Homework 1 Solution
Min Wang
2023-09-16
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
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## filter, lag## The following objects are masked from 'package:base':
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## intersect, setdiff, setequal, unionlibrary(ISLR2)## Warning: package 'ISLR2' was built under R version 4.2.3library(caret)## Loading required package: ggplot2## Loading required package: latticelibrary(car)## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:dplyr':
##
## recodelibrary(mlbench)## Warning: package 'mlbench' was built under R version 4.2.3library(ggplot2)
library(lattice)Exercise 1
We would expect that a flexible model performs better than an inflexible model, given that the former will provide a closer fit with the large sample size.
We would expect that a flexible model performs more worse than an inflexible model because of the possible overfitting issue ofa flexible model.
We would expect that a flexible model would performs better than an inflexible model due to its large flexibility in terms of degrees of freedom.
We would expect that a flexible model performs better than an inflexible model, since the inflexible model will be heavily influenced by the noise of the error terms, thus resulting in an increasing variance.
Exercise 2
- Figure is shown below:
Flexibility Sketch of Statistical Learning
methods
- My explanations are briefly summarized as follows:
(i): (squared) bias - decreases monotonically since increases in flexibility result in a closer fit.
variance - increases monotonically since increases in flexibility result in overfit.
training error - decreases monotonically since increases in flexibility result in a closer fit.
- test error - concave up curve since increases in flexibility result in a closer fit before it overfits.
Exercise 3
- There are 506 rows and 13 columns. 506 rows represent suburbs of Boston and the 13 variables represent housing values.
library(MASS)##
## Attaching package: 'MASS'## The following object is masked from 'package:ISLR2':
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## Boston## The following object is masked from 'package:dplyr':
##
## selectdim(Boston)## [1] 506 14Some findings about the pairwise correlations can be summarized as follows
Several predictors in this data are highly correlated, such as the correlation between rad and tax being more than 0.91.
Some predictors are negatively correlated, such as the nox and dis being -0.77
the predictors age and nox seem to be highly correlated with many other predictors.
pairs(Boston)
library(corrplot)## Warning: package 'corrplot' was built under R version 4.2.3## corrplot 0.92 loadedcorrelationvalue = cor(Boston)
corrplot.mixed(correlationvalue, order = 'AOE')
- Several plots with brief comments for the association between predictors and per capita crime rate are summarized as follows
par(mfrow=c(3,2))
plot(Boston$age, Boston$crim)
# Older homes, more crime
plot(Boston$nox, Boston$crim)
# middle value of nox, more crime
plot(Boston$dis, Boston$crim)
# Closer to work-area, more crime
plot(Boston$rad, Boston$crim)
# Higher index of accessibility to radial highways, more crime
plot(Boston$tax, Boston$crim)
# Higher tax rate, more crime
plot(Boston$ptratio, Boston$crim)
# Higher pupil:teacher ratio, more crime- Histograms with comments are briefly provided as follows.
par(mfrow=c(1,3))
hist(Boston$crim[Boston$crim>1], breaks=20, freq = T, main="Crime More than 1")
# The crime rates are heavily right skewed, indicating that most cities have low crime rates,
# but there are a few citites having high crimial rate, which could reach to above 80.
hist(Boston$tax, breaks=20, freq = T, main="Tax")
# There is a large divide between suburbs with low tax rates and a peak at 600-700
hist(Boston$ptratio, breaks=20, freq = T, main="Ptratio")
# The ptratio seems to be slighly left skewed, indicating a skew towards high ratios.
library(e1071)
skewness(Boston$ptratio)## [1] -0.7975743- 35 census tracts bound the Charles River.
nrow(subset(Boston, chas == 1))## [1] 35- The median for pupil-teacher ratio is 19.05.
median(Boston$ptratio)## [1] 19.05- We observe that census tract of Boston 399 has the lowest median value of the owner occupied homes feature with a high criminal rate. In addition, we observe that nitrogen oxide concentration is relatively high in suburb 399, which has below average rooms per dwelling. Overall, we may conclude that it may not be the best suburb to live in, but not the worst.
t(subset(Boston, medv == min(Boston$medv)))## 399 406
## crim 38.3518 67.9208
## zn 0.0000 0.0000
## indus 18.1000 18.1000
## chas 0.0000 0.0000
## nox 0.6930 0.6930
## rm 5.4530 5.6830
## age 100.0000 100.0000
## dis 1.4896 1.4254
## rad 24.0000 24.0000
## tax 666.0000 666.0000
## ptratio 20.2000 20.2000
## black 396.9000 384.9700
## lstat 30.5900 22.9800
## medv 5.0000 5.0000summary(Boston)## crim zn indus chas
## Min. : 0.00632 Min. : 0.00 Min. : 0.46 Min. :0.00000
## 1st Qu.: 0.08205 1st Qu.: 0.00 1st Qu.: 5.19 1st Qu.:0.00000
## Median : 0.25651 Median : 0.00 Median : 9.69 Median :0.00000
## Mean : 3.61352 Mean : 11.36 Mean :11.14 Mean :0.06917
## 3rd Qu.: 3.67708 3rd Qu.: 12.50 3rd Qu.:18.10 3rd Qu.:0.00000
## Max. :88.97620 Max. :100.00 Max. :27.74 Max. :1.00000
## nox rm age dis
## Min. :0.3850 Min. :3.561 Min. : 2.90 Min. : 1.130
## 1st Qu.:0.4490 1st Qu.:5.886 1st Qu.: 45.02 1st Qu.: 2.100
## Median :0.5380 Median :6.208 Median : 77.50 Median : 3.207
## Mean :0.5547 Mean :6.285 Mean : 68.57 Mean : 3.795
## 3rd Qu.:0.6240 3rd Qu.:6.623 3rd Qu.: 94.08 3rd Qu.: 5.188
## Max. :0.8710 Max. :8.780 Max. :100.00 Max. :12.127
## rad tax ptratio black
## Min. : 1.000 Min. :187.0 Min. :12.60 Min. : 0.32
## 1st Qu.: 4.000 1st Qu.:279.0 1st Qu.:17.40 1st Qu.:375.38
## Median : 5.000 Median :330.0 Median :19.05 Median :391.44
## Mean : 9.549 Mean :408.2 Mean :18.46 Mean :356.67
## 3rd Qu.:24.000 3rd Qu.:666.0 3rd Qu.:20.20 3rd Qu.:396.23
## Max. :24.000 Max. :711.0 Max. :22.00 Max. :396.90
## lstat medv
## Min. : 1.73 Min. : 5.00
## 1st Qu.: 6.95 1st Qu.:17.02
## Median :11.36 Median :21.20
## Mean :12.65 Mean :22.53
## 3rd Qu.:16.95 3rd Qu.:25.00
## Max. :37.97 Max. :50.00- We observe that there are 64 of the census tracts average more than seven rooms per dwelling and that there are 13 of the census tracts average more than seven rooms per dwelling. In summary, there are relatively lower crime and lower lstatcompared with range.
dim(subset(Boston, rm > 7))## [1] 64 14dim(subset(Boston, rm > 8))## [1] 13 14summary(subset(Boston, rm > 8))## crim zn indus chas
## Min. :0.02009 Min. : 0.00 Min. : 2.680 Min. :0.0000
## 1st Qu.:0.33147 1st Qu.: 0.00 1st Qu.: 3.970 1st Qu.:0.0000
## Median :0.52014 Median : 0.00 Median : 6.200 Median :0.0000
## Mean :0.71879 Mean :13.62 Mean : 7.078 Mean :0.1538
## 3rd Qu.:0.57834 3rd Qu.:20.00 3rd Qu.: 6.200 3rd Qu.:0.0000
## Max. :3.47428 Max. :95.00 Max. :19.580 Max. :1.0000
## nox rm age dis
## Min. :0.4161 Min. :8.034 Min. : 8.40 Min. :1.801
## 1st Qu.:0.5040 1st Qu.:8.247 1st Qu.:70.40 1st Qu.:2.288
## Median :0.5070 Median :8.297 Median :78.30 Median :2.894
## Mean :0.5392 Mean :8.349 Mean :71.54 Mean :3.430
## 3rd Qu.:0.6050 3rd Qu.:8.398 3rd Qu.:86.50 3rd Qu.:3.652
## Max. :0.7180 Max. :8.780 Max. :93.90 Max. :8.907
## rad tax ptratio black
## Min. : 2.000 Min. :224.0 Min. :13.00 Min. :354.6
## 1st Qu.: 5.000 1st Qu.:264.0 1st Qu.:14.70 1st Qu.:384.5
## Median : 7.000 Median :307.0 Median :17.40 Median :386.9
## Mean : 7.462 Mean :325.1 Mean :16.36 Mean :385.2
## 3rd Qu.: 8.000 3rd Qu.:307.0 3rd Qu.:17.40 3rd Qu.:389.7
## Max. :24.000 Max. :666.0 Max. :20.20 Max. :396.9
## lstat medv
## Min. :2.47 Min. :21.9
## 1st Qu.:3.32 1st Qu.:41.7
## Median :4.14 Median :48.3
## Mean :4.31 Mean :44.2
## 3rd Qu.:5.12 3rd Qu.:50.0
## Max. :7.44 Max. :50.0summary(Boston)## crim zn indus chas
## Min. : 0.00632 Min. : 0.00 Min. : 0.46 Min. :0.00000
## 1st Qu.: 0.08205 1st Qu.: 0.00 1st Qu.: 5.19 1st Qu.:0.00000
## Median : 0.25651 Median : 0.00 Median : 9.69 Median :0.00000
## Mean : 3.61352 Mean : 11.36 Mean :11.14 Mean :0.06917
## 3rd Qu.: 3.67708 3rd Qu.: 12.50 3rd Qu.:18.10 3rd Qu.:0.00000
## Max. :88.97620 Max. :100.00 Max. :27.74 Max. :1.00000
## nox rm age dis
## Min. :0.3850 Min. :3.561 Min. : 2.90 Min. : 1.130
## 1st Qu.:0.4490 1st Qu.:5.886 1st Qu.: 45.02 1st Qu.: 2.100
## Median :0.5380 Median :6.208 Median : 77.50 Median : 3.207
## Mean :0.5547 Mean :6.285 Mean : 68.57 Mean : 3.795
## 3rd Qu.:0.6240 3rd Qu.:6.623 3rd Qu.: 94.08 3rd Qu.: 5.188
## Max. :0.8710 Max. :8.780 Max. :100.00 Max. :12.127
## rad tax ptratio black
## Min. : 1.000 Min. :187.0 Min. :12.60 Min. : 0.32
## 1st Qu.: 4.000 1st Qu.:279.0 1st Qu.:17.40 1st Qu.:375.38
## Median : 5.000 Median :330.0 Median :19.05 Median :391.44
## Mean : 9.549 Mean :408.2 Mean :18.46 Mean :356.67
## 3rd Qu.:24.000 3rd Qu.:666.0 3rd Qu.:20.20 3rd Qu.:396.23
## Max. :24.000 Max. :711.0 Max. :22.00 Max. :396.90
## lstat medv
## Min. : 1.73 Min. : 5.00
## 1st Qu.: 6.95 1st Qu.:17.02
## Median :11.36 Median :21.20
## Mean :12.65 Mean :22.53
## 3rd Qu.:16.95 3rd Qu.:25.00
## Max. :37.97 Max. :50.00Excercise 4
#install.packages('mlbench') # if it is required.
library(mlbench)
data("Glass")
Glass1 <- Glass[,(1:9)]- Based on the histograms for each predictor shown below, we observe that several predictors are heavily skewed, especially for predictors Mg, K, Fe, and Ba. In what follows, we utlize the the correlation plot to visualize the correlations among these predictors.
#Histgrams before transformations to see how skewed the predictable variables are
par(mfrow=c(3,3))
hist(Glass1$RI, xlab = "RI",type = "count",main="Original")## Warning in plot.window(xlim, ylim, "", ...): graphical parameter "type" is
## obsolete## Warning in title(main = main, sub = sub, xlab = xlab, ylab = ylab, ...):
## graphical parameter "type" is obsolete## Warning in axis(1, ...): graphical parameter "type" is obsolete## Warning in axis(2, at = yt, ...): graphical parameter "type" is obsoletehist(Glass1$Na, xlab = "Na",type = "count", main="Original")## Warning in plot.window(xlim, ylim, "", ...): graphical parameter "type" is
## obsolete## Warning in title(main = main, sub = sub, xlab = xlab, ylab = ylab, ...):
## graphical parameter "type" is obsolete## Warning in axis(1, ...): graphical parameter "type" is obsolete## Warning in axis(2, at = yt, ...): graphical parameter "type" is obsoletehist(Glass1$Mg, xlab = "Mg",type = "count", main="Original")## Warning in plot.window(xlim, ylim, "", ...): graphical parameter "type" is
## obsolete## Warning in title(main = main, sub = sub, xlab = xlab, ylab = ylab, ...):
## graphical parameter "type" is obsolete## Warning in axis(1, ...): graphical parameter "type" is obsolete## Warning in axis(2, at = yt, ...): graphical parameter "type" is obsoletehist(Glass1$Al, xlab = "Al",type = "count", main="Original")## Warning in plot.window(xlim, ylim, "", ...): graphical parameter "type" is
## obsolete## Warning in title(main = main, sub = sub, xlab = xlab, ylab = ylab, ...):
## graphical parameter "type" is obsolete## Warning in axis(1, ...): graphical parameter "type" is obsolete## Warning in axis(2, at = yt, ...): graphical parameter "type" is obsoletehist(Glass1$Si, xlab = "Si",type = "count", main="Original")## Warning in plot.window(xlim, ylim, "", ...): graphical parameter "type" is
## obsolete## Warning in title(main = main, sub = sub, xlab = xlab, ylab = ylab, ...):
## graphical parameter "type" is obsolete## Warning in axis(1, ...): graphical parameter "type" is obsolete## Warning in axis(2, at = yt, ...): graphical parameter "type" is obsoletehist(Glass1$K, xlab = "K",type = "count", main="Original")## Warning in plot.window(xlim, ylim, "", ...): graphical parameter "type" is
## obsolete## Warning in title(main = main, sub = sub, xlab = xlab, ylab = ylab, ...):
## graphical parameter "type" is obsolete## Warning in axis(1, ...): graphical parameter "type" is obsolete## Warning in axis(2, at = yt, ...): graphical parameter "type" is obsoletehist(Glass1$Ca, xlab = "Ca",type = "count", main="Original")## Warning in plot.window(xlim, ylim, "", ...): graphical parameter "type" is
## obsolete## Warning in title(main = main, sub = sub, xlab = xlab, ylab = ylab, ...):
## graphical parameter "type" is obsolete## Warning in axis(1, ...): graphical parameter "type" is obsolete## Warning in axis(2, at = yt, ...): graphical parameter "type" is obsoletehist(Glass1$Ba, xlab = "Ba",type = "count", main="Original")## Warning in plot.window(xlim, ylim, "", ...): graphical parameter "type" is
## obsolete## Warning in title(main = main, sub = sub, xlab = xlab, ylab = ylab, ...):
## graphical parameter "type" is obsolete## Warning in axis(1, ...): graphical parameter "type" is obsolete## Warning in axis(2, at = yt, ...): graphical parameter "type" is obsoletehist(Glass1$Fe, xlab = "Fe",type = "count", main="Original")## Warning in plot.window(xlim, ylim, "", ...): graphical parameter "type" is
## obsolete## Warning in title(main = main, sub = sub, xlab = xlab, ylab = ylab, ...):
## graphical parameter "type" is obsolete## Warning in axis(1, ...): graphical parameter "type" is obsolete## Warning in axis(2, at = yt, ...): graphical parameter "type" is obsolete
We draw the scatter plot among the predictors as follows:
#Scatter plot for predictor variables
pairs(~Na+Mg+Al+Si+K+Ca+Ba+Fe, data=Glass1, main="Scatter Plot Matrix for Glass")
In addition, we can draw the correlation plot below and then find the high correlted predictors with a cutoff value of 0.75
#Correlation Matrix
glassCorr <- cor(Glass1[,1:9])
corrplot(glassCorr, method = "number", tl.cex = .35)
#correlation cutoff
highcorr <- findCorrelation(glassCorr, cutoff = .75)
head(highcorr)## [1] 7- We observe that many predictors contain outliers. In general, when the skewness of a predictor is in between -0.5 to 0.5, we may view the predictor to be symmetrical. As a result, the predictors Mg, K, Ba, and Fe are heavily skewed and the predictors K and Ba are most extremely skewed. Some data tranformation techniques may need to be implemented to deal with the skewness issue.
###Residuals/outliers
residuals <- Glass1[,1:9]
par(mfrow = c(3, 3))
for (i in 1:ncol(residuals)) {
boxplot(residuals[ ,i], ylab = names(residuals[i]), horizontal=T,
main = paste(names(residuals[i]), "Boxplot"), col="steelblue")}
- We observe from the following plot that the data transformation allows us to deal with the skewness of some predictors.
#calculate skewness
skewed <- apply(Glass1[,1:9],2, skewness)
skewed## RI Na Mg Al Si K Ca
## 1.6027151 0.4478343 -1.1364523 0.8946104 -0.7202392 6.4600889 2.0184463
## Ba Fe
## 3.3686800 1.7298107#As an illustration, we consider the data transformation for Ca
#Histograms before & after transformations
par(mfrow = c(1, 2))
hist(Glass1$Ca, prob = T, main = "Original")
hist(1/Glass1$Ca, prob = T, main = "Transformation")
Exercise 5
- Removing predictors with degenerate distributions (near-zero variance predictor) could be a significant improvement in model performance and/or stability without the problematic variables. There are three degenerate predictors: leaf.mild, mycelium, and sclerotia.
#loading the data
data(Soybean)
summary(Soybean)## Class date plant.stand precip temp
## brown-spot : 92 5 :149 0 :354 0 : 74 0 : 80
## alternarialeaf-spot: 91 4 :131 1 :293 1 :112 1 :374
## frog-eye-leaf-spot : 91 3 :118 NA's: 36 2 :459 2 :199
## phytophthora-rot : 88 2 : 93 NA's: 38 NA's: 30
## anthracnose : 44 6 : 90
## brown-stem-rot : 44 (Other):101
## (Other) :233 NA's : 1
## hail crop.hist area.dam sever seed.tmt germ plant.growth
## 0 :435 0 : 65 0 :123 0 :195 0 :305 0 :165 0 :441
## 1 :127 1 :165 1 :227 1 :322 1 :222 1 :213 1 :226
## NA's:121 2 :219 2 :145 2 : 45 2 : 35 2 :193 NA's: 16
## 3 :218 3 :187 NA's:121 NA's:121 NA's:112
## NA's: 16 NA's: 1
##
##
## leaves leaf.halo leaf.marg leaf.size leaf.shread leaf.malf leaf.mild
## 0: 77 0 :221 0 :357 0 : 51 0 :487 0 :554 0 :535
## 1:606 1 : 36 1 : 21 1 :327 1 : 96 1 : 45 1 : 20
## 2 :342 2 :221 2 :221 NA's:100 NA's: 84 2 : 20
## NA's: 84 NA's: 84 NA's: 84 NA's:108
##
##
##
## stem lodging stem.cankers canker.lesion fruiting.bodies ext.decay
## 0 :296 0 :520 0 :379 0 :320 0 :473 0 :497
## 1 :371 1 : 42 1 : 39 1 : 83 1 :104 1 :135
## NA's: 16 NA's:121 2 : 36 2 :177 NA's:106 2 : 13
## 3 :191 3 : 65 NA's: 38
## NA's: 38 NA's: 38
##
##
## mycelium int.discolor sclerotia fruit.pods fruit.spots seed
## 0 :639 0 :581 0 :625 0 :407 0 :345 0 :476
## 1 : 6 1 : 44 1 : 20 1 :130 1 : 75 1 :115
## NA's: 38 2 : 20 NA's: 38 2 : 14 2 : 57 NA's: 92
## NA's: 38 3 : 48 4 :100
## NA's: 84 NA's:106
##
##
## mold.growth seed.discolor seed.size shriveling roots
## 0 :524 0 :513 0 :532 0 :539 0 :551
## 1 : 67 1 : 64 1 : 59 1 : 38 1 : 86
## NA's: 92 NA's:106 NA's: 92 NA's:106 2 : 15
## NA's: 31
##
##
## #frequency of predictors
par(mfrow = c(3,3))
for(i in 2:ncol(Soybean)) {
plot(Soybean[i], main = colnames(Soybean[i]))}
#Near Zero Variance
nearZeroVar(Soybean)## [1] 19 26 28names(Soybean[nearZeroVar(Soybean)])## [1] "leaf.mild" "mycelium" "sclerotia"- The plot_missing() reveals the predictor with its missing percentage. The different Classes were summarized and of Class, out of the 19 only 4 have the missing values. Those 4 with missing values were the class of phytophthora-rot having the maximum of missing values, ~121. As a result, we may conclude that there is an indication of a pattern between missing values and Classes.
#find missing predictors by column
colSums(is.na(Soybean))## Class date plant.stand precip temp
## 0 1 36 38 30
## hail crop.hist area.dam sever seed.tmt
## 121 16 1 121 121
## germ plant.growth leaves leaf.halo leaf.marg
## 112 16 0 84 84
## leaf.size leaf.shread leaf.malf leaf.mild stem
## 84 100 84 108 16
## lodging stem.cankers canker.lesion fruiting.bodies ext.decay
## 121 38 38 106 38
## mycelium int.discolor sclerotia fruit.pods fruit.spots
## 38 38 38 84 106
## seed mold.growth seed.discolor seed.size shriveling
## 92 92 106 92 106
## roots
## 31#graph of missing data
library(DataExplorer)## Warning: package 'DataExplorer' was built under R version 4.2.3plot_missing(Soybean)
#sort/filter missing data together
#check for missing values of each predictor.
sapply(Soybean, function(x) sum(is.na(x)))## Class date plant.stand precip temp
## 0 1 36 38 30
## hail crop.hist area.dam sever seed.tmt
## 121 16 1 121 121
## germ plant.growth leaves leaf.halo leaf.marg
## 112 16 0 84 84
## leaf.size leaf.shread leaf.malf leaf.mild stem
## 84 100 84 108 16
## lodging stem.cankers canker.lesion fruiting.bodies ext.decay
## 121 38 38 106 38
## mycelium int.discolor sclerotia fruit.pods fruit.spots
## 38 38 38 84 106
## seed mold.growth seed.discolor seed.size shriveling
## 92 92 106 92 106
## roots
## 31- Before developing a strategy for handling missing data, either by eliminating predictors or imputation, we need to visualize the missing pattern in detail below
library(VIM)## Warning: package 'VIM' was built under R version 4.2.3## Loading required package: colorspace## Loading required package: grid## VIM is ready to use.## Suggestions and bug-reports can be submitted at: https://github.com/statistikat/VIM/issues##
## Attaching package: 'VIM'## The following object is masked from 'package:datasets':
##
## sleepaggr(Soybean, col=c('navyblue','red'),
numbers=TRUE, sortVars=TRUE,
combined = TRUE,
prop = FALSE,
only.miss = TRUE,
labels=names(Soybean),
cex.axis=.7, gap=3,
ylab=c("Missing Data"))
##
## Variables sorted by number of missings:
## Variable Count
## hail 121
## sever 121
## seed.tmt 121
## lodging 121
## germ 112
## leaf.mild 108
## fruiting.bodies 106
## fruit.spots 106
## seed.discolor 106
## shriveling 106
## leaf.shread 100
## seed 92
## mold.growth 92
## seed.size 92
## leaf.halo 84
## leaf.marg 84
## leaf.size 84
## leaf.malf 84
## fruit.pods 84
## precip 38
## stem.cankers 38
## canker.lesion 38
## ext.decay 38
## mycelium 38
## int.discolor 38
## sclerotia 38
## plant.stand 36
## roots 31
## temp 30
## crop.hist 16
## plant.growth 16
## stem 16
## date 1
## area.dam 1
## Class 0
## leaves 0library(mice)## Warning: package 'mice' was built under R version 4.2.3##
## Attaching package: 'mice'## The following object is masked from 'package:stats':
##
## filter## The following objects are masked from 'package:base':
##
## cbind, rbindset.seed(1)
missingSoybeans <- mice(Soybean, method = "pmm", printFlag = F, seed =112)## Warning: Number of logged events: 1662names(missingSoybeans)## [1] "data" "imp" "m" "where"
## [5] "blocks" "call" "nmis" "method"
## [9] "predictorMatrix" "visitSequence" "formulas" "post"
## [13] "blots" "ignore" "seed" "iteration"
## [17] "lastSeedValue" "chainMean" "chainVar" "loggedEvents"
## [21] "version" "date"summary(missingSoybeans)## Class: mids
## Number of multiple imputations: 5
## Imputation methods:
## Class date plant.stand precip temp
## "" "pmm" "pmm" "pmm" "pmm"
## hail crop.hist area.dam sever seed.tmt
## "pmm" "pmm" "pmm" "pmm" "pmm"
## germ plant.growth leaves leaf.halo leaf.marg
## "pmm" "pmm" "" "pmm" "pmm"
## leaf.size leaf.shread leaf.malf leaf.mild stem
## "pmm" "pmm" "pmm" "pmm" "pmm"
## lodging stem.cankers canker.lesion fruiting.bodies ext.decay
## "pmm" "pmm" "pmm" "pmm" "pmm"
## mycelium int.discolor sclerotia fruit.pods fruit.spots
## "pmm" "pmm" "pmm" "pmm" "pmm"
## seed mold.growth seed.discolor seed.size shriveling
## "pmm" "pmm" "pmm" "pmm" "pmm"
## roots
## "pmm"
## PredictorMatrix:
## Class date plant.stand precip temp hail crop.hist area.dam sever
## Class 0 1 1 1 1 1 1 1 1
## date 1 0 1 1 1 1 1 1 1
## plant.stand 1 1 0 1 1 1 1 1 1
## precip 1 1 1 0 1 1 1 1 1
## temp 1 1 1 1 0 1 1 1 1
## hail 1 1 1 1 1 0 1 1 1
## seed.tmt germ plant.growth leaves leaf.halo leaf.marg leaf.size
## Class 1 1 1 1 1 1 1
## date 1 1 1 1 1 1 1
## plant.stand 1 1 1 1 1 1 1
## precip 1 1 1 1 1 1 1
## temp 1 1 1 1 1 1 1
## hail 1 1 1 1 1 1 1
## leaf.shread leaf.malf leaf.mild stem lodging stem.cankers
## Class 1 1 1 1 1 1
## date 1 1 1 1 1 1
## plant.stand 1 1 1 1 1 1
## precip 1 1 1 1 1 1
## temp 1 1 1 1 1 1
## hail 1 1 1 1 1 1
## canker.lesion fruiting.bodies ext.decay mycelium int.discolor
## Class 1 1 1 1 1
## date 1 1 1 1 1
## plant.stand 1 1 1 1 1
## precip 1 1 1 1 1
## temp 1 1 1 1 1
## hail 1 1 1 1 1
## sclerotia fruit.pods fruit.spots seed mold.growth seed.discolor
## Class 1 1 1 1 1 1
## date 1 1 1 1 1 1
## plant.stand 1 1 1 1 1 1
## precip 1 1 1 1 1 1
## temp 1 1 1 1 1 1
## hail 1 1 1 1 1 1
## seed.size shriveling roots
## Class 1 1 1
## date 1 1 1
## plant.stand 1 1 1
## precip 1 1 1
## temp 1 1 1
## hail 1 1 1
## Number of logged events: 1662
## it im dep meth
## 1 1 1 plant.stand pmm
## 2 1 1 precip pmm
## 3 1 1 precip pmm
## 4 1 1 temp pmm
## 5 1 1 temp pmm
## 6 1 1 hail pmm
## out
## 1 Classcharcoal-rot, Classcyst-nematode, int.discolor1, sclerotia1
## 2 Classbrown-spot, Classcharcoal-rot, Classcyst-nematode, Classdiaporthe-pod-&-stem-blight, Classherbicide-injury, fruit.pods3
## 3 mice detected that your data are (nearly) multi-collinear.\nIt applied a ridge penalty to continue calculations, but the results can be unstable.\nDoes your dataset contain duplicates, linear transformation, or factors with unique respondent names?
## 4 Classbrown-spot, Classcyst-nematode, int.discolor1, fruit.pods2
## 5 mice detected that your data are (nearly) multi-collinear.\nIt applied a ridge penalty to continue calculations, but the results can be unstable.\nDoes your dataset contain duplicates, linear transformation, or factors with unique respondent names?
## 6 Classbrown-spot, Classcharcoal-rot, Classcyst-nematode, Classdiaporthe-pod-&-stem-blight, Classherbicide-injury, Classpurple-seed-stain, leaf.marg1, lodging1, stem.cankers2, ext.decay2, sclerotia1, fruit.pods2, seed1#visualize after imputation to see if missing data remains
md.pattern(missingSoybeans$predictorMatrix)## /\ /\
## { `---' }
## { O O }
## ==> V <== No need for mice. This data set is completely observed.
## \ \|/ /
## `-----'
## Class date plant.stand precip temp hail crop.hist area.dam sever seed.tmt
## 36 1 1 1 1 1 1 1 1 1 1
## 0 0 0 0 0 0 0 0 0 0
## germ plant.growth leaves leaf.halo leaf.marg leaf.size leaf.shread leaf.malf
## 36 1 1 1 1 1 1 1 1
## 0 0 0 0 0 0 0 0
## leaf.mild stem lodging stem.cankers canker.lesion fruiting.bodies ext.decay
## 36 1 1 1 1 1 1 1
## 0 0 0 0 0 0 0
## mycelium int.discolor sclerotia fruit.pods fruit.spots seed mold.growth
## 36 1 1 1 1 1 1 1
## 0 0 0 0 0 0 0
## seed.discolor seed.size shriveling roots
## 36 1 1 1 1 0
## 0 0 0 0 0