(42)
model <- train(Class ~ ., 
               data = Sonar, 
               method = "ranger", 
               tuneGrid = myGrid)

plot(model)

– Fit a random forest with custom tuning

• There is so much here I don’t know. Don’t fool myslef.
• For some reason I have to pyt the splitrule into the tuneGrid. In the class this is not needed. hmmmm

# Fit random forest: model
model <- train(
  quality ~ .,
  tuneGrid = data.frame(mtry = c(2,3,7,2,3,7),
                        splitrule = c("variance","variance","variance","extratrees","extratrees","extratrees")),
  data = wine, 
  method = "ranger",
  trControl = trainControl(
    method = "cv", 
    number = 5, 
    verboseIter = TRUE)
)

## + Fold1: mtry=2, splitrule=variance 
## - Fold1: mtry=2, splitrule=variance 
## + Fold1: mtry=3, splitrule=variance 
## - Fold1: mtry=3, splitrule=variance 
## + Fold1: mtry=7, splitrule=variance 
## - Fold1: mtry=7, splitrule=variance 
## + Fold1: mtry=2, splitrule=extratrees 
## - Fold1: mtry=2, splitrule=extratrees 
## + Fold1: mtry=3, splitrule=extratrees 
## - Fold1: mtry=3, splitrule=extratrees 
## + Fold1: mtry=7, splitrule=extratrees 
## - Fold1: mtry=7, splitrule=extratrees 
## + Fold2: mtry=2, splitrule=variance 
## - Fold2: mtry=2, splitrule=variance 
## + Fold2: mtry=3, splitrule=variance 
## - Fold2: mtry=3, splitrule=variance 
## + Fold2: mtry=7, splitrule=variance 
## - Fold2: mtry=7, splitrule=variance 
## + Fold2: mtry=2, splitrule=extratrees 
## - Fold2: mtry=2, splitrule=extratrees 
## + Fold2: mtry=3, splitrule=extratrees 
## - Fold2: mtry=3, splitrule=extratrees 
## + Fold2: mtry=7, splitrule=extratrees 
## - Fold2: mtry=7, splitrule=extratrees 
## + Fold3: mtry=2, splitrule=variance 
## - Fold3: mtry=2, splitrule=variance 
## + Fold3: mtry=3, splitrule=variance 
## - Fold3: mtry=3, splitrule=variance 
## + Fold3: mtry=7, splitrule=variance 
## - Fold3: mtry=7, splitrule=variance 
## + Fold3: mtry=2, splitrule=extratrees 
## - Fold3: mtry=2, splitrule=extratrees 
## + Fold3: mtry=3, splitrule=extratrees 
## - Fold3: mtry=3, splitrule=extratrees 
## + Fold3: mtry=7, splitrule=extratrees 
## - Fold3: mtry=7, splitrule=extratrees 
## + Fold4: mtry=2, splitrule=variance 
## - Fold4: mtry=2, splitrule=variance 
## + Fold4: mtry=3, splitrule=variance 
## - Fold4: mtry=3, splitrule=variance 
## + Fold4: mtry=7, splitrule=variance 
## - Fold4: mtry=7, splitrule=variance 
## + Fold4: mtry=2, splitrule=extratrees 
## - Fold4: mtry=2, splitrule=extratrees 
## + Fold4: mtry=3, splitrule=extratrees 
## - Fold4: mtry=3, splitrule=extratrees 
## + Fold4: mtry=7, splitrule=extratrees 
## - Fold4: mtry=7, splitrule=extratrees 
## + Fold5: mtry=2, splitrule=variance 
## - Fold5: mtry=2, splitrule=variance 
## + Fold5: mtry=3, splitrule=variance 
## - Fold5: mtry=3, splitrule=variance 
## + Fold5: mtry=7, splitrule=variance 
## - Fold5: mtry=7, splitrule=variance 
## + Fold5: mtry=2, splitrule=extratrees 
## - Fold5: mtry=2, splitrule=extratrees 
## + Fold5: mtry=3, splitrule=extratrees 
## - Fold5: mtry=3, splitrule=extratrees 
## + Fold5: mtry=7, splitrule=extratrees 
## - Fold5: mtry=7, splitrule=extratrees 
## Aggregating results
## Selecting tuning parameters
## Fitting mtry = 7, splitrule = variance on full training set

# Print model to console
model

## Random Forest 
## 
## 100 samples
##  12 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (5 fold) 
## Summary of sample sizes: 80, 80, 80, 80, 80 
## Resampling results across tuning parameters:
## 
##   mtry  splitrule   RMSE       Rsquared   MAE      
##   2     extratrees  0.6998244  0.2294546  0.5205483
##   2     variance    0.6491212  0.3552880  0.4919073
##   3     extratrees  0.6967726  0.2451629  0.5185667
##   3     variance    0.6529793  0.3223926  0.4939690
##   7     extratrees  0.6847887  0.2512857  0.5122317
##   7     variance    0.6461164  0.3229418  0.4852607
## 
## RMSE was used to select the optimal model using  the smallest value.
## The final values used for the model were mtry = 7 and splitrule = variance.

# Plot model
plot(model)

Introducing glmnet

• Instructors favorite type of model
• Extension of glm models (generalized linear models) with built in variable selection
• Helps deal with collinearity (or correlation among predictors in a model) and helps prevent them from being over confident with small sample sizes
• two primary forms
  • lasso regression - penelizes number of non-zero coefficients
  • ridge regression - penalizes absolute magnitude of coefficients
• attemps to find a parsimonious (i.e. simple) model
• this pairs well ith random forest modles as it tends to yield different results
• glmnet models are a combination of lasso and ridge regression models
• they have a lot of parameters to tune
  • alpha [0,1]: pure lasso to pure ridge
  • lambda [0,infinity]:size of penalty. Higher values yeild simpler models, high enough will just predict the mean of resonse variable in training data

Example: “don’t overfit” first kaggle competition the instructor competed in

• This dataset has about as many columns as observations.

# load data
overfit <- read.csv("http://s3.amazonaws.com/assets.datacamp.com/production/course_1048/datasets/overfit.csv")
glimpse(overfit)

## Observations: 250
## Variables: 201
## $ y    <fctr> class2, class2, class2, class1, class2, class2, class2, ...
## $ X1   <dbl> 0.91480604, 0.93707541, 0.28613953, 0.83044763, 0.6417455...
## $ X2   <dbl> 0.33423133, 0.18843433, 0.26971618, 0.53074408, 0.0214502...
## $ X3   <dbl> 0.1365052, 0.1771364, 0.5195605, 0.8111208, 0.1153620, 0....
## $ X4   <dbl> 0.244920995, 0.087635909, 0.391108497, 0.182561425, 0.133...
## $ X5   <dbl> 0.84829322, 0.06274633, 0.81984509, 0.53936029, 0.4990201...
## $ X6   <dbl> 0.73592037, 0.75178575, 0.33261448, 0.05754862, 0.6744154...
## $ X7   <dbl> 0.053911000, 0.955095770, 0.025600940, 0.920763139, 0.366...
## $ X8   <dbl> 0.16517872, 0.72778108, 0.20615786, 0.58646553, 0.9135459...
## $ X9   <dbl> 0.98996559, 0.43849361, 0.69990322, 0.88907696, 0.8341594...
## $ X10  <dbl> 0.24640458, 0.02302811, 0.28421418, 0.81289268, 0.7189183...
## $ X11  <dbl> 0.06038098, 0.93300437, 0.34894162, 0.41179789, 0.9611464...
## $ X12  <dbl> 0.40882313, 0.31586194, 0.49472762, 0.64893000, 0.6498624...
## $ X13  <dbl> 0.27379245, 0.94419670, 0.44598332, 0.54178716, 0.1617544...
## $ X14  <dbl> 0.313369113, 0.688717818, 0.532391957, 0.759994458, 0.649...
## $ X15  <dbl> 0.19940178, 0.56649540, 0.16805282, 0.94363115, 0.5044080...
## $ X16  <dbl> 0.85550816, 0.21655583, 0.31746986, 0.54139804, 0.4303393...
## $ X17  <dbl> 0.59892983, 0.96894761, 0.39053533, 0.85281451, 0.0422875...
## $ X18  <dbl> 0.36410202, 0.43261605, 0.72886793, 0.26279787, 0.7689716...
## $ X19  <dbl> 0.29991068, 0.07423252, 0.92831706, 0.40114898, 0.6653751...
## $ X20  <dbl> 0.51241735, 0.49846335, 0.13677730, 0.45071464, 0.3133368...
## $ X21  <dbl> 0.73149367, 0.56095270, 0.49818835, 0.84105947, 0.4636444...
## $ X22  <dbl> 0.88671723, 0.78957374, 0.54639519, 0.06316993, 0.5761548...
## $ X23  <dbl> 0.84276937, 0.76905791, 0.91884069, 0.35572491, 0.9376524...
## $ X24  <dbl> 0.22653454, 0.29303699, 0.12607726, 0.71019872, 0.8479341...
## $ X25  <dbl> 0.24646324, 0.53030519, 0.21397210, 0.02584904, 0.3420024...
## $ X26  <dbl> 0.03078282, 0.91007049, 0.14263568, 0.43959793, 0.4498638...
## $ X27  <dbl> 0.24399196, 0.88613340, 0.36574050, 0.25022753, 0.7712135...
## $ X28  <dbl> 0.440314306, 0.445281863, 0.080888182, 0.152905060, 0.820...
## $ X29  <dbl> 0.61425763, 0.87616254, 0.09615188, 0.17540170, 0.4545790...
## $ X30  <dbl> 0.60700663, 0.03163189, 0.93982109, 0.74308481, 0.1437081...
## $ X31  <dbl> 0.776540211, 0.023826756, 0.431787197, 0.366538520, 0.395...
## $ X32  <dbl> 0.2101436, 0.7116446, 0.4351647, 0.9759542, 0.7004988, 0....
## $ X33  <dbl> 0.44361558, 0.32834604, 0.20785167, 0.19192139, 0.3723859...
## $ X34  <dbl> 0.23989117, 0.89145398, 0.14831578, 0.42380827, 0.7290696...
## $ X35  <dbl> 0.63630187, 0.68359615, 0.46272876, 0.59296401, 0.1989479...
## $ X36  <dbl> 0.57228237, 0.46182573, 0.13543040, 0.58246224, 0.1145796...
## $ X37  <dbl> 0.41975693, 0.82613983, 0.11230086, 0.20392210, 0.4922106...
## $ X38  <dbl> 0.95004438, 0.11276168, 0.85793189, 0.26989327, 0.2721555...
## $ X39  <dbl> 0.35872817, 0.49724268, 0.25065359, 0.77495504, 0.1394773...
## $ X40  <dbl> 0.49694824, 0.99363492, 0.68541077, 0.71740832, 0.5102301...
## $ X41  <dbl> 0.52838964, 0.64638788, 0.83404903, 0.34576255, 0.6217329...
## $ X42  <dbl> 0.53637297, 0.02224803, 0.97147909, 0.60075658, 0.4173548...
## $ X43  <dbl> 0.003498503, 0.470631273, 0.447381378, 0.418609717, 0.865...
## $ X44  <dbl> 0.031088332, 0.371195921, 0.289065880, 0.142796479, 0.645...
## $ X45  <dbl> 0.78957600, 0.60768116, 0.98599694, 0.65056791, 0.3890770...
## $ X46  <dbl> 0.90801477, 0.22839369, 0.03609499, 0.75519239, 0.1496413...
## $ X47  <dbl> 0.57435600, 0.34725679, 0.54284271, 0.27019571, 0.7032646...
## $ X48  <dbl> 0.04658951, 0.81377534, 0.06971775, 0.45726551, 0.9325349...
## $ X49  <dbl> 0.568608369, 0.217880581, 0.101515466, 0.698102254, 0.192...
## $ X50  <dbl> 0.70674255, 0.93513637, 0.32386434, 0.42993684, 0.2638991...
## $ X51  <dbl> 0.35659105, 0.20800169, 0.10062093, 0.13811304, 0.0237243...
## $ X52  <dbl> 0.6176513, 0.3523196, 0.6447219, 0.2108743, 0.9677561, 0....
## $ X53  <dbl> 0.89379587, 0.48063380, 0.16016976, 0.90606024, 0.7480467...
## $ X54  <dbl> 0.09195006, 0.04368308, 0.03980983, 0.67766094, 0.3246483...
## $ X55  <dbl> 0.40665568, 0.90273489, 0.18040390, 0.05992027, 0.3798599...
## $ X56  <dbl> 0.82231507, 0.46761749, 0.88325679, 0.23977046, 0.0860767...
## $ X57  <dbl> 0.92166222, 0.02544768, 0.71131622, 0.08098793, 0.8367631...
## $ X58  <dbl> 0.70143425, 0.20914840, 0.30949109, 0.75071442, 0.8386771...
## $ X59  <dbl> 0.57086475, 0.31707423, 0.00622546, 0.32235315, 0.7659728...
## $ X60  <dbl> 0.22403629, 0.71769261, 0.23348081, 0.11093189, 0.0150913...
## $ X61  <dbl> 0.61544117, 0.81500369, 0.34300935, 0.38827650, 0.0146181...
## $ X62  <dbl> 0.39420984, 0.94813472, 0.75282056, 0.86577343, 0.3746095...
## $ X63  <dbl> 0.88882277, 0.51720327, 0.34884470, 0.85602299, 0.1388358...
## $ X64  <dbl> 0.609959334, 0.801461577, 0.524867217, 0.672061241, 0.290...
## $ X65  <dbl> 0.47709234, 0.19922838, 0.40166670, 0.57517642, 0.0637341...
## $ X66  <dbl> 0.55782963, 0.58179578, 0.35338641, 0.91979352, 0.1432807...
## $ X67  <dbl> 0.69121938, 0.35959736, 0.51719022, 0.49845355, 0.1268600...
## $ X68  <dbl> 0.79023679, 0.29431606, 0.32632441, 0.02167086, 0.4726536...
## $ X69  <dbl> 0.53079266, 0.64474625, 0.13998155, 0.31667922, 0.8713631...
## $ X70  <dbl> 0.61211085, 0.22469525, 0.44505162, 0.44177333, 0.8194539...
## $ X71  <dbl> 0.992744554, 0.660086332, 0.990871294, 0.843593776, 0.931...
## $ X72  <dbl> 0.66891022, 0.76956286, 0.04286123, 0.09322869, 0.3702975...
## $ X73  <dbl> 0.1782290782, 0.5898728392, 0.3100116646, 0.9048300500, 0...
## $ X74  <dbl> 0.65168895, 0.09957865, 0.61739505, 0.37862555, 0.0233105...
## $ X75  <dbl> 0.13139016, 0.20797646, 0.65724972, 0.05183997, 0.8911270...
## $ X76  <dbl> 0.6016485, 0.5147675, 0.9524858, 0.6899449, 0.6909429, 0....
## $ X77  <dbl> 0.80038216, 0.37053159, 0.43891339, 0.08944712, 0.1671795...
## $ X78  <dbl> 0.03375497, 0.19464773, 0.64983446, 0.21965484, 0.8581793...
## $ X79  <dbl> 0.61489699, 0.07567500, 0.55251763, 0.46364387, 0.9300709...
## $ X80  <dbl> 0.550195466, 0.907458914, 0.782375696, 0.605479471, 0.914...
## $ X81  <dbl> 0.87760735, 0.45543547, 0.42456263, 0.93879964, 0.3861163...
## $ X82  <dbl> 0.87712898, 0.55860808, 0.68894556, 0.67370478, 0.1886578...
## $ X83  <dbl> 0.45917438, 0.96913990, 0.79622297, 0.11110564, 0.4308363...
## $ X84  <dbl> 2.265618e-02, 5.166253e-01, 1.737207e-01, 8.481156e-01, 4...
## $ X85  <dbl> 0.82100470, 0.09394557, 0.17385249, 0.08457514, 0.9957042...
## $ X86  <dbl> 0.9451794, 0.6691676, 0.3524983, 0.2725157, 0.7055095, 0....
## $ X87  <dbl> 0.40031711, 0.36259803, 0.93234951, 0.21494830, 0.1853166...
## $ X88  <dbl> 0.5063815, 0.4020096, 0.1412987, 0.6899701, 0.1049531, 0....
## $ X89  <dbl> 0.38419708, 0.38109557, 0.67869493, 0.75592458, 0.0621395...
## $ X90  <dbl> 0.5978431, 0.3437839, 0.3873761, 0.8271274, 0.7161128, 0....
## $ X91  <dbl> 0.31784285, 0.95808926, 0.26911697, 0.60201218, 0.5659496...
## $ X92  <dbl> 0.63577017, 0.18256200, 0.61096669, 0.09389158, 0.5087271...
## $ X93  <dbl> 0.16898034, 0.16977626, 0.05505954, 0.65476919, 0.8837555...
## $ X94  <dbl> 0.43631094, 0.50747459, 0.70454115, 0.66092330, 0.2501755...
## $ X95  <dbl> 0.74558734, 0.88742323, 0.05273777, 0.12751347, 0.4315957...
## $ X96  <dbl> 0.91218140, 0.74437113, 0.24672669, 0.74064849, 0.8910056...
## $ X97  <dbl> 0.521450796, 0.002551967, 0.774404447, 0.037558054, 0.598...
## $ X98  <dbl> 0.09177065, 0.72371277, 0.47358313, 0.06946549, 0.4187190...
## $ X99  <dbl> 0.73411696, 0.20450219, 0.75417832, 0.30300187, 0.1878361...
## $ X100 <dbl> 0.320770567, 0.593723377, 0.858523079, 0.757005788, 0.591...
## $ X101 <dbl> 0.34108814, 0.07692370, 0.17643467, 0.43990862, 0.9375751...
## $ X102 <dbl> 0.6124809, 0.1278179, 0.2325618, 0.2011980, 0.3795888, 0....
## $ X103 <dbl> 0.0006371774, 0.9994430819, 0.3747437985, 0.0339846939, 0...
## $ X104 <dbl> 0.54743368, 0.47927159, 0.17748406, 0.63595546, 0.5783285...
## $ X105 <dbl> 0.03589639, 0.96449950, 0.45762041, 0.68747009, 0.9666334...
## $ X106 <dbl> 0.64268733, 0.34132692, 0.03583915, 0.19993296, 0.6526820...
## $ X107 <dbl> 0.23045683, 0.25149597, 0.04275977, 0.98033429, 0.4848958...
## $ X108 <dbl> 0.593971942, 0.528231378, 0.809968454, 0.588263725, 0.220...
## $ X109 <dbl> 0.53344042, 0.03137963, 0.04959282, 0.23380904, 0.8963145...
## $ X110 <dbl> 0.95277784, 0.65035223, 0.26233431, 0.96049400, 0.7733770...
## $ X111 <dbl> 0.95001493, 0.80696333, 0.76912510, 0.74866022, 0.5731922...
## $ X112 <dbl> 0.44486670, 0.34772122, 0.80746171, 0.03664129, 0.8928324...
## $ X113 <dbl> 0.01083590, 0.12578299, 0.50185677, 0.18031296, 0.0530103...
## $ X114 <dbl> 0.01484451, 0.17502226, 0.25231490, 0.99640743, 0.8664863...
## $ X115 <dbl> 0.06289119, 0.89214340, 0.28707657, 0.64055932, 0.1317425...
## $ X116 <dbl> 0.581997880, 0.665076771, 0.875653535, 0.070306693, 0.004...
## $ X117 <dbl> 0.5924448, 0.8878863, 0.5235236, 0.3749164, 0.8752077, 0....
## $ X118 <dbl> 0.46235305, 0.86934930, 0.22476541, 0.54021836, 0.6109594...
## $ X119 <dbl> 0.450867994, 0.529698077, 0.158835076, 0.062714112, 0.449...
## $ X120 <dbl> 0.194360079, 0.976134765, 0.987192112, 0.511937499, 0.198...
## $ X121 <dbl> 0.15381438, 0.40933156, 0.22537445, 0.35218675, 0.1101618...
## $ X122 <dbl> 0.982242217, 0.520649012, 0.445695450, 0.462261930, 0.002...
## $ X123 <dbl> 0.29473281, 0.25111598, 0.80001735, 0.23422839, 0.1068260...
## $ X124 <dbl> 0.110216588, 0.080252397, 0.625394831, 0.722216522, 0.076...
## $ X125 <dbl> 0.40581025, 0.77477036, 0.36472709, 0.48756066, 0.7666030...
## $ X126 <dbl> 0.5527448577, 0.8601254835, 0.7557375506, 0.4862461151, 0...
## $ X127 <dbl> 0.287887782, 0.130535906, 0.678490788, 0.731766421, 0.852...
## $ X128 <dbl> 0.55946411, 0.21613476, 0.64567381, 0.05425676, 0.7748187...
## $ X129 <dbl> 0.68992925, 0.65888045, 0.69797577, 0.28211569, 0.3364384...
## $ X130 <dbl> 0.60577396, 0.12628377, 0.45778471, 0.31388965, 0.6482185...
## $ X131 <dbl> 0.63405048, 0.91769299, 0.91924084, 0.71750403, 0.5750649...
## $ X132 <dbl> 0.041380533, 0.404302723, 0.766801183, 0.005256724, 0.354...
## $ X133 <dbl> 0.11652459, 0.03312483, 0.12827443, 0.82357734, 0.3065927...
## $ X134 <dbl> 0.58257253, 0.56697654, 0.98460286, 0.52459081, 0.5602921...
## $ X135 <dbl> 0.70794842, 0.48408234, 0.77778677, 0.02017853, 0.0177778...
## $ X136 <dbl> 0.290923866, 0.461145974, 0.862764690, 0.664291186, 0.342...
## $ X137 <dbl> 0.54379718, 0.79342000, 0.22947185, 0.35309806, 0.3047963...
## $ X138 <dbl> 0.12864488, 0.23981618, 0.57799386, 0.61747643, 0.4213162...
## $ X139 <dbl> 0.80948772, 0.82146921, 0.18526767, 0.25488536, 0.9207230...
## $ X140 <dbl> 0.40163113, 0.79277151, 0.11738340, 0.36496598, 0.5366804...
## $ X141 <dbl> 0.93672809, 0.93622742, 0.89760746, 0.45901700, 0.5760530...
## $ X142 <dbl> 0.27464358, 0.29368103, 0.62729678, 0.44948535, 0.1779099...
## $ X143 <dbl> 0.59995153, 0.16334854, 0.17710410, 0.26653590, 0.0014934...
## $ X144 <dbl> 0.61420305, 0.70992172, 0.07593862, 0.77857178, 0.6301943...
## $ X145 <dbl> 0.84734796, 0.31810196, 0.07364713, 0.02329525, 0.9218279...
## $ X146 <dbl> 0.21923829, 0.15674629, 0.08922226, 0.74250158, 0.1047593...
## $ X147 <dbl> 0.82867974, 0.97047839, 0.47023973, 0.93823417, 0.9565947...
## $ X148 <dbl> 0.94290037, 0.64720576, 0.55771586, 0.39179048, 0.0940794...
## $ X149 <dbl> 0.50831853, 0.71756154, 0.45590210, 0.62706908, 0.8008656...
## $ X150 <dbl> 0.25527703, 0.03806863, 0.45961098, 0.29450119, 0.6976419...
## $ X151 <dbl> 0.75268296, 0.89675927, 0.76857671, 0.22820199, 0.7520310...
## $ X152 <dbl> 0.01497518, 0.04082960, 0.70849826, 0.07697517, 0.1076180...
## $ X153 <dbl> 0.96331279, 0.80074165, 0.39650955, 0.63353348, 0.0972440...
## $ X154 <dbl> 0.16493185, 0.83442190, 0.96948408, 0.69882495, 0.0847765...
## $ X155 <dbl> 0.5734490, 0.7298989, 0.5114832, 0.9638506, 0.8876985, 0....
## $ X156 <dbl> 0.61722732, 0.48946893, 0.98226532, 0.47115250, 0.2279777...
## $ X157 <dbl> 0.01984267, 0.71974924, 0.13222445, 0.15887531, 0.6819612...
## $ X158 <dbl> 0.99238742, 0.76420404, 0.12251792, 0.87889145, 0.9136540...
## $ X159 <dbl> 0.8431326, 0.9155692, 0.2006651, 0.6495318, 0.5322480, 0....
## $ X160 <dbl> 0.4516252, 0.3701119, 0.2851132, 0.7246809, 0.6712590, 0....
## $ X161 <dbl> 0.27610230, 0.30687340, 0.41455622, 0.91913345, 0.5334006...
## $ X162 <dbl> 0.74179679, 0.30933747, 0.66539232, 0.06219363, 0.4495071...
## $ X163 <dbl> 0.48524905, 0.36506517, 0.05123008, 0.49290181, 0.1527127...
## $ X164 <dbl> 0.003358962, 0.837234325, 0.249701695, 0.994318883, 0.331...
## $ X165 <dbl> 0.35415790, 0.13497580, 0.25971016, 0.60124062, 0.2942072...
## $ X166 <dbl> 0.89672245, 0.46684672, 0.53437967, 0.77532677, 0.6948135...
## $ X167 <dbl> 0.88342865, 0.52352974, 0.30868933, 0.79706734, 0.8076349...
## $ X168 <dbl> 0.80612878, 0.62438562, 0.32505099, 0.45196535, 0.8714401...
## $ X169 <dbl> 0.12920871, 0.65226440, 0.55483697, 0.41089107, 0.9276495...
## $ X170 <dbl> 0.191168652, 0.932518969, 0.666639159, 0.996674388, 0.080...
## $ X171 <dbl> 0.285561043, 0.198662249, 0.803086133, 0.394731248, 0.715...
## $ X172 <dbl> 0.88923767, 0.11641914, 0.75219803, 0.70289791, 0.0153314...
## $ X173 <dbl> 0.587049352, 0.133504347, 0.906179729, 0.392166968, 0.941...
## $ X174 <dbl> 0.88877075, 0.85607289, 0.46824726, 0.32963398, 0.0496130...
## $ X175 <dbl> 0.15143056, 0.42410270, 0.43306244, 0.83792064, 0.6613412...
## $ X176 <dbl> 0.212245659, 0.516595498, 0.044004837, 0.018832981, 0.279...
## $ X177 <dbl> 0.15721560, 0.88458393, 0.43112766, 0.94759465, 0.1502022...
## $ X178 <dbl> 0.41750018, 0.15750317, 0.94900001, 0.77882266, 0.4259149...
## $ X179 <dbl> 0.7225748, 0.0794626, 0.9359233, 0.7653506, 0.9541247, 0....
## $ X180 <dbl> 0.75372096, 0.61866392, 0.22093972, 0.49391558, 0.3108216...
## $ X181 <dbl> 0.39552157, 0.87280757, 0.16521581, 0.15224052, 0.9833864...
## $ X182 <dbl> 0.4887184, 0.9823968, 0.8082559, 0.7771462, 0.5740921, 0....
## $ X183 <dbl> 0.50930862, 0.39664574, 0.99125548, 0.34878537, 0.0761662...
## $ X184 <dbl> 0.40526502, 0.04680688, 0.85048518, 0.88635905, 0.2564270...
## $ X185 <dbl> 0.89972692, 0.41385540, 0.14096706, 0.76801954, 0.4703454...
## $ X186 <dbl> 0.20133410, 0.02252797, 0.88720811, 0.64712794, 0.0269461...
## $ X187 <dbl> 0.993279049, 0.551354672, 0.001778496, 0.927141098, 0.934...
## $ X188 <dbl> 0.27672405, 0.80417281, 0.03994549, 0.17404809, 0.2726361...
## $ X189 <dbl> 0.452414463, 0.758011176, 0.527843759, 0.890178879, 0.714...
## $ X190 <dbl> 0.69119399, 0.78047338, 0.25094101, 0.52802851, 0.4105000...
## $ X191 <dbl> 0.54065139, 0.14117820, 0.21067407, 0.82111615, 0.8930576...
## $ X192 <dbl> 0.72225972, 0.13109110, 0.58957105, 0.59130608, 0.9879968...
## $ X193 <dbl> 0.002576062, 0.411775569, 0.891389510, 0.767070756, 0.598...
## $ X194 <dbl> 0.25223405, 0.52042257, 0.77904746, 0.08815411, 0.6051281...
## $ X195 <dbl> 0.55681595, 0.49866879, 0.39123403, 0.82405905, 0.5665961...
## $ X196 <dbl> 0.08803946, 0.67626884, 0.09020876, 0.41487972, 0.0170128...
## $ X197 <dbl> 0.739964231, 0.972430318, 0.659945773, 0.333751146, 0.236...
## $ X198 <dbl> 0.37386198, 0.83937505, 0.83710146, 0.55367959, 0.7016139...
## $ X199 <dbl> 0.671563295, 0.746817349, 0.978584267, 0.704102835, 0.700...
## $ X200 <dbl> 0.0001012264, 0.8653565315, 0.3703812116, 0.6651317959, 0...

# Make a custom trainControl
myControl <- trainControl(
  method = "cv", 
  number = 10,
  summaryFunction = twoClassSummary,
  classProbs = T,
  verboseIter = T
)

# We will start with a simple model that uses default auc and tuning grid (3 alpha, 3 lambda)
# fit a model
set.seed(42)
model <- train(y ~ ., overfit, 
               method = "glmnet",
               trControl = myControl)

## + Fold01: alpha=0.10, lambda=0.01013 
## - Fold01: alpha=0.10, lambda=0.01013 
## + Fold01: alpha=0.55, lambda=0.01013 
## - Fold01: alpha=0.55, lambda=0.01013 
## + Fold01: alpha=1.00, lambda=0.01013 
## - Fold01: alpha=1.00, lambda=0.01013 
## + Fold02: alpha=0.10, lambda=0.01013 
## - Fold02: alpha=0.10, lambda=0.01013 
## + Fold02: alpha=0.55, lambda=0.01013 
## - Fold02: alpha=0.55, lambda=0.01013 
## + Fold02: alpha=1.00, lambda=0.01013 
## - Fold02: alpha=1.00, lambda=0.01013 
## + Fold03: alpha=0.10, lambda=0.01013 
## - Fold03: alpha=0.10, lambda=0.01013 
## + Fold03: alpha=0.55, lambda=0.01013 
## - Fold03: alpha=0.55, lambda=0.01013 
## + Fold03: alpha=1.00, lambda=0.01013 
## - Fold03: alpha=1.00, lambda=0.01013 
## + Fold04: alpha=0.10, lambda=0.01013 
## - Fold04: alpha=0.10, lambda=0.01013 
## + Fold04: alpha=0.55, lambda=0.01013 
## - Fold04: alpha=0.55, lambda=0.01013 
## + Fold04: alpha=1.00, lambda=0.01013 
## - Fold04: alpha=1.00, lambda=0.01013 
## + Fold05: alpha=0.10, lambda=0.01013 
## - Fold05: alpha=0.10, lambda=0.01013 
## + Fold05: alpha=0.55, lambda=0.01013 
## - Fold05: alpha=0.55, lambda=0.01013 
## + Fold05: alpha=1.00, lambda=0.01013 
## - Fold05: alpha=1.00, lambda=0.01013 
## + Fold06: alpha=0.10, lambda=0.01013 
## - Fold06: alpha=0.10, lambda=0.01013 
## + Fold06: alpha=0.55, lambda=0.01013 
## - Fold06: alpha=0.55, lambda=0.01013 
## + Fold06: alpha=1.00, lambda=0.01013 
## - Fold06: alpha=1.00, lambda=0.01013 
## + Fold07: alpha=0.10, lambda=0.01013 
## - Fold07: alpha=0.10, lambda=0.01013 
## + Fold07: alpha=0.55, lambda=0.01013 
## - Fold07: alpha=0.55, lambda=0.01013 
## + Fold07: alpha=1.00, lambda=0.01013 
## - Fold07: alpha=1.00, lambda=0.01013 
## + Fold08: alpha=0.10, lambda=0.01013 
## - Fold08: alpha=0.10, lambda=0.01013 
## + Fold08: alpha=0.55, lambda=0.01013 
## - Fold08: alpha=0.55, lambda=0.01013 
## + Fold08: alpha=1.00, lambda=0.01013 
## - Fold08: alpha=1.00, lambda=0.01013 
## + Fold09: alpha=0.10, lambda=0.01013 
## - Fold09: alpha=0.10, lambda=0.01013 
## + Fold09: alpha=0.55, lambda=0.01013 
## - Fold09: alpha=0.55, lambda=0.01013 
## + Fold09: alpha=1.00, lambda=0.01013 
## - Fold09: alpha=1.00, lambda=0.01013 
## + Fold10: alpha=0.10, lambda=0.01013 
## - Fold10: alpha=0.10, lambda=0.01013 
## + Fold10: alpha=0.55, lambda=0.01013 
## - Fold10: alpha=0.55, lambda=0.01013 
## + Fold10: alpha=1.00, lambda=0.01013 
## - Fold10: alpha=1.00, lambda=0.01013 
## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 0.1, lambda = 0.0101 on full training set

plot(model)

- My plot results always look a lot different than the class example. - They had the highest point as the middle dot on the the top line. - and it was a much lower value, around .40. - Clearly there is a lot of randomness built into these ML models

– Advantage of glmnet

• Basically just that they place constraints on your coefficents to help prevent overfitting compared to simple glm models.

– Make a custom trainControl

• Classification problems are a little more complicated than regression problems because you have to provide a custom summaryFunction to the train() function to use the AUC metric to rank your models.
• Be sure to set classProbs = TRUE, otherwise the twoClassSummary for summaryFunction will break.
• Also don’t quote twoClassSummary. I made that mistake at first.

# Create custom trainControl: myControl
myControl <- trainControl(
  method = "cv", 
  number = 10,
  summaryFunction = twoClassSummary,
  classProbs = T, # IMPORTANT!
  verboseIter = TRUE
)

– Fit glmnet with custom trainControl

• Recall from the video that glmnet is an extention of the generalized linear regression model (or glm) that places constraints on the magnitude of the coefficients to prevent overfitting.
• This is more commonly known as “penalized” regression modeling and is a very useful technique on datasets with many predictors and few values.

# Fit glmnet model: model
model <- train(
  y ~ ., overfit,
  method = "glmnet",
  trControl = myControl
)

## + Fold01: alpha=0.10, lambda=0.01013 
## - Fold01: alpha=0.10, lambda=0.01013 
## + Fold01: alpha=0.55, lambda=0.01013 
## - Fold01: alpha=0.55, lambda=0.01013 
## + Fold01: alpha=1.00, lambda=0.01013 
## - Fold01: alpha=1.00, lambda=0.01013 
## + Fold02: alpha=0.10, lambda=0.01013 
## - Fold02: alpha=0.10, lambda=0.01013 
## + Fold02: alpha=0.55, lambda=0.01013 
## - Fold02: alpha=0.55, lambda=0.01013 
## + Fold02: alpha=1.00, lambda=0.01013 
## - Fold02: alpha=1.00, lambda=0.01013 
## + Fold03: alpha=0.10, lambda=0.01013 
## - Fold03: alpha=0.10, lambda=0.01013 
## + Fold03: alpha=0.55, lambda=0.01013 
## - Fold03: alpha=0.55, lambda=0.01013 
## + Fold03: alpha=1.00, lambda=0.01013 
## - Fold03: alpha=1.00, lambda=0.01013 
## + Fold04: alpha=0.10, lambda=0.01013 
## - Fold04: alpha=0.10, lambda=0.01013 
## + Fold04: alpha=0.55, lambda=0.01013 
## - Fold04: alpha=0.55, lambda=0.01013 
## + Fold04: alpha=1.00, lambda=0.01013 
## - Fold04: alpha=1.00, lambda=0.01013 
## + Fold05: alpha=0.10, lambda=0.01013 
## - Fold05: alpha=0.10, lambda=0.01013 
## + Fold05: alpha=0.55, lambda=0.01013 
## - Fold05: alpha=0.55, lambda=0.01013 
## + Fold05: alpha=1.00, lambda=0.01013 
## - Fold05: alpha=1.00, lambda=0.01013 
## + Fold06: alpha=0.10, lambda=0.01013 
## - Fold06: alpha=0.10, lambda=0.01013 
## + Fold06: alpha=0.55, lambda=0.01013 
## - Fold06: alpha=0.55, lambda=0.01013 
## + Fold06: alpha=1.00, lambda=0.01013 
## - Fold06: alpha=1.00, lambda=0.01013 
## + Fold07: alpha=0.10, lambda=0.01013 
## - Fold07: alpha=0.10, lambda=0.01013 
## + Fold07: alpha=0.55, lambda=0.01013 
## - Fold07: alpha=0.55, lambda=0.01013 
## + Fold07: alpha=1.00, lambda=0.01013 
## - Fold07: alpha=1.00, lambda=0.01013 
## + Fold08: alpha=0.10, lambda=0.01013 
## - Fold08: alpha=0.10, lambda=0.01013 
## + Fold08: alpha=0.55, lambda=0.01013 
## - Fold08: alpha=0.55, lambda=0.01013 
## + Fold08: alpha=1.00, lambda=0.01013 
## - Fold08: alpha=1.00, lambda=0.01013 
## + Fold09: alpha=0.10, lambda=0.01013 
## - Fold09: alpha=0.10, lambda=0.01013 
## + Fold09: alpha=0.55, lambda=0.01013 
## - Fold09: alpha=0.55, lambda=0.01013 
## + Fold09: alpha=1.00, lambda=0.01013 
## - Fold09: alpha=1.00, lambda=0.01013 
## + Fold10: alpha=0.10, lambda=0.01013 
## - Fold10: alpha=0.10, lambda=0.01013 
## + Fold10: alpha=0.55, lambda=0.01013 
## - Fold10: alpha=0.55, lambda=0.01013 
## + Fold10: alpha=1.00, lambda=0.01013 
## - Fold10: alpha=1.00, lambda=0.01013 
## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 0.55, lambda = 0.0101 on full training set

# Print model to console
model

## glmnet 
## 
## 250 samples
## 200 predictors
##   2 classes: 'class1', 'class2' 
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 226, 225, 224, 225, 225, 225, ... 
## Resampling results across tuning parameters:
## 
##   alpha  lambda        ROC        Sens  Spec     
##   0.10   0.0001012745  0.4172101  0.00  0.9742754
##   0.10   0.0010127448  0.4299819  0.00  0.9786232
##   0.10   0.0101274483  0.4361413  0.00  0.9956522
##   0.55   0.0001012745  0.4148551  0.05  0.9445652
##   0.55   0.0010127448  0.4191123  0.05  0.9617754
##   0.55   0.0101274483  0.4596014  0.00  0.9873188
##   1.00   0.0001012745  0.3730072  0.05  0.9315217
##   1.00   0.0010127448  0.3663043  0.00  0.9487319
##   1.00   0.0101274483  0.4227355  0.00  0.9914855
## 
## ROC was used to select the optimal model using  the largest value.
## The final values used for the model were alpha = 0.55 and lambda
##  = 0.01012745.

# Print maximum ROC statistic
max(model$results$ROC)

## [1] 0.4596014

glmnet with custom tuning grid

• randome forest modles are pretty easy to tune as mtry is the main parameter
• glmnet have two key parmeters, alpha and lambda
• but you can fit all lambda values simultaneosuly at each level of alpha
• you can use this trick to get faster grid searches
• the iunstructor usually uses alpha 0 and 1 with 10 levels of lambda form 0 to 0.1

# Make a custom tuning grid
myGrid <- expand.grid(
  alpha = 0:1,
  lambda = seq(0.0001, 0.1, length = 10)
)

# Fit a model
set.seed(42)
model <- train(
  y ~ ., overfit,
  method = "glmnet",
  tuneGrid = myGrid, 
  trControl = myControl)

## + Fold01: alpha=0, lambda=0.1 
## - Fold01: alpha=0, lambda=0.1 
## + Fold01: alpha=1, lambda=0.1 
## - Fold01: alpha=1, lambda=0.1 
## + Fold02: alpha=0, lambda=0.1 
## - Fold02: alpha=0, lambda=0.1 
## + Fold02: alpha=1, lambda=0.1 
## - Fold02: alpha=1, lambda=0.1 
## + Fold03: alpha=0, lambda=0.1 
## - Fold03: alpha=0, lambda=0.1 
## + Fold03: alpha=1, lambda=0.1 
## - Fold03: alpha=1, lambda=0.1 
## + Fold04: alpha=0, lambda=0.1 
## - Fold04: alpha=0, lambda=0.1 
## + Fold04: alpha=1, lambda=0.1 
## - Fold04: alpha=1, lambda=0.1 
## + Fold05: alpha=0, lambda=0.1 
## - Fold05: alpha=0, lambda=0.1 
## + Fold05: alpha=1, lambda=0.1 
## - Fold05: alpha=1, lambda=0.1 
## + Fold06: alpha=0, lambda=0.1 
## - Fold06: alpha=0, lambda=0.1 
## + Fold06: alpha=1, lambda=0.1 
## - Fold06: alpha=1, lambda=0.1 
## + Fold07: alpha=0, lambda=0.1 
## - Fold07: alpha=0, lambda=0.1 
## + Fold07: alpha=1, lambda=0.1 
## - Fold07: alpha=1, lambda=0.1 
## + Fold08: alpha=0, lambda=0.1 
## - Fold08: alpha=0, lambda=0.1 
## + Fold08: alpha=1, lambda=0.1 
## - Fold08: alpha=1, lambda=0.1 
## + Fold09: alpha=0, lambda=0.1 
## - Fold09: alpha=0, lambda=0.1 
## + Fold09: alpha=1, lambda=0.1 
## - Fold09: alpha=1, lambda=0.1 
## + Fold10: alpha=0, lambda=0.1 
## - Fold10: alpha=0, lambda=0.1 
## + Fold10: alpha=1, lambda=0.1 
## - Fold10: alpha=1, lambda=0.1 
## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 1, lambda = 0.0445 on full training set

plot(model)

• For some reason my model is much more fin tuned on the regularization parameter than his.
  • I see data from 0 to .1, where as his goes to 1. and all values are .5 after the first 0 value
  • I see a value just above .04 being by far the best.
• He says that ridge regression typically outperforms lasso but its worth the time to try both.
  • It definitely is better here

The regularization path

• Full regularization path for all models with alpha = 0
• this plot is specific to glmnet models
• on the left is the high intercept only model, with high values of lambda
• on the right is the full model with no penalty, low values of lambda
• this shows how the coefficients are decreased and complexity of the model decreased as lamda (and the coefficient penalty is increased)

# Full regularization path
plot(model$finalModel)

– Why a custom tuning grid?

• the default tuning grid is very small and there are many more potential glmnet models you want to explore

– glmnet with custom trainControl and tuning

• As you saw in the video, the glmnet model actually fits many models at once (one of the great things about the package).
• You can exploit this by passing a large number of lambda values, which control the amount of penalization in the model.
• train() is smart enough to only fit one model per alpha value and pass all of the lambda values at once for simultaneous fitting.

My favorite tuning grid for glmnet models is:

expand.grid(alpha = 0:1,
  lambda = seq(0.0001, 1, length = 100))

##     alpha lambda
## 1       0 0.0001
## 2       1 0.0001
## 3       0 0.0102
## 4       1 0.0102
## 5       0 0.0203
## 6       1 0.0203
## 7       0 0.0304
## 8       1 0.0304
## 9       0 0.0405
## 10      1 0.0405
## 11      0 0.0506
## 12      1 0.0506
## 13      0 0.0607
## 14      1 0.0607
## 15      0 0.0708
## 16      1 0.0708
## 17      0 0.0809
## 18      1 0.0809
## 19      0 0.0910
## 20      1 0.0910
## 21      0 0.1011
## 22      1 0.1011
## 23      0 0.1112
## 24      1 0.1112
## 25      0 0.1213
## 26      1 0.1213
## 27      0 0.1314
## 28      1 0.1314
## 29      0 0.1415
## 30      1 0.1415
## 31      0 0.1516
## 32      1 0.1516
## 33      0 0.1617
## 34      1 0.1617
## 35      0 0.1718
## 36      1 0.1718
## 37      0 0.1819
## 38      1 0.1819
## 39      0 0.1920
## 40      1 0.1920
## 41      0 0.2021
## 42      1 0.2021
## 43      0 0.2122
## 44      1 0.2122
## 45      0 0.2223
## 46      1 0.2223
## 47      0 0.2324
## 48      1 0.2324
## 49      0 0.2425
## 50      1 0.2425
## 51      0 0.2526
## 52      1 0.2526
## 53      0 0.2627
## 54      1 0.2627
## 55      0 0.2728
## 56      1 0.2728
## 57      0 0.2829
## 58      1 0.2829
## 59      0 0.2930
## 60      1 0.2930
## 61      0 0.3031
## 62      1 0.3031
## 63      0 0.3132
## 64      1 0.3132
## 65      0 0.3233
## 66      1 0.3233
## 67      0 0.3334
## 68      1 0.3334
## 69      0 0.3435
## 70      1 0.3435
## 71      0 0.3536
## 72      1 0.3536
## 73      0 0.3637
## 74      1 0.3637
## 75      0 0.3738
## 76      1 0.3738
## 77      0 0.3839
## 78      1 0.3839
## 79      0 0.3940
## 80      1 0.3940
## 81      0 0.4041
## 82      1 0.4041
## 83      0 0.4142
## 84      1 0.4142
## 85      0 0.4243
## 86      1 0.4243
## 87      0 0.4344
## 88      1 0.4344
## 89      0 0.4445
## 90      1 0.4445
## 91      0 0.4546
## 92      1 0.4546
## 93      0 0.4647
## 94      1 0.4647
## 95      0 0.4748
## 96      1 0.4748
## 97      0 0.4849
## 98      1 0.4849
## 99      0 0.4950
## 100     1 0.4950
## 101     0 0.5051
## 102     1 0.5051
## 103     0 0.5152
## 104     1 0.5152
## 105     0 0.5253
## 106     1 0.5253
## 107     0 0.5354
## 108     1 0.5354
## 109     0 0.5455
## 110     1 0.5455
## 111     0 0.5556
## 112     1 0.5556
## 113     0 0.5657
## 114     1 0.5657
## 115     0 0.5758
## 116     1 0.5758
## 117     0 0.5859
## 118     1 0.5859
## 119     0 0.5960
## 120     1 0.5960
## 121     0 0.6061
## 122     1 0.6061
## 123     0 0.6162
## 124     1 0.6162
## 125     0 0.6263
## 126     1 0.6263
## 127     0 0.6364
## 128     1 0.6364
## 129     0 0.6465
## 130     1 0.6465
## 131     0 0.6566
## 132     1 0.6566
## 133     0 0.6667
## 134     1 0.6667
## 135     0 0.6768
## 136     1 0.6768
## 137     0 0.6869
## 138     1 0.6869
## 139     0 0.6970
## 140     1 0.6970
## 141     0 0.7071
## 142     1 0.7071
## 143     0 0.7172
## 144     1 0.7172
## 145     0 0.7273
## 146     1 0.7273
## 147     0 0.7374
## 148     1 0.7374
## 149     0 0.7475
## 150     1 0.7475
## 151     0 0.7576
## 152     1 0.7576
## 153     0 0.7677
## 154     1 0.7677
## 155     0 0.7778
## 156     1 0.7778
## 157     0 0.7879
## 158     1 0.7879
## 159     0 0.7980
## 160     1 0.7980
## 161     0 0.8081
## 162     1 0.8081
## 163     0 0.8182
## 164     1 0.8182
## 165     0 0.8283
## 166     1 0.8283
## 167     0 0.8384
## 168     1 0.8384
## 169     0 0.8485
## 170     1 0.8485
## 171     0 0.8586
## 172     1 0.8586
## 173     0 0.8687
## 174     1 0.8687
## 175     0 0.8788
## 176     1 0.8788
## 177     0 0.8889
## 178     1 0.8889
## 179     0 0.8990
## 180     1 0.8990
## 181     0 0.9091
## 182     1 0.9091
## 183     0 0.9192
## 184     1 0.9192
## 185     0 0.9293
## 186     1 0.9293
## 187     0 0.9394
## 188     1 0.9394
## 189     0 0.9495
## 190     1 0.9495
## 191     0 0.9596
## 192     1 0.9596
## 193     0 0.9697
## 194     1 0.9697
## 195     0 0.9798
## 196     1 0.9798
## 197     0 0.9899
## 198     1 0.9899
## 199     0 1.0000
## 200     1 1.0000

• You also look at the two forms of penalized models with this tuneGrid: ridge regression and lasso regression.
• alpha = 0 is pure ridge regression, and alpha = 1 is pure lasso regression.
• You can fit a mixture of the two models (i.e. an elastic net) using an alpha between 0 and 1.
  • For example, alpha = .05 would be 95% ridge regression and 5% lasso regression.
• I am adding alpha 0.05 just to see how it does.

# Train glmnet with custom trainControl and tuning: model
model <- train(
  y ~ ., overfit,
  tuneGrid = expand.grid(
    alpha = c(0,.05,1), 
    lambda = seq(0.0001, 1, length = 100)),
  method = "glmnet",
  trControl = myControl
)

## + Fold01: alpha=0.00, lambda=1 
## - Fold01: alpha=0.00, lambda=1 
## + Fold01: alpha=0.05, lambda=1 
## - Fold01: alpha=0.05, lambda=1 
## + Fold01: alpha=1.00, lambda=1 
## - Fold01: alpha=1.00, lambda=1 
## + Fold02: alpha=0.00, lambda=1 
## - Fold02: alpha=0.00, lambda=1 
## + Fold02: alpha=0.05, lambda=1 
## - Fold02: alpha=0.05, lambda=1 
## + Fold02: alpha=1.00, lambda=1 
## - Fold02: alpha=1.00, lambda=1 
## + Fold03: alpha=0.00, lambda=1 
## - Fold03: alpha=0.00, lambda=1 
## + Fold03: alpha=0.05, lambda=1 
## - Fold03: alpha=0.05, lambda=1 
## + Fold03: alpha=1.00, lambda=1 
## - Fold03: alpha=1.00, lambda=1 
## + Fold04: alpha=0.00, lambda=1 
## - Fold04: alpha=0.00, lambda=1 
## + Fold04: alpha=0.05, lambda=1 
## - Fold04: alpha=0.05, lambda=1 
## + Fold04: alpha=1.00, lambda=1 
## - Fold04: alpha=1.00, lambda=1 
## + Fold05: alpha=0.00, lambda=1 
## - Fold05: alpha=0.00, lambda=1 
## + Fold05: alpha=0.05, lambda=1 
## - Fold05: alpha=0.05, lambda=1 
## + Fold05: alpha=1.00, lambda=1 
## - Fold05: alpha=1.00, lambda=1 
## + Fold06: alpha=0.00, lambda=1 
## - Fold06: alpha=0.00, lambda=1 
## + Fold06: alpha=0.05, lambda=1 
## - Fold06: alpha=0.05, lambda=1 
## + Fold06: alpha=1.00, lambda=1 
## - Fold06: alpha=1.00, lambda=1 
## + Fold07: alpha=0.00, lambda=1 
## - Fold07: alpha=0.00, lambda=1 
## + Fold07: alpha=0.05, lambda=1 
## - Fold07: alpha=0.05, lambda=1 
## + Fold07: alpha=1.00, lambda=1 
## - Fold07: alpha=1.00, lambda=1 
## + Fold08: alpha=0.00, lambda=1 
## - Fold08: alpha=0.00, lambda=1 
## + Fold08: alpha=0.05, lambda=1 
## - Fold08: alpha=0.05, lambda=1 
## + Fold08: alpha=1.00, lambda=1 
## - Fold08: alpha=1.00, lambda=1 
## + Fold09: alpha=0.00, lambda=1 
## - Fold09: alpha=0.00, lambda=1 
## + Fold09: alpha=0.05, lambda=1 
## - Fold09: alpha=0.05, lambda=1 
## + Fold09: alpha=1.00, lambda=1 
## - Fold09: alpha=1.00, lambda=1 
## + Fold10: alpha=0.00, lambda=1 
## - Fold10: alpha=0.00, lambda=1 
## + Fold10: alpha=0.05, lambda=1 
## - Fold10: alpha=0.05, lambda=1 
## + Fold10: alpha=1.00, lambda=1 
## - Fold10: alpha=1.00, lambda=1 
## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 0.05, lambda = 0.869 on full training set

# Print model to console
model

## glmnet 
## 
## 250 samples
## 200 predictors
##   2 classes: 'class1', 'class2' 
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 225, 226, 225, 225, 226, 225, ... 
## Resampling results across tuning parameters:
## 
##   alpha  lambda  ROC        Sens  Spec     
##   0.00   0.0001  0.4199275  0     0.9871377
##   0.00   0.0102  0.4282609  0     0.9871377
##   0.00   0.0203  0.4303442  0     0.9914855
##   0.00   0.0304  0.4368659  0     0.9956522
##   0.00   0.0405  0.4433877  0     0.9956522
##   0.00   0.0506  0.4412138  0     0.9956522
##   0.00   0.0607  0.4389493  0     1.0000000
##   0.00   0.0708  0.4389493  0     1.0000000
##   0.00   0.0809  0.4454710  0     1.0000000
##   0.00   0.0910  0.4497283  0     1.0000000
##   0.00   0.1011  0.4560688  0     1.0000000
##   0.00   0.1112  0.4538949  0     1.0000000
##   0.00   0.1213  0.4559783  0     1.0000000
##   0.00   0.1314  0.4538043  0     1.0000000
##   0.00   0.1415  0.4581522  0     1.0000000
##   0.00   0.1516  0.4559783  0     1.0000000
##   0.00   0.1617  0.4580616  0     1.0000000
##   0.00   0.1718  0.4580616  0     1.0000000
##   0.00   0.1819  0.4601449  0     1.0000000
##   0.00   0.1920  0.4601449  0     1.0000000
##   0.00   0.2021  0.4600543  0     1.0000000
##   0.00   0.2122  0.4622283  0     1.0000000
##   0.00   0.2223  0.4622283  0     1.0000000
##   0.00   0.2324  0.4601449  0     1.0000000
##   0.00   0.2425  0.4601449  0     1.0000000
##   0.00   0.2526  0.4601449  0     1.0000000
##   0.00   0.2627  0.4623188  0     1.0000000
##   0.00   0.2728  0.4623188  0     1.0000000
##   0.00   0.2829  0.4644928  0     1.0000000
##   0.00   0.2930  0.4666667  0     1.0000000
##   0.00   0.3031  0.4666667  0     1.0000000
##   0.00   0.3132  0.4666667  0     1.0000000
##   0.00   0.3233  0.4666667  0     1.0000000
##   0.00   0.3334  0.4666667  0     1.0000000
##   0.00   0.3435  0.4666667  0     1.0000000
##   0.00   0.3536  0.4666667  0     1.0000000
##   0.00   0.3637  0.4666667  0     1.0000000
##   0.00   0.3738  0.4708333  0     1.0000000
##   0.00   0.3839  0.4708333  0     1.0000000
##   0.00   0.3940  0.4686594  0     1.0000000
##   0.00   0.4041  0.4686594  0     1.0000000
##   0.00   0.4142  0.4686594  0     1.0000000
##   0.00   0.4243  0.4751812  0     1.0000000
##   0.00   0.4344  0.4751812  0     1.0000000
##   0.00   0.4445  0.4751812  0     1.0000000
##   0.00   0.4546  0.4751812  0     1.0000000
##   0.00   0.4647  0.4751812  0     1.0000000
##   0.00   0.4748  0.4751812  0     1.0000000
##   0.00   0.4849  0.4751812  0     1.0000000
##   0.00   0.4950  0.4773551  0     1.0000000
##   0.00   0.5051  0.4773551  0     1.0000000
##   0.00   0.5152  0.4773551  0     1.0000000
##   0.00   0.5253  0.4773551  0     1.0000000
##   0.00   0.5354  0.4773551  0     1.0000000
##   0.00   0.5455  0.4773551  0     1.0000000
##   0.00   0.5556  0.4773551  0     1.0000000
##   0.00   0.5657  0.4773551  0     1.0000000
##   0.00   0.5758  0.4773551  0     1.0000000
##   0.00   0.5859  0.4773551  0     1.0000000
##   0.00   0.5960  0.4773551  0     1.0000000
##   0.00   0.6061  0.4794384  0     1.0000000
##   0.00   0.6162  0.4794384  0     1.0000000
##   0.00   0.6263  0.4794384  0     1.0000000
##   0.00   0.6364  0.4794384  0     1.0000000
##   0.00   0.6465  0.4794384  0     1.0000000
##   0.00   0.6566  0.4816123  0     1.0000000
##   0.00   0.6667  0.4837862  0     1.0000000
##   0.00   0.6768  0.4881341  0     1.0000000
##   0.00   0.6869  0.4903080  0     1.0000000
##   0.00   0.6970  0.4903080  0     1.0000000
##   0.00   0.7071  0.4903080  0     1.0000000
##   0.00   0.7172  0.4903080  0     1.0000000
##   0.00   0.7273  0.4903080  0     1.0000000
##   0.00   0.7374  0.4903080  0     1.0000000
##   0.00   0.7475  0.4924819  0     1.0000000
##   0.00   0.7576  0.4924819  0     1.0000000
##   0.00   0.7677  0.4924819  0     1.0000000
##   0.00   0.7778  0.4924819  0     1.0000000
##   0.00   0.7879  0.4924819  0     1.0000000
##   0.00   0.7980  0.4924819  0     1.0000000
##   0.00   0.8081  0.4924819  0     1.0000000
##   0.00   0.8182  0.4924819  0     1.0000000
##   0.00   0.8283  0.4924819  0     1.0000000
##   0.00   0.8384  0.4924819  0     1.0000000
##   0.00   0.8485  0.4924819  0     1.0000000
##   0.00   0.8586  0.4924819  0     1.0000000
##   0.00   0.8687  0.4924819  0     1.0000000
##   0.00   0.8788  0.4924819  0     1.0000000
##   0.00   0.8889  0.4924819  0     1.0000000
##   0.00   0.8990  0.4924819  0     1.0000000
##   0.00   0.9091  0.4924819  0     1.0000000
##   0.00   0.9192  0.4924819  0     1.0000000
##   0.00   0.9293  0.4924819  0     1.0000000
##   0.00   0.9394  0.4924819  0     1.0000000
##   0.00   0.9495  0.4924819  0     1.0000000
##   0.00   0.9596  0.4924819  0     1.0000000
##   0.00   0.9697  0.4924819  0     1.0000000
##   0.00   0.9798  0.4924819  0     1.0000000
##   0.00   0.9899  0.4924819  0     1.0000000
##   0.00   1.0000  0.4924819  0     1.0000000
##   0.05   0.0001  0.4137681  0     0.9612319
##   0.05   0.0102  0.4281703  0     0.9871377
##   0.05   0.0203  0.4520833  0     0.9956522
##   0.05   0.0304  0.4737319  0     0.9956522
##   0.05   0.0405  0.4672101  0     0.9956522
##   0.05   0.0506  0.4864130  0     0.9956522
##   0.05   0.0607  0.4994565  0     1.0000000
##   0.05   0.0708  0.5015399  0     1.0000000
##   0.05   0.0809  0.5015399  0     1.0000000
##   0.05   0.0910  0.5036232  0     1.0000000
##   0.05   0.1011  0.5165761  0     1.0000000
##   0.05   0.1112  0.5250000  0     1.0000000
##   0.05   0.1213  0.5270833  0     1.0000000
##   0.05   0.1314  0.5270833  0     1.0000000
##   0.05   0.1415  0.5270833  0     1.0000000
##   0.05   0.1516  0.5270833  0     1.0000000
##   0.05   0.1617  0.5335145  0     1.0000000
##   0.05   0.1718  0.5377717  0     1.0000000
##   0.05   0.1819  0.5399457  0     1.0000000
##   0.05   0.1920  0.5442029  0     1.0000000
##   0.05   0.2021  0.5527174  0     1.0000000
##   0.05   0.2122  0.5483696  0     1.0000000
##   0.05   0.2223  0.5505435  0     1.0000000
##   0.05   0.2324  0.5592391  0     1.0000000
##   0.05   0.2425  0.5570652  0     1.0000000
##   0.05   0.2526  0.5570652  0     1.0000000
##   0.05   0.2627  0.5549819  0     1.0000000
##   0.05   0.2728  0.5550725  0     1.0000000
##   0.05   0.2829  0.5528986  0     1.0000000
##   0.05   0.2930  0.5507246  0     1.0000000
##   0.05   0.3031  0.5464674  0     1.0000000
##   0.05   0.3132  0.5442935  0     1.0000000
##   0.05   0.3233  0.5400362  0     1.0000000
##   0.05   0.3334  0.5376812  0     1.0000000
##   0.05   0.3435  0.5334239  0     1.0000000
##   0.05   0.3536  0.5397645  0     1.0000000
##   0.05   0.3637  0.5355072  0     1.0000000
##   0.05   0.3738  0.5312500  0     1.0000000
##   0.05   0.3839  0.5269928  0     1.0000000
##   0.05   0.3940  0.5206522  0     1.0000000
##   0.05   0.4041  0.5206522  0     1.0000000
##   0.05   0.4142  0.5099638  0     1.0000000
##   0.05   0.4243  0.4951087  0     1.0000000
##   0.05   0.4344  0.4886775  0     1.0000000
##   0.05   0.4445  0.4909420  0     1.0000000
##   0.05   0.4546  0.4907609  0     1.0000000
##   0.05   0.4647  0.4951087  0     1.0000000
##   0.05   0.4748  0.4886775  0     1.0000000
##   0.05   0.4849  0.4843297  0     1.0000000
##   0.05   0.4950  0.4800725  0     1.0000000
##   0.05   0.5051  0.4843297  0     1.0000000
##   0.05   0.5152  0.4822464  0     1.0000000
##   0.05   0.5253  0.4759964  0     1.0000000
##   0.05   0.5354  0.4780797  0     1.0000000
##   0.05   0.5455  0.4780797  0     1.0000000
##   0.05   0.5556  0.4694746  0     1.0000000
##   0.05   0.5657  0.4694746  0     1.0000000
##   0.05   0.5758  0.4673007  0     1.0000000
##   0.05   0.5859  0.4802536  0     1.0000000
##   0.05   0.5960  0.4846920  0     1.0000000
##   0.05   0.6061  0.4913043  0     1.0000000
##   0.05   0.6162  0.5021739  0     1.0000000
##   0.05   0.6263  0.5020833  0     1.0000000
##   0.05   0.6364  0.5213768  0     1.0000000
##   0.05   0.6465  0.5321558  0     1.0000000
##   0.05   0.6566  0.5302536  0     1.0000000
##   0.05   0.6667  0.5324275  0     1.0000000
##   0.05   0.6768  0.5301630  0     1.0000000
##   0.05   0.6869  0.5364130  0     1.0000000
##   0.05   0.6970  0.5471920  0     1.0000000
##   0.05   0.7071  0.5598732  0     1.0000000
##   0.05   0.7172  0.5682971  0     1.0000000
##   0.05   0.7273  0.5853261  0     1.0000000
##   0.05   0.7374  0.5938406  0     1.0000000
##   0.05   0.7475  0.6153080  0     1.0000000
##   0.05   0.7576  0.6348732  0     1.0000000
##   0.05   0.7677  0.6478261  0     1.0000000
##   0.05   0.7778  0.6627717  0     1.0000000
##   0.05   0.7879  0.6734601  0     1.0000000
##   0.05   0.7980  0.6778080  0     1.0000000
##   0.05   0.8081  0.6842391  0     1.0000000
##   0.05   0.8182  0.6971920  0     1.0000000
##   0.05   0.8283  0.7015399  0     1.0000000
##   0.05   0.8384  0.7102355  0     1.0000000
##   0.05   0.8485  0.7186594  0     1.0000000
##   0.05   0.8586  0.7208333  0     1.0000000
##   0.05   0.8687  0.7272645  0     1.0000000
##   0.05   0.8788  0.6962862  0     1.0000000
##   0.05   0.8889  0.6941123  0     1.0000000
##   0.05   0.8990  0.6962862  0     1.0000000
##   0.05   0.9091  0.6984601  0     1.0000000
##   0.05   0.9192  0.7006341  0     1.0000000
##   0.05   0.9293  0.6745471  0     1.0000000
##   0.05   0.9394  0.6767210  0     1.0000000
##   0.05   0.9495  0.6767210  0     1.0000000
##   0.05   0.9596  0.6788949  0     1.0000000
##   0.05   0.9697  0.6788949  0     1.0000000
##   0.05   0.9798  0.6788949  0     1.0000000
##   0.05   0.9899  0.6788949  0     1.0000000
##   0.05   1.0000  0.6788949  0     1.0000000
##   1.00   0.0001  0.4460145  0     0.9442029
##   1.00   0.0102  0.4586957  0     0.9871377
##   1.00   0.0203  0.4821558  0     1.0000000
##   1.00   0.0304  0.5280797  0     1.0000000
##   1.00   0.0405  0.6972826  0     1.0000000
##   1.00   0.0506  0.6288949  0     1.0000000
##   1.00   0.0607  0.5000000  0     1.0000000
##   1.00   0.0708  0.5000000  0     1.0000000
##   1.00   0.0809  0.5000000  0     1.0000000
##   1.00   0.0910  0.5000000  0     1.0000000
##   1.00   0.1011  0.5000000  0     1.0000000
##   1.00   0.1112  0.5000000  0     1.0000000
##   1.00   0.1213  0.5000000  0     1.0000000
##   1.00   0.1314  0.5000000  0     1.0000000
##   1.00   0.1415  0.5000000  0     1.0000000
##   1.00   0.1516  0.5000000  0     1.0000000
##   1.00   0.1617  0.5000000  0     1.0000000
##   1.00   0.1718  0.5000000  0     1.0000000
##   1.00   0.1819  0.5000000  0     1.0000000
##   1.00   0.1920  0.5000000  0     1.0000000
##   1.00   0.2021  0.5000000  0     1.0000000
##   1.00   0.2122  0.5000000  0     1.0000000
##   1.00   0.2223  0.5000000  0     1.0000000
##   1.00   0.2324  0.5000000  0     1.0000000
##   1.00   0.2425  0.5000000  0     1.0000000
##   1.00   0.2526  0.5000000  0     1.0000000
##   1.00   0.2627  0.5000000  0     1.0000000
##   1.00   0.2728  0.5000000  0     1.0000000
##   1.00   0.2829  0.5000000  0     1.0000000
##   1.00   0.2930  0.5000000  0     1.0000000
##   1.00   0.3031  0.5000000  0     1.0000000
##   1.00   0.3132  0.5000000  0     1.0000000
##   1.00   0.3233  0.5000000  0     1.0000000
##   1.00   0.3334  0.5000000  0     1.0000000
##   1.00   0.3435  0.5000000  0     1.0000000
##   1.00   0.3536  0.5000000  0     1.0000000
##   1.00   0.3637  0.5000000  0     1.0000000
##   1.00   0.3738  0.5000000  0     1.0000000
##   1.00   0.3839  0.5000000  0     1.0000000
##   1.00   0.3940  0.5000000  0     1.0000000
##   1.00   0.4041  0.5000000  0     1.0000000
##   1.00   0.4142  0.5000000  0     1.0000000
##   1.00   0.4243  0.5000000  0     1.0000000
##   1.00   0.4344  0.5000000  0     1.0000000
##   1.00   0.4445  0.5000000  0     1.0000000
##   1.00   0.4546  0.5000000  0     1.0000000
##   1.00   0.4647  0.5000000  0     1.0000000
##   1.00   0.4748  0.5000000  0     1.0000000
##   1.00   0.4849  0.5000000  0     1.0000000
##   1.00   0.4950  0.5000000  0     1.0000000
##   1.00   0.5051  0.5000000  0     1.0000000
##   1.00   0.5152  0.5000000  0     1.0000000
##   1.00   0.5253  0.5000000  0     1.0000000
##   1.00   0.5354  0.5000000  0     1.0000000
##   1.00   0.5455  0.5000000  0     1.0000000
##   1.00   0.5556  0.5000000  0     1.0000000
##   1.00   0.5657  0.5000000  0     1.0000000
##   1.00   0.5758  0.5000000  0     1.0000000
##   1.00   0.5859  0.5000000  0     1.0000000
##   1.00   0.5960  0.5000000  0     1.0000000
##   1.00   0.6061  0.5000000  0     1.0000000
##   1.00   0.6162  0.5000000  0     1.0000000
##   1.00   0.6263  0.5000000  0     1.0000000
##   1.00   0.6364  0.5000000  0     1.0000000
##   1.00   0.6465  0.5000000  0     1.0000000
##   1.00   0.6566  0.5000000  0     1.0000000
##   1.00   0.6667  0.5000000  0     1.0000000
##   1.00   0.6768  0.5000000  0     1.0000000
##   1.00   0.6869  0.5000000  0     1.0000000
##   1.00   0.6970  0.5000000  0     1.0000000
##   1.00   0.7071  0.5000000  0     1.0000000
##   1.00   0.7172  0.5000000  0     1.0000000
##   1.00   0.7273  0.5000000  0     1.0000000
##   1.00   0.7374  0.5000000  0     1.0000000
##   1.00   0.7475  0.5000000  0     1.0000000
##   1.00   0.7576  0.5000000  0     1.0000000
##   1.00   0.7677  0.5000000  0     1.0000000
##   1.00   0.7778  0.5000000  0     1.0000000
##   1.00   0.7879  0.5000000  0     1.0000000
##   1.00   0.7980  0.5000000  0     1.0000000
##   1.00   0.8081  0.5000000  0     1.0000000
##   1.00   0.8182  0.5000000  0     1.0000000
##   1.00   0.8283  0.5000000  0     1.0000000
##   1.00   0.8384  0.5000000  0     1.0000000
##   1.00   0.8485  0.5000000  0     1.0000000
##   1.00   0.8586  0.5000000  0     1.0000000
##   1.00   0.8687  0.5000000  0     1.0000000
##   1.00   0.8788  0.5000000  0     1.0000000
##   1.00   0.8889  0.5000000  0     1.0000000
##   1.00   0.8990  0.5000000  0     1.0000000
##   1.00   0.9091  0.5000000  0     1.0000000
##   1.00   0.9192  0.5000000  0     1.0000000
##   1.00   0.9293  0.5000000  0     1.0000000
##   1.00   0.9394  0.5000000  0     1.0000000
##   1.00   0.9495  0.5000000  0     1.0000000
##   1.00   0.9596  0.5000000  0     1.0000000
##   1.00   0.9697  0.5000000  0     1.0000000
##   1.00   0.9798  0.5000000  0     1.0000000
##   1.00   0.9899  0.5000000  0     1.0000000
##   1.00   1.0000  0.5000000  0     1.0000000
## 
## ROC was used to select the optimal model using  the largest value.
## The final values used for the model were alpha = 0.05 and lambda = 0.8687.

# Print maximum ROC statistic
max(model$results$ROC)

## [1] 0.7272645

plot(model)

• Apparently the lasso regression is better for this overfit dataset. At low values
• But I can get better with an elastic net and high regularization parameters. hmmmm.
  • I wonder what this mean?

   

---

Preprocessing your data

---

Median imputation

• Real world data is going to have missing values
  • Just throwing out rows with missing data is not the best idea
  • You can create unintended bias in your data
  • In extreme cases you will have no data left or very little of the originial data
• Using median imputation is a good way to deal with missing data
  • this mean replacing the missing values with the mean of the non missing data
  • this works well if the data is missing at random (MAR)

Example of missing data:

# generate some data with missing values
set.seed(42)
mtcars[sample(1:nrow(mtcars), 10), "hp"] <- NA

# split target for predictors
Y <- mtcars$mpg
X <- mtcars[, 2:4]

# Try to fit a caret model
# Notice carets non formula interace
model <- train(X,Y)

## note: only 2 unique complexity parameters in default grid. Truncating the grid to 2 .
## 
## Something is wrong; all the RMSE metric values are missing:
##       RMSE        Rsquared        MAE     
##  Min.   : NA   Min.   : NA   Min.   : NA  
##  1st Qu.: NA   1st Qu.: NA   1st Qu.: NA  
##  Median : NA   Median : NA   Median : NA  
##  Mean   :NaN   Mean   :NaN   Mean   :NaN  
##  3rd Qu.: NA   3rd Qu.: NA   3rd Qu.: NA  
##  Max.   : NA   Max.   : NA   Max.   : NA  
##  NA's   :2     NA's   :2     NA's   :2

## Error: Stopping

• This creates an error
• This missing data create NA in the summary and it propogates into the model and breaks things. At some point its trying to divide by NA maybe.

# Using median imputation fixes this issue
model <- train(X,Y, preProcess = "medianImpute")

## note: only 2 unique complexity parameters in default grid. Truncating the grid to 2 .

print(model)

## Random Forest 
## 
## 32 samples
##  3 predictor
## 
## Pre-processing: median imputation (3) 
## Resampling: Bootstrapped (25 reps) 
## Summary of sample sizes: 32, 32, 32, 32, 32, 32, ... 
## Resampling results across tuning parameters:
## 
##   mtry  RMSE      Rsquared   MAE     
##   2     2.996936  0.7706454  2.421628
##   3     3.026853  0.7676774  2.427185
## 
## RMSE was used to select the optimal model using  the smallest value.
## The final value used for the model was mtry = 2.

• caret does the imputation inside each fold of the cross validation, so you get an hosest assement of the entire modleing process
• The random forest model is calculated after the imputation.

– Apply median imputation

load('data/BreastCancer.RData')

glimpse(breast_cancer_x)

## Observations: 699
## Variables: 9
## $ Cl.thickness    <int> 5, NA, NA, 6, 4, 8, 1, 2, NA, NA, 1, 2, 5, 1, ...
## $ Cell.size       <int> NA, 4, NA, 8, 1, 10, 1, 1, 1, 2, 1, 1, NA, 1, ...
## $ Cell.shape      <int> 1, 4, 1, 8, 1, 10, NA, 2, 1, 1, 1, 1, 3, NA, 5...
## $ Marg.adhesion   <int> 1, NA, 1, NA, 3, 8, NA, 1, NA, 1, 1, 1, 3, 1, ...
## $ Epith.c.size    <int> NA, 7, 2, NA, 2, 7, 2, 2, 2, 2, 1, 2, NA, 2, 7...
## $ Bare.nuclei     <int> 1, 10, NA, 4, 1, 10, 10, 1, 1, 1, 1, 1, 3, 3, ...
## $ Bl.cromatin     <int> 3, 3, 3, 3, 3, NA, 3, 3, NA, 2, 3, 2, 4, 3, 5,...
## $ Normal.nucleoli <int> 1, NA, 1, 7, NA, 7, 1, 1, 1, NA, 1, 1, NA, 1, ...
## $ Mitoses         <int> 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, NA, 1, 1, 4, ...

glimpse(breast_cancer_y)

##  Factor w/ 2 levels "benign","malignant": 1 1 1 1 1 2 1 1 1 1 ...

# Apply median imputation: model
model1 <- train(
  x = breast_cancer_x, y = breast_cancer_y,
  method = "glm",
  trControl = myControl,
  preProcess = 'medianImpute'
)

## + Fold01: parameter=none 
## - Fold01: parameter=none 
## + Fold02: parameter=none 
## - Fold02: parameter=none 
## + Fold03: parameter=none 
## - Fold03: parameter=none 
## + Fold04: parameter=none 
## - Fold04: parameter=none 
## + Fold05: parameter=none 
## - Fold05: parameter=none 
## + Fold06: parameter=none 
## - Fold06: parameter=none 
## + Fold07: parameter=none 
## - Fold07: parameter=none 
## + Fold08: parameter=none 
## - Fold08: parameter=none 
## + Fold09: parameter=none 
## - Fold09: parameter=none 
## + Fold10: parameter=none 
## - Fold10: parameter=none 
## Aggregating results
## Fitting final model on full training set

# Print model to console
model1

## Generalized Linear Model 
## 
## 699 samples
##   9 predictor
##   2 classes: 'benign', 'malignant' 
## 
## Pre-processing: median imputation (9) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 629, 630, 630, 628, 629, 629, ... 
## Resampling results:
## 
##   ROC        Sens      Spec     
##   0.9923543  0.969372  0.9376667

KNN imputation

• There are some problems with median imputation
  • It is fast, but if data is not missing at random than it can cause problems
  • K-nearest neighbors is a good strategy for filling missing values with other similar observations
• e.g. say you are missing hp data from a bunch of the smaller cars in the mtcars dataset using cars size and cylider data to fill hp with similar values to other smaller cars
  • if you just used median imputation you would get much larger hp from the medium and large cars skewing the data
• this is a little bit slower but worth it to get the best model

Example - Median vs KNN imputation:

data(mtcars)
# Generate data with missing values
mtcars[mtcars$disp < 140, "hp"] <- NA
Y <- mtcars$mpg
X <- mtcars[, 2:4]

# Use median imputation
set.seed(42)
model <- train(X,Y,
               method = "glm",
               preProcess = "medianImpute")
print(model)

## Generalized Linear Model 
## 
## 32 samples
##  3 predictor
## 
## Pre-processing: median imputation (3) 
## Resampling: Bootstrapped (25 reps) 
## Summary of sample sizes: 32, 32, 32, 32, 32, 32, ... 
## Resampling results:
## 
##   RMSE      Rsquared   MAE     
##   3.252487  0.7672791  2.587883

# using KNN imputation
set.seed(42)
model <- train(X,Y,
               method = "glm",
               preProcess = "knnImpute")
print(model)

## Generalized Linear Model 
## 
## 32 samples
##  3 predictor
## 
## Pre-processing: nearest neighbor imputation (3), centered (3), scaled (3) 
## Resampling: Bootstrapped (25 reps) 
## Summary of sample sizes: 32, 32, 32, 32, 32, 32, ... 
## Resampling results:
## 
##   RMSE     Rsquared   MAE     
##   3.22105  0.7682637  2.570241

– Use KNN imputation

# Apply KNN imputation: model2
model2 <- train(
  x = breast_cancer_x, y = breast_cancer_y,
  method = "glm",
  trControl = myControl,
  preProcess = "knnImpute"
)

## + Fold01: parameter=none 
## - Fold01: parameter=none 
## + Fold02: parameter=none 
## - Fold02: parameter=none 
## + Fold03: parameter=none 
## - Fold03: parameter=none 
## + Fold04: parameter=none 
## - Fold04: parameter=none 
## + Fold05: parameter=none 
## - Fold05: parameter=none 
## + Fold06: parameter=none 
## - Fold06: parameter=none 
## + Fold07: parameter=none 
## - Fold07: parameter=none 
## + Fold08: parameter=none 
## - Fold08: parameter=none 
## + Fold09: parameter=none 
## - Fold09: parameter=none 
## + Fold10: parameter=none 
## - Fold10: parameter=none 
## Aggregating results
## Fitting final model on full training set

# Print model to console
model2

## Generalized Linear Model 
## 
## 699 samples
##   9 predictor
##   2 classes: 'benign', 'malignant' 
## 
## Pre-processing: nearest neighbor imputation (9), centered (9), scaled (9) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 629, 629, 629, 629, 628, 629, ... 
## Resampling results:
## 
##   ROC       Sens       Spec     
##   0.991657  0.9716425  0.9296667

• Interestingly, this did not work quite as well as the median impute used on the same data set. hmmmm

– Compare KNN and median imputation

• There is a method to resample the models and see how they do if run many times but it works fast
• Interestingly in this case, we do see the median modle perform a little better than the knn_model on average but they are pretty much the same given the error bars here.

resamples <- resamples(x = list(median_model = model1, knn_model = model2))
dotplot(resamples, metric = "ROC")

Multiple preprocessing methods

• The preprocess argument can do a lot more, including chaining multiple steps
• median imputation -> center -> scale -> fit glm is a commonn ‘recipe’ for linear models (order matters)

Example - preprocessing mtcrs:

# Generate some data with missing values
data(mtcars)
set.seed(42)
mtcars[sample(1:nrow(mtcars), 10), "hp"] <- NA
Y <- mtcars$mpg
X <- mtcars[, 2:4]

# Use linear model "recipe"
set.seed(42)
model <- train(
  X,Y, method = "glm",
  preProcess = c("medianImpute", "center", "scale"))
print(min(model$results$RMSE))

## [1] 3.332758

# use pca also. just add it to the "recipe"
set.seed(42)
model <- train(
  X,Y, method = "glm",
  preProcess = c("medianImpute", "center", "scale", "pca"))
print(min(model$results$RMSE))

## [1] 3.25045

- using "spacialSign" project the data onto a sphere
- it is a good way to preprocess data with lots of outliers or high dimensionality

Preprocessing cheat sheet - always start with median imputation - also try knn imputation if data missing not at random - For linear models… - alwasy center and scale (you just get better results) - try pca and spatial sign. sometimes you will get better results - tree-based models and randome forest typically don’t need much preprocessing. - You can usually get away with just median imputation

– Combining preprocessing methods

• Full list of processing methods for preProcess:
  • “BoxCox”, “YeoJohnson”, “expoTrans”, “center”, “scale”, “range”, “knnImpute”, “bagImpute”, “medianImpute”, “pca”, “ica”, “spatialSign”, “corr”, “zv”, “nzv”, and “conditionalX”
• I have no idea what all these do but probably should! This seems important
• Centering and scaling (a.k.a standardization) is common
  • this is particularly useful for fitting regression models
  • You first center by subtracting the mean of each column from each value in that column,
  • then you scale by dividing by the standard deviation.
  • Standardization transforms your data such that for each column, the mean is 0 and the standard deviation is 1.
  • This makes it easier for regression models to find a good solution.

set.seed(42)
load('data/BreastCancer.RData')

# Fit glm with median imputation: model1
model1 <- train(
  x = breast_cancer_x, y = breast_cancer_y,
  method = "glm",
  trControl = myControl,
  preProcess = c('medianImpute')
)

## + Fold01: parameter=none 
## - Fold01: parameter=none 
## + Fold02: parameter=none 
## - Fold02: parameter=none 
## + Fold03: parameter=none 
## - Fold03: parameter=none 
## + Fold04: parameter=none 
## - Fold04: parameter=none 
## + Fold05: parameter=none 
## - Fold05: parameter=none 
## + Fold06: parameter=none 
## - Fold06: parameter=none 
## + Fold07: parameter=none 
## - Fold07: parameter=none 
## + Fold08: parameter=none 
## - Fold08: parameter=none 
## + Fold09: parameter=none 
## - Fold09: parameter=none 
## + Fold10: parameter=none 
## - Fold10: parameter=none 
## Aggregating results
## Fitting final model on full training set

# Print model1
model1

## Generalized Linear Model 
## 
## 699 samples
##   9 predictor
##   2 classes: 'benign', 'malignant' 
## 
## Pre-processing: median imputation (9) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 630, 629, 629, 629, 628, 629, ... 
## Resampling results:
## 
##   ROC        Sens       Spec     
##   0.9914915  0.9694203  0.9333333

# Fit glm with median imputation and standardization: model2
model2 <- train(
  x = breast_cancer_x, y = breast_cancer_y,
  method = "glm",
  trControl = myControl,
  preProcess = c('medianImpute', 'center', 'scale')
)

## + Fold01: parameter=none 
## - Fold01: parameter=none 
## + Fold02: parameter=none 
## - Fold02: parameter=none 
## + Fold03: parameter=none 
## - Fold03: parameter=none 
## + Fold04: parameter=none 
## - Fold04: parameter=none 
## + Fold05: parameter=none 
## - Fold05: parameter=none 
## + Fold06: parameter=none 
## - Fold06: parameter=none 
## + Fold07: parameter=none 
## - Fold07: parameter=none 
## + Fold08: parameter=none 
## - Fold08: parameter=none 
## + Fold09: parameter=none 
## - Fold09: parameter=none 
## + Fold10: parameter=none 
## - Fold10: parameter=none 
## Aggregating results
## Fitting final model on full training set

# Print model2
model2

## Generalized Linear Model 
## 
## 699 samples
##   9 predictor
##   2 classes: 'benign', 'malignant' 
## 
## Pre-processing: median imputation (9), centered (9), scaled (9) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 628, 630, 629, 629, 629, 630, ... 
## Resampling results:
## 
##   ROC        Sens       Spec     
##   0.9915487  0.9695652  0.9501667

• In this case it does not actually give better results
• I wonder if the breast cancer data set they put online is different than the one they use in the class
  • It seems to be the same. Is my seed just different or what?
  • This seems like something I should know about since its makeing the models quite different

Handling low-information predictors

• data is often pretty messy
• some variables don’t contain much info
  • constant (i.e. no variance)
  • nearly constant( i.e. low variance)
• with nearly constant data, its easy for one fold of CV to end up with constant column
  • this will cause problems as you can’t divide by 0 variance
  • they also don’t contain much info and tend to have little impact on the model
  • the instructor usually removes nearly contant columns from the data to reduce bugs, and speed up the modeling

Example: constan column in mtcars

• You can’t scale a column by dividing by a sd of 0, so everything breaks

# Reproduce dataset from last video
data(mtcars)
set.seed(42)
mtcars[sample(1:nrow(mtcars), 10), "hp"] <- NA
Y <- mtcars$mpg
X <- mtcars[, 2:4]

# Add a constant-values column to mtcars
X$bad <- 1

# Try to fit a model with pca + glm
model <- train(
  X,Y, method = "glm",
  preProcess = c("medianImpute", "center", "scale", "pca"))

## Something is wrong; all the RMSE metric values are missing:
##       RMSE        Rsquared        MAE     
##  Min.   : NA   Min.   : NA   Min.   : NA  
##  1st Qu.: NA   1st Qu.: NA   1st Qu.: NA  
##  Median : NA   Median : NA   Median : NA  
##  Mean   :NaN   Mean   :NaN   Mean   :NaN  
##  3rd Qu.: NA   3rd Qu.: NA   3rd Qu.: NA  
##  Max.   : NA   Max.   : NA   Max.   : NA  
##  NA's   :1     NA's   :1     NA's   :1

## Error: Stopping

• “zv” removes constant columns
• “nzv” removes nearly constant columns

# Have caret remove those columns during modeling
set.seed(42)

model <- train(
  X,Y, method = "glm",
  preProcess = c("zv", "medianImpute", "center", "scale","pca"))
min(model$results$RMSE)

## [1] 3.25045

– Remove near zero variance predictors

• nearZeroVar() takes in data x, then looks at the ratio of the most common value to the second most common value, freqCut,
• and the percentage of distinct values out of the number of total samples, uniqueCut.
• By default, caret uses freqCut = 19 and uniqueCut = 10, which is fairly conservative.
• the instructor likes to be a little more aggressive and use freqCut = 2 and uniqueCut = 20 when calling nearZeroVar().

load('data/BloodBrain.RData')
glimpse(bloodbrain_x)

## Observations: 208
## Variables: 132
## $ tpsa                 <dbl> 12.03, 49.33, 50.53, 37.39, 37.39, 37.39,...
## $ nbasic               <int> 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0,...
## $ vsa_hyd              <dbl> 167.06700, 92.64243, 295.16700, 319.11220...
## $ a_aro                <int> 0, 6, 15, 15, 12, 11, 6, 12, 12, 6, 9, 12...
## $ weight               <dbl> 156.293, 151.165, 366.485, 382.552, 326.4...
## $ peoe_vsa.0           <dbl> 76.947490, 38.243390, 58.054730, 62.23933...
## $ peoe_vsa.1           <dbl> 43.44619, 25.52006, 124.74020, 124.74020,...
## $ peoe_vsa.2           <dbl> 0.000000, 0.000000, 21.650840, 13.192320,...
## $ peoe_vsa.3           <dbl> 0.000000, 8.619013, 8.619013, 21.785640, ...
## $ peoe_vsa.4           <dbl> 0.00000, 23.27370, 17.44054, 0.00000, 0.0...
## $ peoe_vsa.5           <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 0...
## $ peoe_vsa.6           <dbl> 17.238030, 0.000000, 8.619013, 8.619013, ...
## $ peoe_vsa.0.1         <dbl> 18.74768, 49.01962, 83.82487, 83.82487, 8...
## $ peoe_vsa.1.1         <dbl> 43.50657, 0.00000, 49.01962, 68.78024, 36...
## $ peoe_vsa.2.1         <dbl> 0.00000, 0.00000, 0.00000, 0.00000, 0.000...
## $ peoe_vsa.3.1         <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 0...
## $ peoe_vsa.4.1         <dbl> 0.000000, 0.000000, 5.682576, 5.682576, 5...
## $ peoe_vsa.5.1         <dbl> 0.000000, 13.566920, 2.503756, 0.000000, ...
## $ peoe_vsa.6.1         <dbl> 0.000000, 7.904431, 2.640647, 2.640647, 2...
## $ a_acc                <int> 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 1, 2, 3,...
## $ a_acid               <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ a_base               <int> 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 0, 0,...
## $ vsa_acc              <dbl> 0.000000, 13.566920, 8.186332, 8.186332, ...
## $ vsa_acid             <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ vsa_base             <dbl> 5.682576, 0.000000, 0.000000, 0.000000, 0...
## $ vsa_don              <dbl> 5.682576, 5.682576, 5.682576, 5.682576, 5...
## $ vsa_other            <dbl> 0.000000, 28.107600, 43.560890, 28.324700...
## $ vsa_pol              <dbl> 0.00000, 13.56692, 0.00000, 0.00000, 0.00...
## $ slogp_vsa0           <dbl> 18.010750, 25.385230, 14.124200, 14.12420...
## $ slogp_vsa1           <dbl> 0.000000, 23.269540, 34.796280, 34.796280...
## $ slogp_vsa2           <dbl> 3.981969, 23.862220, 0.000000, 0.000000, ...
## $ slogp_vsa3           <dbl> 0.00000, 0.00000, 76.24500, 76.24500, 76....
## $ slogp_vsa4           <dbl> 4.410796, 0.000000, 3.185575, 3.185575, 3...
## $ slogp_vsa5           <dbl> 32.897190, 0.000000, 9.507346, 0.000000, ...
## $ slogp_vsa6           <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 0...
## $ slogp_vsa7           <dbl> 0.00000, 70.57274, 148.12580, 144.03540, ...
## $ slogp_vsa8           <dbl> 113.210400, 0.000000, 75.473630, 75.47363...
## $ slogp_vsa9           <dbl> 33.326020, 41.326190, 28.274170, 55.46144...
## $ smr_vsa0             <dbl> 0.000000, 23.862220, 12.631660, 3.124314,...
## $ smr_vsa1             <dbl> 18.01075, 25.38523, 27.78542, 27.78542, 2...
## $ smr_vsa2             <dbl> 4.410796, 0.000000, 0.000000, 0.000000, 0...
## $ smr_vsa3             <dbl> 3.981969, 5.243428, 8.429003, 8.429003, 8...
## $ smr_vsa4             <dbl> 0.000000, 20.767500, 29.582260, 21.401420...
## $ smr_vsa5             <dbl> 113.21040, 70.57274, 235.05870, 235.05870...
## $ smr_vsa6             <dbl> 0.000000, 5.258784, 76.245000, 76.245000,...
## $ smr_vsa7             <dbl> 66.22321, 33.32602, 0.00000, 31.27769, 0....
## $ tpsa.1               <dbl> 16.61, 49.33, 51.73, 38.59, 38.59, 38.59,...
## $ logp.o.w.            <dbl> 2.94800, 0.88900, 4.43900, 5.25400, 3.800...
## $ frac.anion7.         <dbl> 0.000, 0.001, 0.000, 0.000, 0.000, 0.000,...
## $ frac.cation7.        <dbl> 0.999, 0.000, 0.986, 0.986, 0.986, 0.986,...
## $ andrewbind           <dbl> 3.4, -3.3, 12.8, 12.8, 10.3, 10.0, 10.4, ...
## $ rotatablebonds       <int> 3, 2, 8, 8, 8, 8, 8, 7, 4, 5, 4, 7, 1, 3,...
## $ mlogp                <dbl> 2.50245, 1.05973, 4.66091, 3.82458, 3.272...
## $ clogp                <dbl> 2.970000, 0.494000, 5.136999, 5.877599, 4...
## $ mw                   <dbl> 155.2856, 151.1664, 365.4794, 381.5440, 3...
## $ nocount              <int> 1, 3, 5, 4, 4, 4, 4, 3, 2, 4, 6, 4, 3, 6,...
## $ hbdnr                <int> 1, 2, 1, 1, 1, 1, 2, 1, 1, 0, 0, 0, 1, 3,...
## $ rule.of.5violations  <int> 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,...
## $ prx                  <int> 0, 1, 6, 2, 2, 2, 1, 0, 0, 4, 5, 0, 1, 12...
## $ ub                   <dbl> 0.0, 3.0, 5.3, 5.3, 4.2, 3.6, 3.0, 4.7, 4...
## $ pol                  <int> 0, 2, 3, 3, 2, 2, 2, 3, 4, 1, 2, 4, 4, 2,...
## $ inthb                <int> 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,...
## $ adistm               <dbl> 0.0000, 395.3757, 1364.5514, 702.6387, 74...
## $ adistd               <dbl> 0.0000, 10.8921, 25.6784, 10.0232, 10.575...
## $ polar_area           <dbl> 21.1242, 117.4081, 82.0943, 65.0890, 66.1...
## $ nonpolar_area        <dbl> 379.0702, 247.5371, 637.7242, 667.9713, 6...
## $ psa_npsa             <dbl> 0.0557, 0.4743, 0.1287, 0.0974, 0.1100, 0...
## $ tcsa                 <dbl> 0.0097, 0.0134, 0.0111, 0.0108, 0.0118, 0...
## $ tcpa                 <dbl> 0.1842, 0.0417, 0.0972, 0.1218, 0.1186, 0...
## $ tcnp                 <dbl> 0.0103, 0.0198, 0.0125, 0.0119, 0.0130, 0...
## $ ovality              <dbl> 1.0960, 1.1173, 1.3005, 1.3013, 1.2711, 1...
## $ surface_area         <dbl> 400.1944, 364.9453, 719.8185, 733.0603, 6...
## $ volume               <dbl> 656.0650, 555.0969, 1224.4553, 1257.2002,...
## $ most_negative_charge <dbl> -0.6174, -0.8397, -0.8012, -0.7608, -0.85...
## $ most_positive_charge <dbl> 0.3068, 0.4967, 0.5414, 0.4800, 0.4547, 0...
## $ sum_absolute_charge  <dbl> 3.8918, 4.8925, 7.9796, 7.9308, 7.8516, 7...
## $ dipole_moment        <dbl> 1.1898, 4.2109, 3.5234, 3.1463, 3.2676, 3...
## $ homo                 <dbl> -9.6672, -8.9618, -8.6271, -8.5592, -8.67...
## $ lumo                 <dbl> 3.4038, 0.1942, 0.0589, -0.2651, 0.3149, ...
## $ hardness             <dbl> 6.5355, 4.5780, 4.3430, 4.1471, 4.4940, 4...
## $ ppsa1                <dbl> 349.1390, 223.1310, 517.8218, 507.6144, 5...
## $ ppsa2                <dbl> 679.3832, 545.8328, 2066.0186, 2012.9060,...
## $ ppsa3                <dbl> 30.9705, 42.3030, 63.9503, 61.6890, 61.56...
## $ pnsa1                <dbl> 51.0554, 141.8143, 201.9967, 225.4459, 15...
## $ pnsa2                <dbl> -99.3477, -346.9123, -805.9311, -893.9880...
## $ pnsa3                <dbl> -10.4876, -44.0368, -43.7587, -42.0328, -...
## $ fpsa1                <dbl> 0.8724, 0.6114, 0.7194, 0.6925, 0.7623, 0...
## $ fpsa2                <dbl> 1.6976, 1.4957, 2.8702, 2.7459, 2.9927, 2...
## $ fpsa3                <dbl> 0.0774, 0.1159, 0.0888, 0.0842, 0.0922, 0...
## $ fnsa1                <dbl> 0.1276, 0.3886, 0.2806, 0.3075, 0.2377, 0...
## $ fnsa2                <dbl> -0.2482, -0.9506, -1.1196, -1.2195, -0.93...
## $ fnsa3                <dbl> -0.0262, -0.1207, -0.0608, -0.0573, -0.05...
## $ wpsa1                <dbl> 139.7235, 81.4306, 372.7377, 372.1120, 34...
## $ wpsa2                <dbl> 271.8854, 199.1991, 1487.1583, 1475.5815,...
## $ wpsa3                <dbl> 12.3942, 15.4383, 46.0326, 45.2218, 41.12...
## $ wnsa1                <dbl> 20.4321, 51.7544, 145.4010, 165.2654, 106...
## $ wnsa2                <dbl> -39.7584, -126.6040, -580.1241, -655.3471...
## $ wnsa3                <dbl> -4.1971, -16.0710, -31.4983, -30.8126, -2...
## $ dpsa1                <dbl> 298.0836, 81.3167, 315.8251, 282.1685, 35...
## $ dpsa2                <dbl> 778.7310, 892.7451, 2871.9497, 2906.8940,...
## $ dpsa3                <dbl> 41.4580, 86.3398, 107.7089, 103.7218, 101...
## $ rpcg                 <dbl> 0.1577, 0.2030, 0.1357, 0.1210, 0.1158, 0...
## $ rncg                 <dbl> 0.3173, 0.3433, 0.2008, 0.1919, 0.2182, 0...
## $ wpcs                 <dbl> 2.3805, 1.3116, 1.1351, 0.7623, 0.7884, 2...
## $ wncs                 <dbl> 1.9117, 2.2546, 1.5725, 1.5302, 1.6795, 1...
## $ sadh1                <dbl> 15.0988, 45.2163, 16.7192, 17.2491, 16.02...
## $ sadh2                <dbl> 15.0988, 22.6082, 16.7192, 17.2491, 16.02...
## $ sadh3                <dbl> 0.0377, 0.1239, 0.0232, 0.0235, 0.0240, 0...
## $ chdh1                <dbl> 0.3068, 0.7960, 0.4550, 0.4354, 0.4366, 0...
## $ chdh2                <dbl> 0.3068, 0.3980, 0.4550, 0.4354, 0.4366, 0...
## $ chdh3                <dbl> 0.0008, 0.0022, 0.0006, 0.0006, 0.0007, 0...
## $ scdh1                <dbl> 4.6321, 17.6195, 7.6077, 7.5102, 6.9970, ...
## $ scdh2                <dbl> 4.6321, 8.8098, 7.6077, 7.5102, 6.9970, 7...
## $ scdh3                <dbl> 0.0116, 0.0483, 0.0106, 0.0102, 0.0105, 0...
## $ saaa1                <dbl> 6.0255, 65.6236, 57.5440, 39.8638, 42.454...
## $ saaa2                <dbl> 6.0255, 32.8118, 14.3860, 13.2879, 14.151...
## $ saaa3                <dbl> 0.0151, 0.1798, 0.0799, 0.0544, 0.0636, 0...
## $ chaa1                <dbl> -0.6174, -0.8371, -1.3671, -1.2332, -1.14...
## $ chaa2                <dbl> -0.6174, -0.4185, -0.3418, -0.4111, -0.38...
## $ chaa3                <dbl> -0.0015, -0.0023, -0.0019, -0.0017, -0.00...
## $ scaa1                <dbl> -3.7199, -27.5143, -21.7898, -17.5957, -1...
## $ scaa2                <dbl> -3.7199, -13.7571, -5.4475, -5.8652, -5.6...
## $ scaa3                <dbl> -0.0093, -0.0754, -0.0303, -0.0240, -0.02...
## $ ctdh                 <int> 1, 2, 1, 1, 1, 1, 2, 1, 1, 0, 0, 0, 1, 3,...
## $ ctaa                 <int> 1, 2, 4, 3, 3, 3, 3, 3, 1, 3, 5, 3, 2, 3,...
## $ mchg                 <dbl> 0.9241, 1.2685, 1.2562, 1.1962, 1.2934, 1...
## $ achg                 <dbl> 0.9241, 1.0420, 1.2562, 1.1962, 1.2934, 1...
## $ rdta                 <dbl> 1.0000, 1.0000, 0.2500, 0.3333, 0.3333, 0...
## $ n_sp2                <dbl> 0.0000, 0.0000, 26.9733, 21.7065, 24.2061...
## $ n_sp3                <dbl> 6.0255, 6.5681, 10.8567, 11.0017, 10.8109...
## $ o_sp2                <dbl> 0.0000, 32.0102, 0.0000, 0.0000, 0.0000, ...
## $ o_sp3                <dbl> 0.0000, 33.6135, 27.5451, 15.1316, 15.133...

glimpse(bloodbrain_y)

##  num [1:208] 1.08 -0.4 0.22 0.14 0.69 0.44 -0.43 1.38 0.75 0.88 ...

# Identify near zero variance predictors: remove_cols
remove_cols <- nearZeroVar(bloodbrain_x, names = TRUE, 
                           freqCut = 2, uniqueCut = 20)

# Get all column names from bloodbrain_x: all_cols
all_cols <- names(bloodbrain_x)

# Remove from data: bloodbrain_x_small
bloodbrain_x_small <- bloodbrain_x[ , setdiff(all_cols, remove_cols)]

– Fit model on reduced blood-brain data

# Fit model on reduced data: model
model <- train(x = bloodbrain_x_small, y = bloodbrain_y, method = "glm")

# Print model to console
model

## Generalized Linear Model 
## 
## 208 samples
## 112 predictors
## 
## No pre-processing
## Resampling: Bootstrapped (25 reps) 
## Summary of sample sizes: 208, 208, 208, 208, 208, 208, ... 
## Resampling results:
## 
##   RMSE      Rsquared   MAE     
##   1.737597  0.1226598  1.136949

Principle components analysis (PCA)

• PCA combines the low-variance and correlated variables in your data set into a single set of high-variance, perpendicular predictors.
  • low variance are probamatic for CV but they can contain useful information
  • its always better to find a systematic way to use that information rather than throw it away
  • perpendicular predictors are useful because they are perfectly uncorrelated
  • linear model tend to have trouble with correlation between variables (also known as colinearity) and pca elegantly removes this issue
• PCA searches for high-variance linear combinations of the input data that are perpendicular to each other
  • the first component of pca is the highest variance component
  • the second component has the second highest variance and so on
  • given an x and y variable that are correlated, the first component reflects the similarity between x and y, while the second component reflects the difference
  • this idea makes sense in two dimension, but it extens to multiple dimension

Example: blood-brain data

# Basic model
set.seed(42)
data(BloodBrain)

model <- train(
  bbbDescr, logBBB, method = "glm"
)
model

## Generalized Linear Model 
## 
## 208 samples
## 134 predictors
## 
## No pre-processing
## Resampling: Bootstrapped (25 reps) 
## Summary of sample sizes: 208, 208, 208, 208, 208, 208, ... 
## Resampling results:
## 
##   RMSE      Rsquared    MAE     
##   6.523485  0.05478762  4.021009

# Adding preprocesing steps including "zv"
model2 <- train(
  bbbDescr, logBBB, method = "glm",
  trControl = trainControl(method = "cv", number = 10, verbose = F),
  preProcess = c("zv", "center", "scale")
)
model2

## Generalized Linear Model 
## 
## 208 samples
## 134 predictors
## 
## Pre-processing: centered (134), scaled (134) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 187, 187, 187, 188, 187, 186, ... 
## Resampling results:
## 
##   RMSE      Rsquared   MAE      
##   1.069966  0.2257437  0.7691277

# change "zv" to "nzv"
model3 <- train(
  bbbDescr, logBBB, method = "glm",
  trControl = trainControl(method = "cv", number = 10, verbose = F),
  preProcess = c("nzv", "center", "scale")
)
model3

## Generalized Linear Model 
## 
## 208 samples
## 134 predictors
## 
## Pre-processing: centered (127), scaled (127), remove (7) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 188, 188, 186, 188, 188, 187, ... 
## Resampling results:
## 
##   RMSE      Rsquared   MAE     
##   1.085857  0.2134409  0.748278

# now keep the low variance predictors in the model but use pca
model4 <- train(
  bbbDescr, logBBB, method = "glm",
  trControl = trainControl(method = "cv", number = 10, verbose = F),
  preProcess = c("zv", "center", "scale", "pca")
)
model4

## Generalized Linear Model 
## 
## 208 samples
## 134 predictors
## 
## Pre-processing: centered (134), scaled (134), principal component
##  signal extraction (134) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 188, 187, 187, 188, 186, 187, ... 
## Resampling results:
## 
##   RMSE       Rsquared   MAE      
##   0.5627461  0.5152928  0.4224397

• keeping the low variance predictors and using pca gives, by far, the best results

– Using PCA as an alternative to nearZeroVar()

• its often better to use pca with low variance predictors
• sometimes multiple low variance preditors end up combining into one high variance PCA variable which has a good impact on the model
• this is a good trick for linear models especially
• apparently using “pca” as a preprocess will also center and scale your model

# Fit glm model using PCA: model
model <- train(
  x = bloodbrain_x, y = bloodbrain_y,
  method = "glm", preProcess = c("pca")
)

# Print model to console
model

## Generalized Linear Model 
## 
## 208 samples
## 132 predictors
## 
## Pre-processing: principal component signal extraction (132),
##  centered (132), scaled (132) 
## Resampling: Bootstrapped (25 reps) 
## Summary of sample sizes: 208, 208, 208, 208, 208, 208, ... 
## Resampling results:
## 
##   RMSE       Rsquared   MAE      
##   0.6015217  0.4534377  0.4511828

• This is a lot better results than the previous bloodbrain model where we used nearZeroVar() first to remove data.

   

---

Selecting models: a case study in churn prediction

---

Reusing a trainControl

• Lets use a raelistic dataset now, customer churn at a telecom company
• In order to do an apples to apples comparison between models, we need to ensure that each model using the exact same folds for training/test splits.
• We can do this by prespecifying a trainControl object which specifies which rows you use for model building and which are used as holdouts
  • This object can be used across multiple models

Example: customer churn data

• We make train/test set CV indicies using caret’s createFolds function
• Notice that it conserves the class distribution of 14% churn

library(C50)
data(churn)
table(churnTrain$churn) / nrow(churnTrain)

## 
##       yes        no 
## 0.1449145 0.8550855

# Create train/test indexes
set.seed(42)
myFolds <- createFolds(churnTrain$churn, k = 5)

# Compare class distribution
i <- myFolds$Fold1
table(churnTrain$churn[i]) / length(i)

## 
##       yes        no 
## 0.1441441 0.8558559

• We use these fold to create a trainControl object which we can then use to create multiple models
• notice the the myControl object has information about the training as well as the fold indices.
• This lets us compare models farily

myControl <- trainControl(
  summaryFunction = twoClassSummary, 
  classProbs = T,
  verboseIter = T,
  savePredictions = T,
  index = myFolds
)

myControl

## $method
## [1] "boot"
## 
## $number
## [1] 25
## 
## $repeats
## [1] NA
## 
## $search
## [1] "grid"
## 
## $p
## [1] 0.75
## 
## $initialWindow
## NULL
## 
## $horizon
## [1] 1
## 
## $fixedWindow
## [1] TRUE
## 
## $skip
## [1] 0
## 
## $verboseIter
## [1] TRUE
## 
## $returnData
## [1] TRUE
## 
## $returnResamp
## [1] "final"
## 
## $savePredictions
## [1] TRUE
## 
## $classProbs
## [1] TRUE
## 
## $summaryFunction
## function (data, lev = NULL, model = NULL) 
## {
##     lvls <- levels(data$obs)
##     if (length(lvls) > 2) 
##         stop(paste("Your outcome has", length(lvls), "levels. The twoClassSummary() function isn't appropriate."))
##     requireNamespaceQuietStop("ModelMetrics")
##     if (!all(levels(data[, "pred"]) == lvls)) 
##         stop("levels of observed and predicted data do not match")
##     data$y = as.numeric(data$obs == lvls[2])
##     rocAUC <- ModelMetrics::auc(ifelse(data$obs == lev[2], 0, 
##         1), data[, lvls[1]])
##     out <- c(rocAUC, sensitivity(data[, "pred"], data[, "obs"], 
##         lev[1]), specificity(data[, "pred"], data[, "obs"], lev[2]))
##     names(out) <- c("ROC", "Sens", "Spec")
##     out
## }
## <environment: namespace:caret>
## 
## $selectionFunction
## [1] "best"
## 
## $preProcOptions
## $preProcOptions$thresh
## [1] 0.95
## 
## $preProcOptions$ICAcomp
## [1] 3
## 
## $preProcOptions$k
## [1] 5
## 
## $preProcOptions$freqCut
## [1] 19
## 
## $preProcOptions$uniqueCut
## [1] 10
## 
## $preProcOptions$cutoff
## [1] 0.9
## 
## 
## $sampling
## NULL
## 
## $index
## $index$Fold1
##   [1]   21   34   35   38   41   48   49   56   60   68   70   76   83   85
##  [15]   94  102  104  109  110  116  122  126  136  143  151  154  157  163
##  [29]  169  170  179  183  184  186  192  195  200  203  209  213  215  217
##  [43]  227  229  231  232  238  240  241  243  246  250  252  257  261  268
##  [57]  274  281  282  288  291  301  314  317  323  328  333  335  336  365
##  [71]  372  384  398  406  421  423  429  436  440  441  442  443  452  462
##  [85]  463  466  469  471  473  478  480  482  483  485  487  491  493  494
##  [99]  495  496  499  509  515  520  527  529  530  536  548  551  557  581
## [113]  583  588  589  590  599  601  606  610  611  612  614  620  621  624
## [127]  634  636  644  645  650  651  652  653  654  657  662  664  668  671
## [141]  673  682  685  697  701  703  710  716  736  738  741  745  747  750
## [155]  754  755  758  762  764  769  772  775  779  784  794  796  803  805
## [169]  806  807  808  811  821  828  831  834  850  851  854  860  864  866
## [183]  874  877  878  883  885  887  898  904  905  907  909  910  920  931
## [197]  945  954  958  987  992  995  999 1000 1004 1015 1018 1024 1025 1028
## [211] 1031 1038 1041 1042 1059 1062 1067 1087 1104 1112 1116 1123 1125 1127
## [225] 1129 1132 1157 1170 1178 1179 1184 1185 1187 1188 1198 1200 1204 1215
## [239] 1227 1228 1232 1235 1237 1240 1262 1265 1266 1269 1282 1283 1290 1303
## [253] 1307 1309 1312 1317 1319 1320 1322 1323 1324 1331 1341 1365 1368 1370
## [267] 1373 1377 1378 1383 1388 1392 1394 1396 1401 1416 1420 1428 1433 1441
## [281] 1444 1447 1451 1453 1456 1462 1466 1473 1483 1484 1489 1498 1500 1508
## [295] 1511 1515 1519 1523 1530 1539 1543 1545 1553 1569 1577 1578 1580 1583
## [309] 1585 1587 1596 1603 1606 1607 1610 1636 1638 1643 1644 1648 1650 1652
## [323] 1662 1665 1667 1669 1673 1689 1692 1705 1707 1723 1726 1729 1733 1735
## [337] 1739 1743 1750 1752 1756 1758 1761 1767 1773 1774 1775 1777 1778 1782
## [351] 1785 1792 1794 1808 1809 1822 1825 1829 1833 1836 1839 1842 1844 1862
## [365] 1867 1868 1870 1882 1883 1890 1894 1895 1898 1906 1920 1931 1935 1939
## [379] 1943 1944 1945 1947 1948 1950 1964 1970 1974 1978 1984 1988 1989 1991
## [393] 1996 2001 2006 2014 2018 2027 2031 2032 2034 2037 2043 2044 2048 2053
## [407] 2055 2056 2059 2060 2065 2079 2080 2095 2105 2110 2113 2126 2137 2139
## [421] 2146 2151 2158 2160 2173 2175 2177 2178 2182 2196 2204 2206 2207 2217
## [435] 2218 2224 2225 2245 2248 2253 2260 2261 2262 2265 2267 2271 2277 2285
## [449] 2291 2294 2300 2309 2317 2318 2319 2330 2341 2342 2348 2349 2352 2356
## [463] 2362 2369 2371 2372 2373 2379 2383 2384 2385 2399 2405 2407 2409 2410
## [477] 2427 2431 2435 2447 2451 2462 2470 2473 2475 2476 2481 2485 2487 2491
## [491] 2494 2495 2497 2504 2507 2509 2510 2527 2534 2535 2537 2540 2541 2543
## [505] 2546 2551 2553 2556 2569 2575 2576 2583 2598 2599 2611 2613 2621 2638
## [519] 2644 2645 2658 2660 2685 2690 2691 2697 2698 2699 2715 2718 2719 2725
## [533] 2726 2727 2728 2735 2737 2741 2742 2743 2744 2747 2748 2765 2772 2773
## [547] 2774 2788 2792 2803 2805 2811 2817 2819 2821 2828 2835 2840 2862 2865
## [561] 2866 2868 2870 2878 2888 2914 2916 2926 2927 2934 2935 2939 2944 2945
## [575] 2960 2963 2964 2967 2980 2994 2997 3001 3010 3012 3014 3015 3017 3018
## [589] 3020 3023 3026 3033 3034 3038 3040 3041 3045 3051 3053 3055 3057 3061
## [603] 3069 3084 3091 3098 3100 3112 3115 3119 3123 3128 3133 3137 3139 3142
## [617] 3151 3160 3166 3177 3179 3181 3182 3184 3193 3195 3197 3198 3203 3205
## [631] 3206 3207 3211 3218 3223 3224 3229 3232 3235 3237 3240 3257 3261 3266
## [645] 3269 3273 3278 3279 3281 3282 3283 3292 3294 3301 3302 3304 3307 3309
## [659] 3311 3314 3315 3319 3323 3329 3331 3333
## 
## $index$Fold2
##   [1]    5    6   13   17   23   26   27   30   31   32   36   39   42   46
##  [15]   51   52   71   84   86   89   91   93   96   99  101  106  112  118
##  [29]  121  129  131  133  147  148  150  152  155  156  166  176  180  182
##  [43]  193  202  207  210  212  219  223  224  225  239  242  255  259  262
##  [57]  263  266  267  269  271  275  279  285  293  298  306  311  313  319
##  [71]  324  326  330  338  345  350  352  360  362  363  369  376  377  381
##  [85]  391  393  397  399  405  407  410  411  412  415  418  431  438  439
##  [99]  444  446  447  450  455  457  461  475  498  501  512  526  528  539
## [113]  552  555  559  574  575  577  600  602  603  609  616  619  631  637
## [127]  641  648  656  666  672  675  678  684  690  705  708  712  713  715
## [141]  717  727  730  733  739  748  752  760  763  770  773  782  793  797
## [155]  798  799  802  812  814  816  818  820  822  827  830  833  837  838
## [169]  839  841  842  845  858  859  861  873  886  890  892  893  902  906
## [183]  915  926  943  947  951  963  964  965  970  980  982  986  991  996
## [197] 1001 1013 1014 1020 1032 1035 1050 1051 1052 1071 1081 1089 1091 1093
## [211] 1097 1099 1100 1108 1113 1114 1121 1122 1130 1133 1137 1140 1144 1146
## [225] 1148 1149 1150 1152 1153 1158 1161 1162 1164 1165 1171 1173 1194 1195
## [239] 1203 1207 1208 1212 1214 1217 1221 1224 1225 1229 1231 1242 1245 1246
## [253] 1249 1250 1256 1274 1277 1278 1281 1288 1289 1293 1294 1299 1301 1305
## [267] 1316 1318 1326 1327 1328 1329 1336 1337 1339 1345 1351 1354 1356 1357
## [281] 1367 1369 1376 1398 1399 1403 1405 1407 1409 1413 1414 1423 1429 1431
## [295] 1438 1440 1457 1458 1468 1469 1479 1481 1486 1496 1504 1507 1510 1514
## [309] 1520 1528 1538 1542 1544 1559 1561 1564 1566 1572 1573 1576 1582 1586
## [323] 1592 1593 1597 1611 1613 1633 1646 1657 1658 1661 1674 1675 1676 1677
## [337] 1680 1681 1684 1697 1700 1706 1708 1709 1712 1714 1715 1716 1717 1718
## [351] 1720 1730 1747 1753 1754 1755 1762 1765 1776 1783 1787 1789 1791 1797
## [365] 1798 1812 1813 1815 1823 1834 1835 1846 1848 1849 1853 1856 1861 1863
## [379] 1864 1865 1878 1879 1884 1889 1904 1914 1917 1918 1923 1926 1928 1930
## [393] 1941 1942 1946 1955 1958 1960 1962 1968 1971 1975 1995 1997 1998 1999
## [407] 2003 2010 2022 2028 2035 2036 2045 2050 2061 2067 2071 2072 2073 2078
## [421] 2081 2083 2085 2086 2087 2088 2090 2099 2109 2114 2117 2125 2130 2134
## [435] 2135 2143 2145 2154 2156 2162 2166 2168 2179 2180 2190 2198 2200 2208
## [449] 2223 2231 2232 2233 2234 2239 2243 2244 2246 2249 2254 2256 2264 2266
## [463] 2273 2279 2281 2286 2288 2296 2316 2320 2322 2323 2326 2327 2328 2331
## [477] 2335 2337 2338 2340 2343 2344 2354 2361 2368 2381 2395 2400 2413 2418
## [491] 2422 2426 2440 2444 2445 2452 2453 2454 2461 2466 2469 2478 2482 2489
## [505] 2490 2493 2500 2501 2506 2508 2518 2519 2523 2536 2539 2549 2557 2559
## [519] 2564 2574 2578 2585 2595 2596 2604 2622 2623 2626 2627 2629 2633 2636
## [533] 2640 2647 2648 2649 2656 2663 2667 2671 2672 2676 2678 2681 2687 2692
## [547] 2694 2695 2700 2704 2716 2731 2734 2738 2750 2755 2759 2764 2766 2771
## [561] 2780 2782 2784 2786 2787 2804 2806 2808 2810 2829 2834 2843 2853 2863
## [575] 2871 2876 2896 2905 2910 2915 2925 2930 2941 2946 2948 2949 2951 2957
## [589] 2958 2971 2979 2981 2982 2989 2993 3005 3008 3009 3016 3024 3025 3029
## [603] 3030 3037 3039 3042 3044 3047 3048 3054 3062 3063 3066 3071 3074 3075
## [617] 3076 3077 3078 3080 3082 3087 3089 3096 3103 3113 3114 3125 3129 3130
## [631] 3135 3136 3143 3145 3147 3148 3152 3158 3163 3169 3173 3180 3183 3191
## [645] 3194 3196 3212 3226 3227 3228 3231 3234 3236 3239 3250 3255 3263 3264
## [659] 3276 3291 3295 3299 3300 3305 3321 3327 3330
## 
## $index$Fold3
##   [1]    1    8    9   14   19   20   22   25   28   29   50   64   65   72
##  [15]   74   75   77   87   92   97  107  108  111  113  114  115  117  120
##  [29]  124  125  127  134  139  140  153  164  165  174  187  189  190  191
##  [43]  198  199  205  208  214  218  221  222  226  233  234  244  256  280
##  [57]  292  294  302  303  318  322  327  331  337  346  354  361  364  367
##  [71]  370  373  375  379  385  389  390  395  396  400  401  404  408  414
##  [85]  416  422  424  426  435  464  472  474  481  484  488  490  502  503
##  [99]  504  507  508  525  543  544  549  550  560  561  563  567  568  570
## [113]  571  572  576  578  580  582  594  595  596  604  618  623  629  630
## [127]  635  639  642  643  647  658  663  669  680  688  689  693  694  696
## [141]  698  699  700  702  709  711  714  721  723  725  744  753  756  761
## [155]  774  780  787  790  804  809  823  825  832  835  846  857  865  879
## [169]  880  888  891  896  899  901  912  914  925  928  932  937  939  946
## [183]  949  961  962  966  968  969  973  974  975  981  984  988  990 1003
## [197] 1005 1006 1012 1019 1022 1026 1029 1030 1033 1034 1040 1045 1046 1047
## [211] 1053 1054 1060 1061 1063 1065 1068 1069 1072 1073 1075 1076 1082 1090
## [225] 1095 1098 1107 1117 1120 1131 1143 1147 1160 1167 1168 1169 1176 1177
## [239] 1182 1189 1191 1193 1196 1206 1209 1213 1216 1218 1230 1238 1247 1248
## [253] 1251 1253 1258 1261 1263 1267 1271 1279 1285 1291 1296 1297 1298 1300
## [267] 1302 1308 1310 1315 1321 1330 1346 1355 1358 1364 1366 1371 1379 1381
## [281] 1382 1386 1391 1397 1408 1417 1418 1422 1425 1426 1434 1435 1442 1449
## [295] 1461 1472 1474 1475 1476 1477 1478 1487 1488 1494 1495 1502 1505 1506
## [309] 1518 1521 1524 1525 1546 1548 1549 1550 1554 1556 1557 1560 1568 1570
## [323] 1588 1589 1594 1595 1598 1599 1600 1602 1609 1621 1623 1624 1627 1628
## [337] 1639 1651 1653 1654 1659 1663 1670 1695 1696 1698 1701 1702 1703 1704
## [351] 1713 1736 1737 1740 1745 1746 1768 1771 1772 1779 1784 1786 1799 1802
## [365] 1806 1810 1811 1816 1818 1820 1821 1831 1838 1843 1845 1847 1851 1859
## [379] 1873 1875 1885 1886 1896 1900 1901 1902 1909 1910 1911 1912 1913 1916
## [393] 1919 1925 1932 1933 1934 1940 1949 1957 1961 1976 1977 1980 1994 2000
## [407] 2002 2008 2012 2015 2024 2029 2033 2042 2049 2058 2062 2070 2082 2084
## [421] 2091 2094 2104 2106 2116 2118 2131 2132 2138 2141 2153 2159 2161 2163
## [435] 2164 2170 2171 2174 2183 2191 2192 2193 2194 2215 2219 2222 2228 2235
## [449] 2236 2247 2251 2257 2258 2270 2272 2274 2276 2280 2282 2284 2292 2293
## [463] 2299 2304 2305 2307 2311 2332 2333 2346 2357 2358 2360 2364 2365 2375
## [477] 2376 2382 2389 2391 2392 2396 2398 2403 2411 2412 2415 2436 2437 2438
## [491] 2439 2441 2457 2458 2464 2465 2474 2477 2483 2488 2492 2496 2499 2512
## [505] 2513 2515 2520 2522 2529 2530 2533 2547 2548 2550 2554 2555 2561 2562
## [519] 2567 2571 2573 2581 2586 2587 2590 2593 2594 2600 2601 2602 2605 2608
## [533] 2609 2610 2612 2618 2620 2624 2634 2639 2641 2643 2652 2653 2657 2662
## [547] 2669 2673 2674 2686 2711 2713 2720 2723 2724 2733 2736 2739 2745 2746
## [561] 2752 2753 2757 2789 2790 2791 2798 2801 2816 2818 2830 2831 2833 2836
## [575] 2837 2856 2857 2869 2872 2874 2880 2881 2886 2893 2897 2909 2929 2932
## [589] 2933 2937 2943 2959 2962 2974 2978 2984 2988 2991 2995 2998 2999 3002
## [603] 3006 3013 3021 3027 3031 3032 3049 3064 3068 3070 3083 3092 3093 3097
## [617] 3101 3104 3106 3107 3109 3110 3118 3124 3126 3127 3134 3140 3149 3153
## [631] 3155 3159 3162 3164 3171 3176 3185 3189 3190 3192 3202 3214 3215 3216
## [645] 3220 3221 3225 3233 3238 3241 3242 3244 3245 3248 3251 3254 3259 3277
## [659] 3288 3289 3306 3308 3312 3313 3318 3326 3328
## 
## $index$Fold4
##   [1]   10   16   24   33   37   54   55   57   59   63   66   67   73   80
##  [15]   81   88   98  103  105  119  123  132  137  138  141  142  145  146
##  [29]  149  161  162  171  172  177  181  194  196  197  201  204  211  228
##  [43]  245  249  253  254  258  260  264  270  272  273  289  296  297  304
##  [57]  307  310  312  315  320  321  325  329  332  339  341  343  347  348
##  [71]  349  353  356  357  359  371  374  382  383  388  392  394  427  430
##  [85]  432  433  434  437  445  448  449  451  454  467  477  492  510  514
##  [99]  516  517  519  523  535  537  542  545  546  554  556  558  566  573
## [113]  579  584  587  591  592  597  598  605  608  615  617  622  625  626
## [127]  628  632  646  649  655  667  674  677  681  686  692  695  704  707
## [141]  718  722  724  726  728  732  735  737  740  759  765  766  776  777
## [155]  785  801  810  813  815  817  824  840  844  849  853  856  863  868
## [169]  872  875  876  882  884  889  897  900  908  911  913  919  921  922
## [183]  927  929  933  934  938  941  942  950  952  955  957  959  971  976
## [197]  977  983  985  993  994  997  998 1008 1010 1011 1016 1017 1027 1043
## [211] 1044 1048 1055 1057 1058 1066 1074 1077 1079 1080 1083 1084 1086 1092
## [225] 1094 1102 1106 1110 1111 1119 1124 1126 1128 1134 1138 1142 1156 1159
## [239] 1163 1172 1183 1186 1190 1192 1199 1205 1210 1211 1219 1223 1226 1233
## [253] 1234 1244 1254 1255 1259 1268 1276 1280 1284 1286 1287 1292 1314 1325
## [267] 1332 1334 1335 1342 1343 1347 1350 1352 1353 1359 1362 1363 1372 1374
## [281] 1380 1390 1395 1402 1404 1411 1421 1427 1430 1432 1436 1437 1443 1448
## [295] 1450 1452 1455 1465 1467 1470 1471 1491 1492 1497 1503 1509 1513 1516
## [309] 1517 1527 1529 1535 1537 1540 1551 1552 1555 1558 1567 1574 1579 1584
## [323] 1590 1601 1604 1605 1614 1615 1616 1617 1620 1626 1629 1630 1631 1634
## [337] 1635 1640 1645 1660 1664 1668 1671 1672 1678 1679 1682 1690 1691 1693
## [351] 1710 1719 1721 1727 1728 1732 1734 1748 1749 1763 1770 1796 1803 1804
## [365] 1805 1817 1824 1827 1830 1832 1837 1857 1858 1860 1876 1877 1888 1897
## [379] 1922 1924 1936 1938 1951 1952 1953 1954 1959 1965 1966 1969 1972 1973
## [393] 1979 1982 1986 1992 2007 2009 2020 2021 2026 2039 2040 2051 2052 2063
## [407] 2064 2068 2069 2076 2077 2092 2096 2097 2102 2103 2107 2108 2111 2120
## [421] 2121 2122 2123 2124 2127 2128 2133 2140 2142 2144 2147 2148 2165 2167
## [435] 2172 2181 2185 2186 2197 2199 2202 2203 2205 2214 2238 2240 2241 2250
## [449] 2263 2269 2278 2283 2287 2289 2290 2297 2306 2310 2314 2315 2324 2325
## [463] 2336 2345 2351 2355 2363 2366 2367 2370 2374 2377 2380 2386 2390 2397
## [477] 2401 2406 2414 2419 2420 2421 2425 2428 2429 2434 2442 2449 2468 2472
## [491] 2484 2486 2498 2503 2505 2514 2516 2521 2524 2526 2528 2532 2538 2542
## [505] 2552 2558 2565 2566 2568 2577 2579 2580 2588 2589 2597 2603 2607 2615
## [519] 2616 2619 2625 2628 2632 2635 2650 2651 2654 2655 2659 2664 2665 2666
## [533] 2670 2677 2679 2680 2683 2688 2689 2693 2696 2701 2703 2706 2708 2709
## [547] 2729 2732 2740 2749 2754 2756 2758 2768 2770 2775 2778 2779 2783 2785
## [561] 2794 2795 2797 2799 2814 2822 2823 2824 2827 2841 2842 2844 2848 2854
## [575] 2858 2859 2861 2867 2875 2877 2884 2885 2889 2890 2892 2894 2895 2902
## [589] 2904 2908 2911 2912 2913 2917 2918 2919 2920 2921 2924 2931 2936 2940
## [603] 2942 2947 2954 2956 2965 2972 2975 2977 2983 2985 2986 2987 2990 3003
## [617] 3043 3052 3072 3073 3079 3081 3085 3094 3095 3099 3102 3105 3116 3122
## [631] 3131 3138 3144 3150 3157 3161 3167 3172 3174 3175 3178 3187 3201 3204
## [645] 3208 3210 3219 3222 3230 3243 3247 3249 3256 3260 3262 3267 3271 3272
## [659] 3274 3284 3287 3310 3317 3320 3324 3332
## 
## $index$Fold5
##   [1]    2    3    4    7   11   12   15   18   40   43   44   45   47   53
##  [15]   58   61   62   69   78   79   82   90   95  100  128  130  135  144
##  [29]  158  159  160  167  168  173  175  178  185  188  206  216  220  230
##  [43]  235  236  237  247  248  251  265  276  277  278  283  284  286  287
##  [57]  290  295  299  300  305  308  309  316  334  340  342  344  351  355
##  [71]  358  366  368  378  380  386  387  402  403  409  413  417  419  420
##  [85]  425  428  453  456  458  459  460  465  468  470  476  479  486  489
##  [99]  497  500  505  506  511  513  518  521  522  524  531  532  533  534
## [113]  538  540  541  547  553  562  564  565  569  585  586  593  607  613
## [127]  627  633  638  640  659  660  661  665  670  676  679  683  687  691
## [141]  706  719  720  729  731  734  742  743  746  749  751  757  767  768
## [155]  771  778  781  783  786  788  789  791  792  795  800  819  826  829
## [169]  836  843  847  848  852  855  862  867  869  870  871  881  894  895
## [183]  903  916  917  918  923  924  930  935  936  940  944  948  953  956
## [197]  960  967  972  978  979  989 1002 1007 1009 1021 1023 1036 1037 1039
## [211] 1049 1056 1064 1070 1078 1085 1088 1096 1101 1103 1105 1109 1115 1118
## [225] 1135 1136 1139 1141 1145 1151 1154 1155 1166 1174 1175 1180 1181 1197
## [239] 1201 1202 1220 1222 1236 1239 1241 1243 1252 1257 1260 1264 1270 1272
## [253] 1273 1275 1295 1304 1306 1311 1313 1333 1338 1340 1344 1348 1349 1360
## [267] 1361 1375 1384 1385 1387 1389 1393 1400 1406 1410 1412 1415 1419 1424
## [281] 1439 1445 1446 1454 1459 1460 1463 1464 1480 1482 1485 1490 1493 1499
## [295] 1501 1512 1522 1526 1531 1532 1533 1534 1536 1541 1547 1562 1563 1565
## [309] 1571 1575 1581 1591 1608 1612 1618 1619 1622 1625 1632 1637 1641 1642
## [323] 1647 1649 1655 1656 1666 1683 1685 1686 1687 1688 1694 1699 1711 1722
## [337] 1724 1725 1731 1738 1741 1742 1744 1751 1757 1759 1760 1764 1766 1769
## [351] 1780 1781 1788 1790 1793 1795 1800 1801 1807 1814 1819 1826 1828 1840
## [365] 1841 1850 1852 1854 1855 1866 1869 1871 1872 1874 1880 1881 1887 1891
## [379] 1892 1893 1899 1903 1905 1907 1908 1915 1921 1927 1929 1937 1956 1963
## [393] 1967 1981 1983 1985 1987 1990 1993 2004 2005 2011 2013 2016 2017 2019
## [407] 2023 2025 2030 2038 2041 2046 2047 2054 2057 2066 2074 2075 2089 2093
## [421] 2098 2100 2101 2112 2115 2119 2129 2136 2149 2150 2152 2155 2157 2169
## [435] 2176 2184 2187 2188 2189 2195 2201 2209 2210 2211 2212 2213 2216 2220
## [449] 2221 2226 2227 2229 2230 2237 2242 2252 2255 2259 2268 2275 2295 2298
## [463] 2301 2302 2303 2308 2312 2313 2321 2329 2334 2339 2347 2350 2353 2359
## [477] 2378 2387 2388 2393 2394 2402 2404 2408 2416 2417 2423 2424 2430 2432
## [491] 2433 2443 2446 2448 2450 2455 2456 2459 2460 2463 2467 2471 2479 2480
## [505] 2502 2511 2517 2525 2531 2544 2545 2560 2563 2570 2572 2582 2584 2591
## [519] 2592 2606 2614 2617 2630 2631 2637 2642 2646 2661 2668 2675 2682 2684
## [533] 2702 2705 2707 2710 2712 2714 2717 2721 2722 2730 2751 2760 2761 2762
## [547] 2763 2767 2769 2776 2777 2781 2793 2796 2800 2802 2807 2809 2812 2813
## [561] 2815 2820 2825 2826 2832 2838 2839 2845 2846 2847 2849 2850 2851 2852
## [575] 2855 2860 2864 2873 2879 2882 2883 2887 2891 2898 2899 2900 2901 2903
## [589] 2906 2907 2922 2923 2928 2938 2950 2952 2953 2955 2961 2966 2968 2969
## [603] 2970 2973 2976 2992 2996 3000 3004 3007 3011 3019 3022 3028 3035 3036
## [617] 3046 3050 3056 3058 3059 3060 3065 3067 3086 3088 3090 3108 3111 3117
## [631] 3120 3121 3132 3141 3146 3154 3156 3165 3168 3170 3186 3188 3199 3200
## [645] 3209 3213 3217 3246 3252 3253 3258 3265 3268 3270 3275 3280 3285 3286
## [659] 3290 3293 3296 3297 3298 3303 3316 3322 3325
## 
## 
## $indexOut
## NULL
## 
## $indexFinal
## NULL
## 
## $timingSamps
## [1] 0
## 
## $predictionBounds
## [1] FALSE FALSE
## 
## $seeds
## [1] NA
## 
## $adaptive
## $adaptive$min
## [1] 5
## 
## $adaptive$alpha
## [1] 0.05
## 
## $adaptive$method
## [1] "gls"
## 
## $adaptive$complete
## [1] TRUE
## 
## 
## $trim
## [1] FALSE
## 
## $allowParallel
## [1] TRUE

– Why reuse a trainControl?

• So you can use the same summaryFunction and tuning parameters for multiple models
• So you don’t have to repeat code when fiting multiple models
• So you can compare models on the exact same training and test data

– Make custom train/test indices

• In the class we use a slightly preprocessed and paired down dataset
  • there are less observations
  • factor variables have been split into booleans and things are more cleaned up for fitting a model

glimpse(churn_x)

## Observations: 250
## Variables: 70
## $ stateAK                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateAL                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateAR                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateAZ                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateCA                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateCO                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateCT                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateDC                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,...
## $ stateDE                       <int> 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,...
## $ stateFL                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateGA                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateHI                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateIA                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateID                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateIL                       <int> 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,...
## $ stateIN                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateKS                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateKY                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateLA                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateMA                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateMD                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateME                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateMI                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateMN                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateMO                       <int> 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateMS                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateMT                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateNC                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateND                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateNE                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateNH                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateNJ                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,...
## $ stateNM                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateNV                       <int> 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,...
## $ stateNY                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateOH                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateOK                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateOR                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ statePA                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,...
## $ stateRI                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateSC                       <int> 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateSD                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateTN                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateTX                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateUT                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateVA                       <int> 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,...
## $ stateVT                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateWA                       <int> 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,...
## $ stateWI                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateWV                       <int> 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ stateWY                       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ account_length                <int> 137, 83, 48, 67, 143, 163, 100, ...
## $ area_codearea_code_415        <int> 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1,...
## $ area_codearea_code_510        <int> 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0,...
## $ international_planyes         <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ voice_mail_planyes            <int> 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0,...
## $ number_vmail_messages         <int> 0, 0, 34, 0, 0, 0, 39, 0, 43, 30...
## $ total_day_minutes             <dbl> 109.8, 196.7, 198.0, 164.5, 133....
## $ total_day_calls               <int> 112, 117, 70, 79, 107, 100, 74, ...
## $ total_day_charge              <dbl> 18.67, 33.44, 33.66, 27.97, 22.6...
## $ total_eve_minutes             <dbl> 223.5, 272.0, 273.7, 110.3, 223....
## $ total_eve_calls               <int> 88, 89, 121, 108, 117, 46, 80, 8...
## $ total_eve_charge              <dbl> 19.00, 23.12, 23.26, 9.38, 19.03...
## $ total_night_minutes           <dbl> 247.5, 199.9, 217.9, 203.9, 180....
## $ total_night_calls             <int> 96, 62, 71, 102, 85, 116, 89, 88...
## $ total_night_charge            <dbl> 11.14, 9.00, 9.81, 9.18, 8.12, 9...
## $ total_intl_minutes            <dbl> 17.8, 10.1, 7.6, 9.8, 10.2, 12.8...
## $ total_intl_calls              <int> 2, 11, 4, 2, 13, 3, 4, 5, 5, 2, ...
## $ total_intl_charge             <dbl> 4.81, 2.73, 2.05, 2.65, 2.75, 3....
## $ number_customer_service_calls <int> 1, 3, 1, 1, 1, 5, 2, 0, 2, 3, 2,...

glimpse(churn_y)

##  Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 1 1 ...

# Create custom indices: myFolds
myFolds <- createFolds(churn_y, k = 5)

# Create reusable trainControl object: myControl
myControl <- trainControl(
  summaryFunction = twoClassSummary,
  classProbs = TRUE, # IMPORTANT!
  verboseIter = TRUE,
  savePredictions = TRUE,
  index = myFolds
)

Reintroduce glmnet

• the glmnet is linear model with built-in variable selection
• it is a great baseline model for any prediction problem
• its alsmost alwasy the instructors first model
• advantages (simple, fast, interpretable)
  • its fast
  • uses variable selection to avoid noisy variables
  • it provides interpretable coefficents so you can understand patterns in your data
  • its just as interprtable as models from lm or glm functions
  • in this case it will let a business analyst actualy understand the drivers of churn. Its also good to use for predictions.

Example: glmnet on churn data

set.seed(42)

model_glmnet <- train(
  churn ~ ., churnTrain, 
  metric = "ROC",
  method = "glmnet",
  tuneGrid = expand.grid(
    alpha = 0:1, 
    lambda = 0:10/10
  ),
  trControl = myControl
)

## + Fold1: alpha=0, lambda=1 
## - Fold1: alpha=0, lambda=1 
## + Fold1: alpha=1, lambda=1 
## - Fold1: alpha=1, lambda=1 
## + Fold2: alpha=0, lambda=1 
## - Fold2: alpha=0, lambda=1 
## + Fold2: alpha=1, lambda=1 
## - Fold2: alpha=1, lambda=1 
## + Fold3: alpha=0, lambda=1 
## - Fold3: alpha=0, lambda=1 
## + Fold3: alpha=1, lambda=1 
## - Fold3: alpha=1, lambda=1 
## + Fold4: alpha=0, lambda=1 
## - Fold4: alpha=0, lambda=1 
## + Fold4: alpha=1, lambda=1 
## - Fold4: alpha=1, lambda=1 
## + Fold5: alpha=0, lambda=1 
## - Fold5: alpha=0, lambda=1 
## + Fold5: alpha=1, lambda=1 
## - Fold5: alpha=1, lambda=1 
## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 0, lambda = 1 on full training set

# Plot the results
plot(model_glmnet)

plot(model_glmnet$finalModel)

• caret automatically chooses the best values for lambda so we don’t need to do anything after looking at this plot

– Fit the baseline model

# Fit glmnet model: model_glmnet
model_glmnet <- train(
  x = churn_x, y = churn_y,
  metric = "ROC",
  method = "glmnet",
  trControl = myControl
)

## + Fold1: alpha=0.10, lambda=0.01821 
## - Fold1: alpha=0.10, lambda=0.01821 
## + Fold1: alpha=0.55, lambda=0.01821 
## - Fold1: alpha=0.55, lambda=0.01821 
## + Fold1: alpha=1.00, lambda=0.01821 
## - Fold1: alpha=1.00, lambda=0.01821 
## + Fold2: alpha=0.10, lambda=0.01821 
## - Fold2: alpha=0.10, lambda=0.01821 
## + Fold2: alpha=0.55, lambda=0.01821 
## - Fold2: alpha=0.55, lambda=0.01821 
## + Fold2: alpha=1.00, lambda=0.01821 
## - Fold2: alpha=1.00, lambda=0.01821 
## + Fold3: alpha=0.10, lambda=0.01821 
## - Fold3: alpha=0.10, lambda=0.01821 
## + Fold3: alpha=0.55, lambda=0.01821 
## - Fold3: alpha=0.55, lambda=0.01821 
## + Fold3: alpha=1.00, lambda=0.01821 
## - Fold3: alpha=1.00, lambda=0.01821 
## + Fold4: alpha=0.10, lambda=0.01821 
## - Fold4: alpha=0.10, lambda=0.01821 
## + Fold4: alpha=0.55, lambda=0.01821 
## - Fold4: alpha=0.55, lambda=0.01821 
## + Fold4: alpha=1.00, lambda=0.01821 
## - Fold4: alpha=1.00, lambda=0.01821 
## + Fold5: alpha=0.10, lambda=0.01821 
## - Fold5: alpha=0.10, lambda=0.01821 
## + Fold5: alpha=0.55, lambda=0.01821 
## - Fold5: alpha=0.55, lambda=0.01821 
## + Fold5: alpha=1.00, lambda=0.01821 
## - Fold5: alpha=1.00, lambda=0.01821 
## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 1, lambda = 0.0182 on full training set

Reintroduce random forest

• random forest is always the second model the instructor tries (after glm_net)
• they are slower then glmnet and less interpretable (kinda like a black box), but they are often (not always) more accurate than glmnet and they are easier to tune.
• They also require little preprocessing, and handle missing data well.
• They also capture threshold effects and variable interactions well. Both of these cases occur often in real world data.

Eample: random forest on churn data

• The default caret tuning values work great so we don’t need to make a custom tuning grid
• caret will sutomatically shoose the best results for mtry and splitrule

set.seed(42)
churnTrain$churn <- factor(churnTrain$churn, levels = c("no", "yes"))
model_rf <- train(
  churn ~ ., churnTrain, 
  metric = "ROC",
  method = "ranger",
  trControl = myControl
)

## + Fold1: mtry= 2, splitrule=gini 
## - Fold1: mtry= 2, splitrule=gini 
## + Fold1: mtry=35, splitrule=gini 
## - Fold1: mtry=35, splitrule=gini 
## + Fold1: mtry=69, splitrule=gini 
## - Fold1: mtry=69, splitrule=gini 
## + Fold1: mtry= 2, splitrule=extratrees 
## - Fold1: mtry= 2, splitrule=extratrees 
## + Fold1: mtry=35, splitrule=extratrees 
## - Fold1: mtry=35, splitrule=extratrees 
## + Fold1: mtry=69, splitrule=extratrees 
## - Fold1: mtry=69, splitrule=extratrees 
## + Fold2: mtry= 2, splitrule=gini 
## - Fold2: mtry= 2, splitrule=gini 
## + Fold2: mtry=35, splitrule=gini 
## - Fold2: mtry=35, splitrule=gini 
## + Fold2: mtry=69, splitrule=gini 
## - Fold2: mtry=69, splitrule=gini 
## + Fold2: mtry= 2, splitrule=extratrees 
## - Fold2: mtry= 2, splitrule=extratrees 
## + Fold2: mtry=35, splitrule=extratrees 
## - Fold2: mtry=35, splitrule=extratrees 
## + Fold2: mtry=69, splitrule=extratrees 
## - Fold2: mtry=69, splitrule=extratrees 
## + Fold3: mtry= 2, splitrule=gini 
## - Fold3: mtry= 2, splitrule=gini 
## + Fold3: mtry=35, splitrule=gini 
## - Fold3: mtry=35, splitrule=gini 
## + Fold3: mtry=69, splitrule=gini 
## - Fold3: mtry=69, splitrule=gini 
## + Fold3: mtry= 2, splitrule=extratrees 
## - Fold3: mtry= 2, splitrule=extratrees 
## + Fold3: mtry=35, splitrule=extratrees 
## - Fold3: mtry=35, splitrule=extratrees 
## + Fold3: mtry=69, splitrule=extratrees 
## - Fold3: mtry=69, splitrule=extratrees 
## + Fold4: mtry= 2, splitrule=gini 
## - Fold4: mtry= 2, splitrule=gini 
## + Fold4: mtry=35, splitrule=gini 
## - Fold4: mtry=35, splitrule=gini 
## + Fold4: mtry=69, splitrule=gini 
## - Fold4: mtry=69, splitrule=gini 
## + Fold4: mtry= 2, splitrule=extratrees 
## - Fold4: mtry= 2, splitrule=extratrees 
## + Fold4: mtry=35, splitrule=extratrees 
## - Fold4: mtry=35, splitrule=extratrees 
## + Fold4: mtry=69, splitrule=extratrees 
## - Fold4: mtry=69, splitrule=extratrees 
## + Fold5: mtry= 2, splitrule=gini 
## - Fold5: mtry= 2, splitrule=gini 
## + Fold5: mtry=35, splitrule=gini 
## - Fold5: mtry=35, splitrule=gini 
## + Fold5: mtry=69, splitrule=gini 
## - Fold5: mtry=69, splitrule=gini 
## + Fold5: mtry= 2, splitrule=extratrees 
## - Fold5: mtry= 2, splitrule=extratrees 
## + Fold5: mtry=35, splitrule=extratrees 
## - Fold5: mtry=35, splitrule=extratrees 
## + Fold5: mtry=69, splitrule=extratrees 
## - Fold5: mtry=69, splitrule=extratrees 
## Aggregating results
## Selecting tuning parameters
## Fitting mtry = 35, splitrule = extratrees on full training set

plot(model_rf)

– Random forest with custom trainControl

# Fit random forest: model_rf
model_rf <- train(
  x = churn_x, y = churn_y,
  metric = "ROC",
  method = "ranger",
  trControl = myControl
)

## + Fold1: mtry= 2, splitrule=gini 
## - Fold1: mtry= 2, splitrule=gini 
## + Fold1: mtry=36, splitrule=gini 
## - Fold1: mtry=36, splitrule=gini 
## + Fold1: mtry=70, splitrule=gini 
## - Fold1: mtry=70, splitrule=gini 
## + Fold1: mtry= 2, splitrule=extratrees 
## - Fold1: mtry= 2, splitrule=extratrees 
## + Fold1: mtry=36, splitrule=extratrees 
## - Fold1: mtry=36, splitrule=extratrees 
## + Fold1: mtry=70, splitrule=extratrees 
## - Fold1: mtry=70, splitrule=extratrees 
## + Fold2: mtry= 2, splitrule=gini 
## - Fold2: mtry= 2, splitrule=gini 
## + Fold2: mtry=36, splitrule=gini 
## - Fold2: mtry=36, splitrule=gini 
## + Fold2: mtry=70, splitrule=gini 
## - Fold2: mtry=70, splitrule=gini 
## + Fold2: mtry= 2, splitrule=extratrees 
## - Fold2: mtry= 2, splitrule=extratrees 
## + Fold2: mtry=36, splitrule=extratrees 
## - Fold2: mtry=36, splitrule=extratrees 
## + Fold2: mtry=70, splitrule=extratrees 
## - Fold2: mtry=70, splitrule=extratrees 
## + Fold3: mtry= 2, splitrule=gini 
## - Fold3: mtry= 2, splitrule=gini 
## + Fold3: mtry=36, splitrule=gini 
## - Fold3: mtry=36, splitrule=gini 
## + Fold3: mtry=70, splitrule=gini 
## - Fold3: mtry=70, splitrule=gini 
## + Fold3: mtry= 2, splitrule=extratrees 
## - Fold3: mtry= 2, splitrule=extratrees 
## + Fold3: mtry=36, splitrule=extratrees 
## - Fold3: mtry=36, splitrule=extratrees 
## + Fold3: mtry=70, splitrule=extratrees 
## - Fold3: mtry=70, splitrule=extratrees 
## + Fold4: mtry= 2, splitrule=gini 
## - Fold4: mtry= 2, splitrule=gini 
## + Fold4: mtry=36, splitrule=gini 
## - Fold4: mtry=36, splitrule=gini 
## + Fold4: mtry=70, splitrule=gini 
## - Fold4: mtry=70, splitrule=gini 
## + Fold4: mtry= 2, splitrule=extratrees 
## - Fold4: mtry= 2, splitrule=extratrees 
## + Fold4: mtry=36, splitrule=extratrees 
## - Fold4: mtry=36, splitrule=extratrees 
## + Fold4: mtry=70, splitrule=extratrees 
## - Fold4: mtry=70, splitrule=extratrees 
## + Fold5: mtry= 2, splitrule=gini 
## - Fold5: mtry= 2, splitrule=gini 
## + Fold5: mtry=36, splitrule=gini 
## - Fold5: mtry=36, splitrule=gini 
## + Fold5: mtry=70, splitrule=gini 
## - Fold5: mtry=70, splitrule=gini 
## + Fold5: mtry= 2, splitrule=extratrees 
## - Fold5: mtry= 2, splitrule=extratrees 
## + Fold5: mtry=36, splitrule=extratrees 
## - Fold5: mtry=36, splitrule=extratrees 
## + Fold5: mtry=70, splitrule=extratrees 
## - Fold5: mtry=70, splitrule=extratrees 
## Aggregating results
## Selecting tuning parameters
## Fitting mtry = 36, splitrule = extratrees on full training set

Comparing models

• Now we need to decide which model makes the best predictions on new data
• We want the model with the highes average AUC across all the folds as well as the lowest standard deviation in AUC
• the caret package provides the resamples() function which is very useful for collecting the results from multiple models

# make a model list
model_list <-list(
  glmnet = model_glmnet, 
  rf = model_rf)

# collect resamples from the CV folds
resamps <- resamples(model_list)

# summarize the results
summary(resamps)

## 
## Call:
## summary.resamples(object = resamps)
## 
## Models: glmnet, rf 
## Number of resamples: 5 
## 
## ROC 
##             Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
## glmnet 0.3919540 0.5509890 0.6317241 0.5916097 0.6686561 0.7147253    0
## rf     0.5894253 0.6587091 0.6676923 0.6716094 0.7055172 0.7367033    0
## 
## Sens 
##             Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
## glmnet 0.9314286 0.9425287 0.9485714 0.9518621 0.9655172 0.9712644    0
## rf     0.9885057 0.9885057 0.9942529 0.9931100 0.9942857 1.0000000    0
## 
## Spec 
##        Min.    1st Qu. Median       Mean   3rd Qu.       Max. NA's
## glmnet 0.04 0.07692308   0.08 0.15476923 0.1923077 0.38461538    0
## rf     0.00 0.00000000   0.00 0.02338462 0.0400000 0.07692308    0

– Create a resamples object

• You can compare models in caret using the resamples() function, provided they have the same training data and use the same trainControl object with preset cross-validation folds.
• resamples() takes as input a list of models and can be used to compare dozens of models at once (though in this case you are only comparing two models).

# Create model_list
model_list <- list(item1 = model_glmnet, 
                   item2 = model_rf)

# Pass model_list to resamples(): resamples
resamples <- resamples(model_list)

# Summarize the results
summary(resamples)

## 
## Call:
## summary.resamples(object = resamples)
## 
## Models: item1, item2 
## Number of resamples: 5 
## 
## ROC 
##            Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
## item1 0.3919540 0.5509890 0.6317241 0.5916097 0.6686561 0.7147253    0
## item2 0.5894253 0.6587091 0.6676923 0.6716094 0.7055172 0.7367033    0
## 
## Sens 
##            Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
## item1 0.9314286 0.9425287 0.9485714 0.9518621 0.9655172 0.9712644    0
## item2 0.9885057 0.9885057 0.9942529 0.9931100 0.9942857 1.0000000    0
## 
## Spec 
##       Min.    1st Qu. Median       Mean   3rd Qu.       Max. NA's
## item1 0.04 0.07692308   0.08 0.15476923 0.1923077 0.38461538    0
## item2 0.00 0.00000000   0.00 0.02338462 0.0400000 0.07692308    0

dotplot(resamples, metric = "ROC")

More on resamples

• resamples also provide a bunch of charting functions to see the best model
• This inspired Zach to create the caretEnsemble package
• box and wisker plot bwplot is a good way to find the best model visually
• dot plot dotplot is a visually simpler way to view the data and works well when there are many models
• density plot densityplot shows the full distibution of AUC scores and is a good way to find outlier folds
• scatter plot xyplot can directly compare the AUC on each fold

bwplot(resamps, metric = "ROC")

dotplot(resamps, metric = "ROC")

densityplot(resamps, metric = "ROC")

xyplot(resamps, metric = "ROC")

- rf, gbm, svm, glmnet, rpart are all models we could use here. I’d like to try doing all of these and comparing with the dotplot chart -

– Create a box-and-whisker plot

• caret provides a variety of methods to use for comparing models. All of these methods are based on the resamples() function.
• The instructors favorite is the box-and-whisker plot, which allows you to compare the distribution of predictive accuracy (in this case AUC) for the two models.
  • In general, you want the model with the higher median AUC, as well as a smaller range between min and max AUC.
• You can make this plot using the bwplot() function, which makes a box and whisker plot of the model’s out of sample scores.
• If you do not specify a metric to plot, bwplot() will automatically plot 3 of them.

# Create bwplot
bwplot(resamples)

bwplot(resamples, metric = "ROC")

– Create a scatterplot

• Another useful plot for comparing models is the scatterplot, also known as the xy-plot.
• This plot shows you how similar the two models’ performances are on different folds.
• It’s particularly useful for identifying if one model is consistently better than the other across all folds, or if there are situations when the inferior model produces better predictions on a particular subset of the data.

# Create xyplot
xyplot(resamples, metric = "ROC")

– Ensembling models

• I had to look up a little tutorial on caretEnsemble to get this working
• I need to have a model_list that is a caretList

library(caretEnsemble)

model_list <- caretList(
  churn ~ ., churnTrain,
  trControl = myControl,
  methodList = c("glm", "rpart", "rf", "gbm", "glmnet")
  )

## + Fold1: parameter=none 
## - Fold1: parameter=none 
## + Fold2: parameter=none 
## - Fold2: parameter=none 
## + Fold3: parameter=none 
## - Fold3: parameter=none 
## + Fold4: parameter=none 
## - Fold4: parameter=none 
## + Fold5: parameter=none 
## - Fold5: parameter=none 
## Aggregating results
## Fitting final model on full training set
## + Fold1: cp=0.07867 
## - Fold1: cp=0.07867 
## + Fold2: cp=0.07867 
## - Fold2: cp=0.07867 
## + Fold3: cp=0.07867 
## - Fold3: cp=0.07867 
## + Fold4: cp=0.07867 
## - Fold4: cp=0.07867 
## + Fold5: cp=0.07867 
## - Fold5: cp=0.07867 
## Aggregating results
## Selecting tuning parameters
## Fitting cp = 0.089 on full training set
## + Fold1: mtry= 2 
## - Fold1: mtry= 2 
## + Fold1: mtry=35 
## - Fold1: mtry=35 
## + Fold1: mtry=69 
## - Fold1: mtry=69 
## + Fold2: mtry= 2 
## - Fold2: mtry= 2 
## + Fold2: mtry=35 
## - Fold2: mtry=35 
## + Fold2: mtry=69 
## - Fold2: mtry=69 
## + Fold3: mtry= 2 
## - Fold3: mtry= 2 
## + Fold3: mtry=35 
## - Fold3: mtry=35 
## + Fold3: mtry=69 
## - Fold3: mtry=69 
## + Fold4: mtry= 2 
## - Fold4: mtry= 2 
## + Fold4: mtry=35 
## - Fold4: mtry=35 
## + Fold4: mtry=69 
## - Fold4: mtry=69 
## + Fold5: mtry= 2 
## - Fold5: mtry= 2 
## + Fold5: mtry=35 
## - Fold5: mtry=35 
## + Fold5: mtry=69 
## - Fold5: mtry=69 
## Aggregating results
## Selecting tuning parameters
## Fitting mtry = 35 on full training set
## + Fold1: shrinkage=0.1, interaction.depth=1, n.minobsinnode=10, n.trees=150 
## Iter   TrainDeviance   ValidDeviance   StepSize   Improve
##      1        0.8403             nan     0.1000   -0.0134
##      2        0.8370             nan     0.1000   -0.0166
##      3        0.8210             nan     0.1000    0.0058
##      4        0.8075             nan     0.1000   -0.0077
##      5        0.7931             nan     0.1000    0.0030
##      6        0.7826             nan     0.1000   -0.0022
##      7        0.7900             nan     0.1000   -0.0211
##      8        0.7750             nan     0.1000   -0.0098
##      9        0.7696             nan     0.1000   -0.0119
##     10        0.7550             nan     0.1000   -0.0072
##     20        0.6562             nan     0.1000   -0.0054
##     40        0.5646             nan     0.1000   -0.0046
##     60        0.4938             nan     0.1000   -0.0039
##     80        0.4435             nan     0.1000   -0.0072
##    100        0.3876             nan     0.1000   -0.0086
##    120        0.3637             nan     0.1000   -0.0062
##    140        0.3177             nan     0.1000   -0.0063
##    150        0.2954             nan     0.1000   -0.0045
## 
## - Fold1: shrinkage=0.1, interaction.depth=1, n.minobsinnode=10, n.trees=150 
## + Fold1: shrinkage=0.1, interaction.depth=2, n.minobsinnode=10, n.trees=150 
## Iter   TrainDeviance   ValidDeviance   StepSize   Improve
##      1        0.8615             nan     0.1000   -0.0087
##      2        0.8489             nan     0.1000   -0.0054
##      3        0.8463             nan     0.1000   -0.0077
##      4        0.8512             nan     0.1000   -0.0197
##      5        0.8234             nan     0.1000    0.0111
##      6        0.7983             nan     0.1000    0.0064
##      7        0.7715             nan     0.1000   -0.0198
##      8        0.7670             nan     0.1000   -0.0063
##      9        0.7488             nan     0.1000    0.0005
##     10        0.7357             nan     0.1000    0.0008
##     20        0.6776             nan     0.1000   -0.0083
##     40        0.5274             nan     0.1000   -0.0053
##     60        0.4571             nan     0.1000   -0.0090
##     80        0.4178             nan     0.1000   -0.0051
##    100        0.3963             nan     0.1000   -0.0041
##    120        0.3522             nan     0.1000   -0.0065
##    140        0.3122             nan     0.1000   -0.0029
##    150        0.2918             nan     0.1000   -0.0015
## 
## - Fold1: shrinkage=0.1, interaction.depth=2, n.minobsinnode=10, n.trees=150 
## + Fold1: shrinkage=0.1, interaction.depth=3, n.minobsinnode=10, n.trees=150 
## Iter   TrainDeviance   ValidDeviance   StepSize   Improve
##      1        0.8568             nan     0.1000   -0.0040
##      2        0.8529             nan     0.1000   -0.0071
##      3        0.8266             nan     0.1000    0.0007
##      4        0.8177             nan     0.1000   -0.0070
##      5        0.8202             nan     0.1000   -0.0161
##      6        0.7961             nan     0.1000    0.0097
##      7        0.7887             nan     0.1000   -0.0088
##      8        0.7695             nan     0.1000    0.0070
##      9        0.7507             nan     0.1000   -0.0046
##     10        0.7418             nan     0.1000   -0.0036
##     20        0.6477             nan     0.1000   -0.0003
##     40        0.5290             nan     0.1000   -0.0041
##     60        0.4959             nan     0.1000   -0.0030
##     80        0.4265             nan     0.1000   -0.0088
##    100        0.3639             nan     0.1000   -0.0044
##    120        0.3433             nan     0.1000   -0.0073
##    140        0.3011             nan     0.1000   -0.0082
##    150        0.2841             nan     0.1000   -0.0041
## 
## - Fold1: shrinkage=0.1, interaction.depth=3, n.minobsinnode=10, n.trees=150 
## + Fold2: shrinkage=0.1, interaction.depth=1, n.minobsinnode=10, n.trees=150 
## Iter   TrainDeviance   ValidDeviance   StepSize   Improve
##      1        0.6156             nan     0.1000    0.0027
##      2        0.6138             nan     0.1000   -0.0046
##      3        0.6007             nan     0.1000    0.0018
##      4        0.5981             nan     0.1000   -0.0085
##      5        0.6002             nan     0.1000   -0.0118
##      6        0.5765             nan     0.1000    0.0011
##      7        0.5590             nan     0.1000    0.0014
##      8        0.5473             nan     0.1000    0.0028
##      9        0.5505             nan     0.1000   -0.0084
##     10        0.5315             nan     0.1000   -0.0007
##     20        0.4621             nan     0.1000    0.0044
##     40        0.3285             nan     0.1000   -0.0040
##     60        0.2439             nan     0.1000   -0.0011
##     80        0.2040             nan     0.1000   -0.0011
##    100        0.1716             nan     0.1000   -0.0052
##    120        0.1646             nan     0.1000   -0.0054
##    140        0.1454             nan     0.1000   -0.0048
##    150        0.1198             nan     0.1000   -0.0018
## 
## - Fold2: shrinkage=0.1, interaction.depth=1, n.minobsinnode=10, n.trees=150 
## + Fold2: shrinkage=0.1, interaction.depth=2, n.minobsinnode=10, n.trees=150 
## Iter   TrainDeviance   ValidDeviance   StepSize   Improve
##      1        0.6073             nan     0.1000    0.0108
##      2        0.5748             nan     0.1000   -0.0061
##      3        0.5644             nan     0.1000   -0.0158
##      4        0.5641             nan     0.1000   -0.0073
##      5        0.5683             nan     0.1000   -0.0139
##      6        0.5473             nan     0.1000    0.0017
##      7        0.5467             nan     0.1000   -0.0088
##      8        0.5483             nan     0.1000   -0.0086
##      9        0.5487             nan     0.1000   -0.0065
##     10        0.5511             nan     0.1000   -0.0077
##     20        0.4399             nan     0.1000    0.0025
##     40        0.3290             nan     0.1000   -0.0076
##     60        0.2538             nan     0.1000   -0.0050
##     80        0.1917             nan     0.1000   -0.0039
##    100        0.1555             nan     0.1000   -0.0003
##    120        0.1394             nan     0.1000   -0.0009
##    140        0.0982             nan     0.1000   -0.0032
##    150        0.0948             nan     0.1000   -0.0009
## 
## - Fold2: shrinkage=0.1, interaction.depth=2, n.minobsinnode=10, n.trees=150 
## + Fold2: shrinkage=0.1, interaction.depth=3, n.minobsinnode=10, n.trees=150 
## Iter   TrainDeviance   ValidDeviance   StepSize   Improve
##      1        0.6237             nan     0.1000    0.0072
##      2        0.6059             nan     0.1000   -0.0229
##      3        0.5988             nan     0.1000   -0.0016
##      4        0.5831             nan     0.1000   -0.0032
##      5        0.5814             nan     0.1000   -0.0094
##      6        0.5820             nan     0.1000   -0.0107
##      7        0.5617             nan     0.1000    0.0085
##      8        0.5458             nan     0.1000    0.0053
##      9        0.5331             nan     0.1000    0.0039
##     10        0.5123             nan     0.1000   -0.0078
##     20        0.4402             nan     0.1000    0.0028
##     40        0.2933             nan     0.1000    0.0001
##     60        0.2296             nan     0.1000   -0.0051
##     80        0.1823             nan     0.1000   -0.0022
##    100        0.1696             nan     0.1000   -0.0053
##    120        0.1243             nan     0.1000   -0.0007
##    140        0.1020             nan     0.1000   -0.0003
##    150        0.0927             nan     0.1000   -0.0022
## 
## - Fold2: shrinkage=0.1, interaction.depth=3, n.minobsinnode=10, n.trees=150 
## + Fold3: shrinkage=0.1, interaction.depth=1, n.minobsinnode=10, n.trees=150 
## Iter   TrainDeviance   ValidDeviance   StepSize   Improve
##      1        0.7816             nan     0.1000    0.0085
##      2        0.7765             nan     0.1000   -0.0035
##      3        0.7715             nan     0.1000   -0.0108
##      4        0.7581             nan     0.1000   -0.0150
##      5        0.7390             nan     0.1000    0.0003
##      6        0.7356             nan     0.1000   -0.0061
##      7        0.7152             nan     0.1000    0.0046
##      8        0.7154             nan     0.1000   -0.0084
##      9        0.6916             nan     0.1000   -0.0019
##     10        0.6863             nan     0.1000   -0.0118
##     20        0.6230             nan     0.1000    0.0006
##     40        0.5171             nan     0.1000   -0.0071
##     60        0.4101             nan     0.1000   -0.0047
##     80        0.3340             nan     0.1000   -0.0031
##    100        0.2788             nan     0.1000   -0.0020
##    120        0.2446             nan     0.1000   -0.0018
##    140        0.2179             nan     0.1000   -0.0036
##    150        0.1881             nan     0.1000   -0.0024
## 
## - Fold3: shrinkage=0.1, interaction.depth=1, n.minobsinnode=10, n.trees=150 
## + Fold3: shrinkage=0.1, interaction.depth=2, n.minobsinnode=10, n.trees=150 
## Iter   TrainDeviance   ValidDeviance   StepSize   Improve
##      1        0.8080             nan     0.1000    0.0045
##      2        0.7980             nan     0.1000    0.0000
##      3        0.7547             nan     0.1000    0.0005
##      4        0.7501             nan     0.1000   -0.0133
##      5        0.7419             nan     0.1000   -0.0075
##      6        0.7340             nan     0.1000   -0.0060
##      7        0.7208             nan     0.1000    0.0026
##      8        0.7172             nan     0.1000   -0.0076
##      9        0.7029             nan     0.1000   -0.0062
##     10        0.6964             nan     0.1000   -0.0072
##     20        0.6357             nan     0.1000   -0.0028
##     40        0.5346             nan     0.1000    0.0120
##     60        0.4005             nan     0.1000   -0.0042
##     80        0.3155             nan     0.1000   -0.0056
##    100        0.2720             nan     0.1000   -0.0061
##    120        0.2180             nan     0.1000   -0.0063
##    140        0.1779             nan     0.1000   -0.0021
##    150        0.1716             nan     0.1000   -0.0042
## 
## - Fold3: shrinkage=0.1, interaction.depth=2, n.minobsinnode=10, n.trees=150 
## + Fold3: shrinkage=0.1, interaction.depth=3, n.minobsinnode=10, n.trees=150 
## Iter   TrainDeviance   ValidDeviance   StepSize   Improve
##      1        0.8149             nan     0.1000   -0.0113
##      2        0.7841             nan     0.1000    0.0123
##      3        0.7777             nan     0.1000    0.0026
##      4        0.7441             nan     0.1000    0.0021
##      5        0.7418             nan     0.1000   -0.0096
##      6        0.7263             nan     0.1000    0.0018
##      7        0.7120             nan     0.1000    0.0011
##      8        0.7086             nan     0.1000   -0.0009
##      9        0.6852             nan     0.1000    0.0033
##     10        0.6891             nan     0.1000   -0.0136
##     20        0.6271             nan     0.1000   -0.0102
##     40        0.5138             nan     0.1000   -0.0041
##     60        0.4358             nan     0.1000   -0.0038
##     80        0.3644             nan     0.1000   -0.0078
##    100        0.3223             nan     0.1000   -0.0024
##    120        0.2947             nan     0.1000   -0.0059
##    140        0.2486             nan     0.1000   -0.0088
##    150        0.2276             nan     0.1000   -0.0018
## 
## - Fold3: shrinkage=0.1, interaction.depth=3, n.minobsinnode=10, n.trees=150 
## + Fold4: shrinkage=0.1, interaction.depth=1, n.minobsinnode=10, n.trees=150 
## Iter   TrainDeviance   ValidDeviance   StepSize   Improve
##      1        0.7213             nan     0.1000    0.0123
##      2        0.7020             nan     0.1000    0.0006
##      3        0.7051             nan     0.1000   -0.0104
##      4        0.6583             nan     0.1000    0.0154
##      5        0.6413             nan     0.1000    0.0066
##      6        0.6173             nan     0.1000   -0.0025
##      7        0.6101             nan     0.1000    0.0006
##      8        0.6100             nan     0.1000   -0.0105
##      9        0.6109             nan     0.1000   -0.0078
##     10        0.6109             nan     0.1000   -0.0057
##     20        0.5028             nan     0.1000   -0.0138
##     40        0.3675             nan     0.1000    0.0003
##     60        0.3089             nan     0.1000    0.0005
##     80        0.2607             nan     0.1000    0.0003
##    100        0.2106             nan     0.1000    0.0024
##    120        0.1770             nan     0.1000   -0.0041
##    140        0.1431             nan     0.1000   -0.0070
##    150        0.1249             nan     0.1000   -0.0009
## 
## - Fold4: shrinkage=0.1, interaction.depth=1, n.minobsinnode=10, n.trees=150 
## + Fold4: shrinkage=0.1, interaction.depth=2, n.minobsinnode=10, n.trees=150 
## Iter   TrainDeviance   ValidDeviance   StepSize   Improve
##      1        0.7094             nan     0.1000    0.0149
##      2        0.6741             nan     0.1000    0.0148
##      3        0.6713             nan     0.1000   -0.0136
##      4        0.6558             nan     0.1000    0.0060
##      5        0.6561             nan     0.1000   -0.0138
##      6        0.6565             nan     0.1000   -0.0088
##      7        0.6383             nan     0.1000    0.0049
##      8        0.6099             nan     0.1000    0.0102
##      9        0.5894             nan     0.1000    0.0013
##     10        0.5810             nan     0.1000   -0.0001
##     20        0.4673             nan     0.1000   -0.0070
##     40        0.3712             nan     0.1000   -0.0009
##     60        0.2936             nan     0.1000   -0.0057
##     80        0.2237             nan     0.1000   -0.0021
##    100        0.1845             nan     0.1000   -0.0024
##    120        0.1709             nan     0.1000    0.0007
##    140        0.1179             nan     0.1000   -0.0028
##    150        0.1037             nan     0.1000   -0.0017
## 
## - Fold4: shrinkage=0.1, interaction.depth=2, n.minobsinnode=10, n.trees=150 
## + Fold4: shrinkage=0.1, interaction.depth=3, n.minobsinnode=10, n.trees=150 
## Iter   TrainDeviance   ValidDeviance   StepSize   Improve
##      1        0.7037             nan     0.1000    0.0205
##      2        0.6815             nan     0.1000    0.0049
##      3        0.6575             nan     0.1000    0.0089
##      4        0.6560             nan     0.1000   -0.0129
##      5        0.6554             nan     0.1000   -0.0093
##      6        0.6261             nan     0.1000    0.0020
##      7        0.6256             nan     0.1000   -0.0075
##      8        0.6072             nan     0.1000    0.0040
##      9        0.6024             nan     0.1000   -0.0034
##     10        0.5812             nan     0.1000   -0.0121
##     20        0.5227             nan     0.1000    0.0064
##     40        0.3991             nan     0.1000   -0.0083
##     60        0.3173             nan     0.1000   -0.0068
##     80        0.2659             nan     0.1000   -0.0031
##    100        0.2367             nan     0.1000   -0.0073
##    120        0.1710             nan     0.1000   -0.0026
##    140        0.1351             nan     0.1000   -0.0026
##    150        0.1188             nan     0.1000   -0.0007
## 
## - Fold4: shrinkage=0.1, interaction.depth=3, n.minobsinnode=10, n.trees=150 
## + Fold5: shrinkage=0.1, interaction.depth=1, n.minobsinnode=10, n.trees=150 
## Iter   TrainDeviance   ValidDeviance   StepSize   Improve
##      1        0.7175             nan     0.1000   -0.0001
##      2        0.6991             nan     0.1000    0.0083
##      3        0.6792             nan     0.1000    0.0015
##      4        0.6812             nan     0.1000   -0.0097
##      5        0.6689             nan     0.1000   -0.0046
##      6        0.6724             nan     0.1000   -0.0216
##      7        0.6697             nan     0.1000   -0.0105
##      8        0.6524             nan     0.1000   -0.0110
##      9        0.6340             nan     0.1000   -0.0004
##     10        0.6204             nan     0.1000    0.0016
##     20        0.5511             nan     0.1000   -0.0138
##     40        0.4604             nan     0.1000   -0.0073
##     60        0.3763             nan     0.1000   -0.0054
##     80        0.3186             nan     0.1000   -0.0051
##    100        0.2823             nan     0.1000   -0.0020
##    120        0.2383             nan     0.1000   -0.0053
##    140        0.2150             nan     0.1000   -0.0056
##    150        0.2003             nan     0.1000   -0.0078
## 
## - Fold5: shrinkage=0.1, interaction.depth=1, n.minobsinnode=10, n.trees=150 
## + Fold5: shrinkage=0.1, interaction.depth=2, n.minobsinnode=10, n.trees=150 
## Iter   TrainDeviance   ValidDeviance   StepSize   Improve
##      1        0.6945             nan     0.1000   -0.0120
##      2        0.6767             nan     0.1000   -0.0152
##      3        0.6635             nan     0.1000   -0.0067
##      4        0.6589             nan     0.1000   -0.0060
##      5        0.6448             nan     0.1000   -0.0047
##      6        0.6453             nan     0.1000   -0.0099
##      7        0.6229             nan     0.1000   -0.0015
##      8        0.6116             nan     0.1000    0.0000
##      9        0.5964             nan     0.1000   -0.0039
##     10        0.5984             nan     0.1000   -0.0098
##     20        0.5789             nan     0.1000   -0.0030
##     40        0.4388             nan     0.1000   -0.0097
##     60        0.3718             nan     0.1000   -0.0080
##     80        0.3201             nan     0.1000   -0.0079
##    100        0.2790             nan     0.1000   -0.0082
##    120        0.2428             nan     0.1000   -0.0054
##    140        0.1996             nan     0.1000   -0.0032
##    150        0.1976             nan     0.1000   -0.0060
## 
## - Fold5: shrinkage=0.1, interaction.depth=2, n.minobsinnode=10, n.trees=150 
## + Fold5: shrinkage=0.1, interaction.depth=3, n.minobsinnode=10, n.trees=150 
## Iter   TrainDeviance   ValidDeviance   StepSize   Improve
##      1        0.7307             nan     0.1000   -0.0048
##      2        0.7179             nan     0.1000    0.0029
##      3        0.7001             nan     0.1000   -0.0047
##      4        0.6828             nan     0.1000    0.0076
##      5        0.6681             nan     0.1000   -0.0008
##      6        0.6579             nan     0.1000   -0.0099
##      7        0.6347             nan     0.1000    0.0009
##      8        0.6375             nan     0.1000   -0.0120
##      9        0.6425             nan     0.1000   -0.0121
##     10        0.6457             nan     0.1000   -0.0123
##     20        0.5627             nan     0.1000   -0.0090
##     40        0.4499             nan     0.1000   -0.0051
##     60        0.3633             nan     0.1000   -0.0073
##     80        0.3097             nan     0.1000   -0.0018
##    100        0.2779             nan     0.1000   -0.0021
##    120        0.2452             nan     0.1000   -0.0022
##    140        0.2358             nan     0.1000    0.0009
##    150        0.2072             nan     0.1000   -0.0060
## 
## - Fold5: shrinkage=0.1, interaction.depth=3, n.minobsinnode=10, n.trees=150 
## Aggregating results
## Selecting tuning parameters
## Fitting n.trees = 150, interaction.depth = 3, shrinkage = 0.1, n.minobsinnode = 10 on full training set
## Iter   TrainDeviance   ValidDeviance   StepSize   Improve
##      1        0.7763             nan     0.1000    0.0256
##      2        0.7409             nan     0.1000    0.0187
##      3        0.7140             nan     0.1000    0.0126
##      4        0.6918             nan     0.1000    0.0103
##      5        0.6727             nan     0.1000    0.0080
##      6        0.6457             nan     0.1000    0.0133
##      7        0.6244             nan     0.1000    0.0089
##      8        0.6082             nan     0.1000    0.0074
##      9        0.5961             nan     0.1000    0.0056
##     10        0.5780             nan     0.1000    0.0085
##     20        0.4833             nan     0.1000    0.0034
##     40        0.4047             nan     0.1000    0.0008
##     60        0.3611             nan     0.1000    0.0010
##     80        0.3324             nan     0.1000    0.0001
##    100        0.3092             nan     0.1000    0.0006
##    120        0.2934             nan     0.1000   -0.0002
##    140        0.2789             nan     0.1000   -0.0002
##    150        0.2727             nan     0.1000    0.0001
## 
## + Fold1: alpha=0.10, lambda=0.01829 
## - Fold1: alpha=0.10, lambda=0.01829 
## + Fold1: alpha=0.55, lambda=0.01829 
## - Fold1: alpha=0.55, lambda=0.01829 
## + Fold1: alpha=1.00, lambda=0.01829 
## - Fold1: alpha=1.00, lambda=0.01829 
## + Fold2: alpha=0.10, lambda=0.01829 
## - Fold2: alpha=0.10, lambda=0.01829 
## + Fold2: alpha=0.55, lambda=0.01829 
## - Fold2: alpha=0.55, lambda=0.01829 
## + Fold2: alpha=1.00, lambda=0.01829 
## - Fold2: alpha=1.00, lambda=0.01829 
## + Fold3: alpha=0.10, lambda=0.01829 
## - Fold3: alpha=0.10, lambda=0.01829 
## + Fold3: alpha=0.55, lambda=0.01829 
## - Fold3: alpha=0.55, lambda=0.01829 
## + Fold3: alpha=1.00, lambda=0.01829 
## - Fold3: alpha=1.00, lambda=0.01829 
## + Fold4: alpha=0.10, lambda=0.01829 
## - Fold4: alpha=0.10, lambda=0.01829 
## + Fold4: alpha=0.55, lambda=0.01829 
## - Fold4: alpha=0.55, lambda=0.01829 
## + Fold4: alpha=1.00, lambda=0.01829 
## - Fold4: alpha=1.00, lambda=0.01829 
## + Fold5: alpha=0.10, lambda=0.01829 
## - Fold5: alpha=0.10, lambda=0.01829 
## + Fold5: alpha=0.55, lambda=0.01829 
## - Fold5: alpha=0.55, lambda=0.01829 
## + Fold5: alpha=1.00, lambda=0.01829 
## - Fold5: alpha=1.00, lambda=0.01829 
## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 1, lambda = 0.0183 on full training set

# Create ensemble model: stack
stack <- caretStack(
  model_list, 
  method = "glm", 
  metric = "ROC",
  trControl=trainControl(
    method="boot",
    number=10,
    savePredictions="final",
    classProbs=TRUE,
    summaryFunction=twoClassSummary
  ))

# Look at summary
summary(stack)

## 
## Call:
## NULL
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.8956  -0.5425  -0.4428  -0.4033   2.3576  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -2.63237    0.04982 -52.839  < 2e-16 ***
## glm          0.08619    0.04733   1.821 0.068567 .  
## rpart        1.02053    0.28036   3.640 0.000273 ***
## rf           5.37613    0.19904  27.011  < 2e-16 ***
## gbm          0.15405    0.10395   1.482 0.138357    
## glmnet      -0.62098    0.13222  -4.696 2.65e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 13600  on 16414  degrees of freedom
## Residual deviance: 12510  on 16409  degrees of freedom
## AIC: 12522
## 
## Number of Fisher Scoring iterations: 4

dotplot(resamples(model_list), metric = "ROC")

---

Conclusion

---

• Wow, I am finally starting to learn these things.
• This class was a great high level overview of how to do things and how to interpret and compare results
• Not I just need to figure out what I am actually doing. : )
• Maybe I can start reading up on kaggle and see if I can learn more about these methods and their power for prediction on real world data sets and problems