Diabetes_Classification Modeling
August 2019
Description
Diabetes is a disease that affects your body’s ability to produce or use insulin. Insulin is a hormone. When your body turns the food you eat into energy (also called sugar or glucose), insulin is released to help transport this energy to the cells. Insulin acts as a “key.” Its chemical message tells the cell to open and receive glucose. If you produce little or no insulin, or are insulin resistant, too much sugar remains in your blood. Blood glucose levels are higher than normal for individuals with diabetes. There are two main types of diabetes: Type 1 and Type 2.
Dataset source
Based on several studies, a commonly used dataset was the Pima Indians Diabetes Dataset from the University of California, Irvine (UCI) Machine Learning Database This dataset describes the medical records for female patients at least 21 years old of Pima Indian heritage
library(tidyverse)## -- Attaching packages --------------------------------------------------------------- tidyverse 1.2.1 --## v ggplot2 3.2.0 v purrr 0.3.2
## v tibble 2.1.3 v dplyr 0.8.3
## v tidyr 0.8.3 v stringr 1.4.0
## v readr 1.3.1 v forcats 0.4.0## -- Conflicts ------------------------------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()library(DataExplorer)
library(funModeling) ## Loading required package: Hmisc## Loading required package: lattice## Loading required package: survival## Loading required package: Formula##
## Attaching package: 'Hmisc'## The following objects are masked from 'package:dplyr':
##
## src, summarize## The following objects are masked from 'package:base':
##
## format.pval, units## funModeling v.1.8 :)
## Examples and tutorials at livebook.datascienceheroes.comlibrary(ggplot2)
library(corrplot)## corrplot 0.84 loadedlibrary(caret)##
## Attaching package: 'caret'## The following object is masked from 'package:survival':
##
## cluster## The following object is masked from 'package:purrr':
##
## liftlibrary(caretEnsemble)##
## Attaching package: 'caretEnsemble'## The following object is masked from 'package:ggplot2':
##
## autoplotlibrary(psych)##
## Attaching package: 'psych'## The following object is masked from 'package:Hmisc':
##
## describe## The following objects are masked from 'package:ggplot2':
##
## %+%, alphalibrary(Amelia)## Loading required package: Rcpp## ##
## ## Amelia II: Multiple Imputation
## ## (Version 1.7.5, built: 2018-05-07)
## ## Copyright (C) 2005-2019 James Honaker, Gary King and Matthew Blackwell
## ## Refer to http://gking.harvard.edu/amelia/ for more information
## ##library(mice)##
## Attaching package: 'mice'## The following object is masked from 'package:tidyr':
##
## complete## The following objects are masked from 'package:base':
##
## cbind, rbindlibrary(GGally)## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2##
## Attaching package: 'GGally'## The following object is masked from 'package:funModeling':
##
## range01## The following object is masked from 'package:dplyr':
##
## nasalibrary(rpart)
library(randomForest)## randomForest 4.6-14## Type rfNews() to see new features/changes/bug fixes.##
## Attaching package: 'randomForest'## The following object is masked from 'package:psych':
##
## outlier## The following object is masked from 'package:dplyr':
##
## combine## The following object is masked from 'package:ggplot2':
##
## marginlibrary(dplyr)
library(heplots)## Loading required package: car## Loading required package: carData## Registered S3 methods overwritten by 'car':
## method from
## influence.merMod lme4
## cooks.distance.influence.merMod lme4
## dfbeta.influence.merMod lme4
## dfbetas.influence.merMod lme4##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logit## The following object is masked from 'package:dplyr':
##
## recode## The following object is masked from 'package:purrr':
##
## somelibrary(candisc)##
## Attaching package: 'candisc'## The following object is masked from 'package:stats':
##
## cancor##Loading dataset and overview
Fields description follow:
preg = Number of times pregnant
plas = Plasma glucose concentration a 2 hours in an oral glucose tolerance test
pres = Diastolic blood pressure (mm Hg)
skin = Triceps skin fold thickness (mm)
test = 2-Hour serum insulin (mu U/ml)
mass = Body mass index (weight in kg/(height in m)^2)
pedi = Diabetes pedigree function
age = Age (years)
outcome = Class variable (1:tested positive for diabetes, 0: tested negative for diabetes)
##——————–
# loading data (.csv)
diabetes <- read_csv("C:/Users/Joe/Documents/Datasets/diabetes.csv")## Parsed with column specification:
## cols(
## Pregnancies = col_double(),
## Glucose = col_double(),
## BloodPressure = col_double(),
## SkinThickness = col_double(),
## Insulin = col_double(),
## BMI = col_double(),
## DiabetesPedigreeFunction = col_double(),
## Age = col_double(),
## Outcome = col_double()
## )diabetes$Outcome <- factor(diabetes$Outcome, levels = c(0,1), labels = c("False", "True"))
dim(diabetes)## [1] 768 9summary(diabetes)## Pregnancies Glucose BloodPressure SkinThickness
## Min. : 0.000 Min. : 0.0 Min. : 0.00 Min. : 0.00
## 1st Qu.: 1.000 1st Qu.: 99.0 1st Qu.: 62.00 1st Qu.: 0.00
## Median : 3.000 Median :117.0 Median : 72.00 Median :23.00
## Mean : 3.845 Mean :120.9 Mean : 69.11 Mean :20.54
## 3rd Qu.: 6.000 3rd Qu.:140.2 3rd Qu.: 80.00 3rd Qu.:32.00
## Max. :17.000 Max. :199.0 Max. :122.00 Max. :99.00
## Insulin BMI DiabetesPedigreeFunction Age
## Min. : 0.0 Min. : 0.00 Min. :0.0780 Min. :21.00
## 1st Qu.: 0.0 1st Qu.:27.30 1st Qu.:0.2437 1st Qu.:24.00
## Median : 30.5 Median :32.00 Median :0.3725 Median :29.00
## Mean : 79.8 Mean :31.99 Mean :0.4719 Mean :33.24
## 3rd Qu.:127.2 3rd Qu.:36.60 3rd Qu.:0.6262 3rd Qu.:41.00
## Max. :846.0 Max. :67.10 Max. :2.4200 Max. :81.00
## Outcome
## False:500
## True :268
##
##
##
## table(diabetes$Outcome)##
## False True
## 500 268str(diabetes)## Classes 'spec_tbl_df', 'tbl_df', 'tbl' and 'data.frame': 768 obs. of 9 variables:
## $ Pregnancies : num 6 1 8 1 0 5 3 10 2 8 ...
## $ Glucose : num 148 85 183 89 137 116 78 115 197 125 ...
## $ BloodPressure : num 72 66 64 66 40 74 50 0 70 96 ...
## $ SkinThickness : num 35 29 0 23 35 0 32 0 45 0 ...
## $ Insulin : num 0 0 0 94 168 0 88 0 543 0 ...
## $ BMI : num 33.6 26.6 23.3 28.1 43.1 25.6 31 35.3 30.5 0 ...
## $ DiabetesPedigreeFunction: num 0.627 0.351 0.672 0.167 2.288 ...
## $ Age : num 50 31 32 21 33 30 26 29 53 54 ...
## $ Outcome : Factor w/ 2 levels "False","True": 2 1 2 1 2 1 2 1 2 2 ...
## - attr(*, "spec")=
## .. cols(
## .. Pregnancies = col_double(),
## .. Glucose = col_double(),
## .. BloodPressure = col_double(),
## .. SkinThickness = col_double(),
## .. Insulin = col_double(),
## .. BMI = col_double(),
## .. DiabetesPedigreeFunction = col_double(),
## .. Age = col_double(),
## .. Outcome = col_double()
## .. )glimpse(diabetes)## Observations: 768
## Variables: 9
## $ Pregnancies <dbl> 6, 1, 8, 1, 0, 5, 3, 10, 2, 8, 4, 10,...
## $ Glucose <dbl> 148, 85, 183, 89, 137, 116, 78, 115, ...
## $ BloodPressure <dbl> 72, 66, 64, 66, 40, 74, 50, 0, 70, 96...
## $ SkinThickness <dbl> 35, 29, 0, 23, 35, 0, 32, 0, 45, 0, 0...
## $ Insulin <dbl> 0, 0, 0, 94, 168, 0, 88, 0, 543, 0, 0...
## $ BMI <dbl> 33.6, 26.6, 23.3, 28.1, 43.1, 25.6, 3...
## $ DiabetesPedigreeFunction <dbl> 0.627, 0.351, 0.672, 0.167, 2.288, 0....
## $ Age <dbl> 50, 31, 32, 21, 33, 30, 26, 29, 53, 5...
## $ Outcome <fct> True, False, True, False, True, False...head(diabetes)## # A tibble: 6 x 9
## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 6 148 72 35 0 33.6
## 2 1 85 66 29 0 26.6
## 3 8 183 64 0 0 23.3
## 4 1 89 66 23 94 28.1
## 5 0 137 40 35 168 43.1
## 6 5 116 74 0 0 25.6
## # ... with 3 more variables: DiabetesPedigreeFunction <dbl>, Age <dbl>,
## # Outcome <fct>df_status(diabetes)## variable q_zeros p_zeros q_na p_na q_inf p_inf type
## 1 Pregnancies 111 14.45 0 0 0 0 numeric
## 2 Glucose 5 0.65 0 0 0 0 numeric
## 3 BloodPressure 35 4.56 0 0 0 0 numeric
## 4 SkinThickness 227 29.56 0 0 0 0 numeric
## 5 Insulin 374 48.70 0 0 0 0 numeric
## 6 BMI 11 1.43 0 0 0 0 numeric
## 7 DiabetesPedigreeFunction 0 0.00 0 0 0 0 numeric
## 8 Age 0 0.00 0 0 0 0 numeric
## 9 Outcome 0 0.00 0 0 0 0 factor
## unique
## 1 17
## 2 136
## 3 47
## 4 51
## 5 186
## 6 248
## 7 517
## 8 52
## 9 2ggplot(diabetes, aes(Outcome,BMI))+geom_boxplot()
ggplot(diabetes, aes(Pregnancies,Glucose, col=Outcome))+geom_point()
ggplot(diabetes, aes(BMI,Age ,col=Outcome))+geom_point()
- Glucose and Outcome Notice zero values in Glucose column
ggplot(diabetes, aes(Glucose))+
geom_bar(aes(group=Outcome,fill=Outcome)) + facet_wrap(~Outcome) 
2. Blood Pressure and Outcome
—Notice count number for zero values —
ggplot(diabetes, aes(BloodPressure))+
geom_bar(aes(group=Outcome,fill=Outcome)) + facet_wrap(~Outcome) 
Skin Thickness and Outcome
Notice very high number of zero values
ggplot(diabetes, aes(SkinThickness))+
geom_bar(aes(group=Outcome,fill=Outcome)) + facet_wrap(~Outcome) 
4. Insulin and Outcome
Notice very high number of zero values
ggplot(diabetes, aes(Insulin))+
geom_bar(aes(group=Outcome,fill=Outcome)) + facet_wrap(~Outcome) 
- BMI and Outcome Notice very high count of zero values
ggplot(diabetes, aes(BMI))+
geom_bar(aes(group=Outcome,fill=Outcome)) + facet_wrap(~Outcome) 
- Pedigree Function and Outcome
ggplot(diabetes, aes(DiabetesPedigreeFunction))+
geom_bar(aes(group=Outcome,fill=Outcome)) + facet_wrap(~Outcome) 
Age and Outcome
Notice the imbalance
ggplot(diabetes, aes(Age))+
geom_bar(aes(group=Outcome,fill=Outcome)) + facet_wrap(~Outcome) 
Correlations between variables ( excluding column Outcome)
dia_corr <- cor(diabetes[,-9])
corrplot(dia_corr, method="number")
## ## zero is meaningful for number of pregnancies ## Replacing zero values with NA in other variable ( columns)
diabetes[, 2:7][diabetes[, 2:7] == 0] <- NA
plot_missing(diabetes)
library(naniar)
gg_miss_var(diabetes)
sort(sapply(diabetes, function(x) { sum(is.na(x)) }), decreasing=TRUE)## Insulin SkinThickness BloodPressure
## 374 227 35
## BMI Glucose Pregnancies
## 11 5 0
## DiabetesPedigreeFunction Age Outcome
## 0 0 0NA values : Insulin column has not number of NA with 48.7%
Skin Thickness zero value = 29,56%
Using MICE package to replace NA values
## Load mice package for Multivariate Imputation by Chained Equations (MICE)
library(mice)
md.pattern(diabetes)
## Pregnancies DiabetesPedigreeFunction Age Outcome Glucose BMI
## 392 1 1 1 1 1 1
## 140 1 1 1 1 1 1
## 192 1 1 1 1 1 1
## 2 1 1 1 1 1 1
## 26 1 1 1 1 1 1
## 1 1 1 1 1 1 0
## 1 1 1 1 1 1 0
## 2 1 1 1 1 1 0
## 7 1 1 1 1 1 0
## 1 1 1 1 1 0 1
## 4 1 1 1 1 0 1
## 0 0 0 0 5 11
## BloodPressure SkinThickness Insulin
## 392 1 1 1 0
## 140 1 1 0 1
## 192 1 0 0 2
## 2 0 1 0 2
## 26 0 0 0 3
## 1 1 1 1 1
## 1 1 1 0 2
## 2 1 0 0 3
## 7 0 0 0 4
## 1 1 1 1 1
## 4 1 1 0 2
## 35 227 374 652## in number
library(VIM)## Loading required package: colorspace## Loading required package: grid## Loading required package: data.table##
## Attaching package: 'data.table'## The following objects are masked from 'package:dplyr':
##
## between, first, last## The following object is masked from 'package:purrr':
##
## transpose## VIM is ready to use.
## Since version 4.0.0 the GUI is in its own package VIMGUI.
##
## Please use the package to use the new (and old) GUI.## Suggestions and bug-reports can be submitted at: https://github.com/alexkowa/VIM/issues##
## Attaching package: 'VIM'## The following object is masked from 'package:datasets':
##
## sleepaggr(diabetes, prop = F, numbers = T)
scattmatrixMiss(diabetes, interactive = F, highlight = c("Insulin"))
Imputing the missing data
The mice() function takes care of the imputing process imputting values for variable —- except number of pregnancies and outcome
creating a separate dataset for outcome
tempData <- mice(diabetes[,-c(1,9)],m=5,maxit=50,meth='pmm',seed=500)##
## iter imp variable
## 1 1 Glucose BloodPressure SkinThickness Insulin BMI
## 1 2 Glucose BloodPressure SkinThickness Insulin BMI
## 1 3 Glucose BloodPressure SkinThickness Insulin BMI
## 1 4 Glucose BloodPressure SkinThickness Insulin BMI
## 1 5 Glucose BloodPressure SkinThickness Insulin BMI
## 2 1 Glucose BloodPressure SkinThickness Insulin BMI
## 2 2 Glucose BloodPressure SkinThickness Insulin BMI
## 2 3 Glucose BloodPressure SkinThickness Insulin BMI
## 2 4 Glucose BloodPressure SkinThickness Insulin BMI
## 2 5 Glucose BloodPressure SkinThickness Insulin BMI
## 3 1 Glucose BloodPressure SkinThickness Insulin BMI
## 3 2 Glucose BloodPressure SkinThickness Insulin BMI
## 3 3 Glucose BloodPressure SkinThickness Insulin BMI
## 3 4 Glucose BloodPressure SkinThickness Insulin BMI
## 3 5 Glucose BloodPressure SkinThickness Insulin BMI
## 4 1 Glucose BloodPressure SkinThickness Insulin BMI
## 4 2 Glucose BloodPressure SkinThickness Insulin BMI
## 4 3 Glucose BloodPressure SkinThickness Insulin BMI
## 4 4 Glucose BloodPressure SkinThickness Insulin BMI
## 4 5 Glucose BloodPressure SkinThickness Insulin BMI
## 5 1 Glucose BloodPressure SkinThickness Insulin BMI
## 5 2 Glucose BloodPressure SkinThickness Insulin BMI
## 5 3 Glucose BloodPressure SkinThickness Insulin BMI
## 5 4 Glucose BloodPressure SkinThickness Insulin BMI
## 5 5 Glucose BloodPressure SkinThickness Insulin BMI
## 6 1 Glucose BloodPressure SkinThickness Insulin BMI
## 6 2 Glucose BloodPressure SkinThickness Insulin BMI
## 6 3 Glucose BloodPressure SkinThickness Insulin BMI
## 6 4 Glucose BloodPressure SkinThickness Insulin BMI
## 6 5 Glucose BloodPressure SkinThickness Insulin BMI
## 7 1 Glucose BloodPressure SkinThickness Insulin BMI
## 7 2 Glucose BloodPressure SkinThickness Insulin BMI
## 7 3 Glucose BloodPressure SkinThickness Insulin BMI
## 7 4 Glucose BloodPressure SkinThickness Insulin BMI
## 7 5 Glucose BloodPressure SkinThickness Insulin BMI
## 8 1 Glucose BloodPressure SkinThickness Insulin BMI
## 8 2 Glucose BloodPressure SkinThickness Insulin BMI
## 8 3 Glucose BloodPressure SkinThickness Insulin BMI
## 8 4 Glucose BloodPressure SkinThickness Insulin BMI
## 8 5 Glucose BloodPressure SkinThickness Insulin BMI
## 9 1 Glucose BloodPressure SkinThickness Insulin BMI
## 9 2 Glucose BloodPressure SkinThickness Insulin BMI
## 9 3 Glucose BloodPressure SkinThickness Insulin BMI
## 9 4 Glucose BloodPressure SkinThickness Insulin BMI
## 9 5 Glucose BloodPressure SkinThickness Insulin BMI
## 10 1 Glucose BloodPressure SkinThickness Insulin BMI
## 10 2 Glucose BloodPressure SkinThickness Insulin BMI
## 10 3 Glucose BloodPressure SkinThickness Insulin BMI
## 10 4 Glucose BloodPressure SkinThickness Insulin BMI
## 10 5 Glucose BloodPressure SkinThickness Insulin BMI
## 11 1 Glucose BloodPressure SkinThickness Insulin BMI
## 11 2 Glucose BloodPressure SkinThickness Insulin BMI
## 11 3 Glucose BloodPressure SkinThickness Insulin BMI
## 11 4 Glucose BloodPressure SkinThickness Insulin BMI
## 11 5 Glucose BloodPressure SkinThickness Insulin BMI
## 12 1 Glucose BloodPressure SkinThickness Insulin BMI
## 12 2 Glucose BloodPressure SkinThickness Insulin BMI
## 12 3 Glucose BloodPressure SkinThickness Insulin BMI
## 12 4 Glucose BloodPressure SkinThickness Insulin BMI
## 12 5 Glucose BloodPressure SkinThickness Insulin BMI
## 13 1 Glucose BloodPressure SkinThickness Insulin BMI
## 13 2 Glucose BloodPressure SkinThickness Insulin BMI
## 13 3 Glucose BloodPressure SkinThickness Insulin BMI
## 13 4 Glucose BloodPressure SkinThickness Insulin BMI
## 13 5 Glucose BloodPressure SkinThickness Insulin BMI
## 14 1 Glucose BloodPressure SkinThickness Insulin BMI
## 14 2 Glucose BloodPressure SkinThickness Insulin BMI
## 14 3 Glucose BloodPressure SkinThickness Insulin BMI
## 14 4 Glucose BloodPressure SkinThickness Insulin BMI
## 14 5 Glucose BloodPressure SkinThickness Insulin BMI
## 15 1 Glucose BloodPressure SkinThickness Insulin BMI
## 15 2 Glucose BloodPressure SkinThickness Insulin BMI
## 15 3 Glucose BloodPressure SkinThickness Insulin BMI
## 15 4 Glucose BloodPressure SkinThickness Insulin BMI
## 15 5 Glucose BloodPressure SkinThickness Insulin BMI
## 16 1 Glucose BloodPressure SkinThickness Insulin BMI
## 16 2 Glucose BloodPressure SkinThickness Insulin BMI
## 16 3 Glucose BloodPressure SkinThickness Insulin BMI
## 16 4 Glucose BloodPressure SkinThickness Insulin BMI
## 16 5 Glucose BloodPressure SkinThickness Insulin BMI
## 17 1 Glucose BloodPressure SkinThickness Insulin BMI
## 17 2 Glucose BloodPressure SkinThickness Insulin BMI
## 17 3 Glucose BloodPressure SkinThickness Insulin BMI
## 17 4 Glucose BloodPressure SkinThickness Insulin BMI
## 17 5 Glucose BloodPressure SkinThickness Insulin BMI
## 18 1 Glucose BloodPressure SkinThickness Insulin BMI
## 18 2 Glucose BloodPressure SkinThickness Insulin BMI
## 18 3 Glucose BloodPressure SkinThickness Insulin BMI
## 18 4 Glucose BloodPressure SkinThickness Insulin BMI
## 18 5 Glucose BloodPressure SkinThickness Insulin BMI
## 19 1 Glucose BloodPressure SkinThickness Insulin BMI
## 19 2 Glucose BloodPressure SkinThickness Insulin BMI
## 19 3 Glucose BloodPressure SkinThickness Insulin BMI
## 19 4 Glucose BloodPressure SkinThickness Insulin BMI
## 19 5 Glucose BloodPressure SkinThickness Insulin BMI
## 20 1 Glucose BloodPressure SkinThickness Insulin BMI
## 20 2 Glucose BloodPressure SkinThickness Insulin BMI
## 20 3 Glucose BloodPressure SkinThickness Insulin BMI
## 20 4 Glucose BloodPressure SkinThickness Insulin BMI
## 20 5 Glucose BloodPressure SkinThickness Insulin BMI
## 21 1 Glucose BloodPressure SkinThickness Insulin BMI
## 21 2 Glucose BloodPressure SkinThickness Insulin BMI
## 21 3 Glucose BloodPressure SkinThickness Insulin BMI
## 21 4 Glucose BloodPressure SkinThickness Insulin BMI
## 21 5 Glucose BloodPressure SkinThickness Insulin BMI
## 22 1 Glucose BloodPressure SkinThickness Insulin BMI
## 22 2 Glucose BloodPressure SkinThickness Insulin BMI
## 22 3 Glucose BloodPressure SkinThickness Insulin BMI
## 22 4 Glucose BloodPressure SkinThickness Insulin BMI
## 22 5 Glucose BloodPressure SkinThickness Insulin BMI
## 23 1 Glucose BloodPressure SkinThickness Insulin BMI
## 23 2 Glucose BloodPressure SkinThickness Insulin BMI
## 23 3 Glucose BloodPressure SkinThickness Insulin BMI
## 23 4 Glucose BloodPressure SkinThickness Insulin BMI
## 23 5 Glucose BloodPressure SkinThickness Insulin BMI
## 24 1 Glucose BloodPressure SkinThickness Insulin BMI
## 24 2 Glucose BloodPressure SkinThickness Insulin BMI
## 24 3 Glucose BloodPressure SkinThickness Insulin BMI
## 24 4 Glucose BloodPressure SkinThickness Insulin BMI
## 24 5 Glucose BloodPressure SkinThickness Insulin BMI
## 25 1 Glucose BloodPressure SkinThickness Insulin BMI
## 25 2 Glucose BloodPressure SkinThickness Insulin BMI
## 25 3 Glucose BloodPressure SkinThickness Insulin BMI
## 25 4 Glucose BloodPressure SkinThickness Insulin BMI
## 25 5 Glucose BloodPressure SkinThickness Insulin BMI
## 26 1 Glucose BloodPressure SkinThickness Insulin BMI
## 26 2 Glucose BloodPressure SkinThickness Insulin BMI
## 26 3 Glucose BloodPressure SkinThickness Insulin BMI
## 26 4 Glucose BloodPressure SkinThickness Insulin BMI
## 26 5 Glucose BloodPressure SkinThickness Insulin BMI
## 27 1 Glucose BloodPressure SkinThickness Insulin BMI
## 27 2 Glucose BloodPressure SkinThickness Insulin BMI
## 27 3 Glucose BloodPressure SkinThickness Insulin BMI
## 27 4 Glucose BloodPressure SkinThickness Insulin BMI
## 27 5 Glucose BloodPressure SkinThickness Insulin BMI
## 28 1 Glucose BloodPressure SkinThickness Insulin BMI
## 28 2 Glucose BloodPressure SkinThickness Insulin BMI
## 28 3 Glucose BloodPressure SkinThickness Insulin BMI
## 28 4 Glucose BloodPressure SkinThickness Insulin BMI
## 28 5 Glucose BloodPressure SkinThickness Insulin BMI
## 29 1 Glucose BloodPressure SkinThickness Insulin BMI
## 29 2 Glucose BloodPressure SkinThickness Insulin BMI
## 29 3 Glucose BloodPressure SkinThickness Insulin BMI
## 29 4 Glucose BloodPressure SkinThickness Insulin BMI
## 29 5 Glucose BloodPressure SkinThickness Insulin BMI
## 30 1 Glucose BloodPressure SkinThickness Insulin BMI
## 30 2 Glucose BloodPressure SkinThickness Insulin BMI
## 30 3 Glucose BloodPressure SkinThickness Insulin BMI
## 30 4 Glucose BloodPressure SkinThickness Insulin BMI
## 30 5 Glucose BloodPressure SkinThickness Insulin BMI
## 31 1 Glucose BloodPressure SkinThickness Insulin BMI
## 31 2 Glucose BloodPressure SkinThickness Insulin BMI
## 31 3 Glucose BloodPressure SkinThickness Insulin BMI
## 31 4 Glucose BloodPressure SkinThickness Insulin BMI
## 31 5 Glucose BloodPressure SkinThickness Insulin BMI
## 32 1 Glucose BloodPressure SkinThickness Insulin BMI
## 32 2 Glucose BloodPressure SkinThickness Insulin BMI
## 32 3 Glucose BloodPressure SkinThickness Insulin BMI
## 32 4 Glucose BloodPressure SkinThickness Insulin BMI
## 32 5 Glucose BloodPressure SkinThickness Insulin BMI
## 33 1 Glucose BloodPressure SkinThickness Insulin BMI
## 33 2 Glucose BloodPressure SkinThickness Insulin BMI
## 33 3 Glucose BloodPressure SkinThickness Insulin BMI
## 33 4 Glucose BloodPressure SkinThickness Insulin BMI
## 33 5 Glucose BloodPressure SkinThickness Insulin BMI
## 34 1 Glucose BloodPressure SkinThickness Insulin BMI
## 34 2 Glucose BloodPressure SkinThickness Insulin BMI
## 34 3 Glucose BloodPressure SkinThickness Insulin BMI
## 34 4 Glucose BloodPressure SkinThickness Insulin BMI
## 34 5 Glucose BloodPressure SkinThickness Insulin BMI
## 35 1 Glucose BloodPressure SkinThickness Insulin BMI
## 35 2 Glucose BloodPressure SkinThickness Insulin BMI
## 35 3 Glucose BloodPressure SkinThickness Insulin BMI
## 35 4 Glucose BloodPressure SkinThickness Insulin BMI
## 35 5 Glucose BloodPressure SkinThickness Insulin BMI
## 36 1 Glucose BloodPressure SkinThickness Insulin BMI
## 36 2 Glucose BloodPressure SkinThickness Insulin BMI
## 36 3 Glucose BloodPressure SkinThickness Insulin BMI
## 36 4 Glucose BloodPressure SkinThickness Insulin BMI
## 36 5 Glucose BloodPressure SkinThickness Insulin BMI
## 37 1 Glucose BloodPressure SkinThickness Insulin BMI
## 37 2 Glucose BloodPressure SkinThickness Insulin BMI
## 37 3 Glucose BloodPressure SkinThickness Insulin BMI
## 37 4 Glucose BloodPressure SkinThickness Insulin BMI
## 37 5 Glucose BloodPressure SkinThickness Insulin BMI
## 38 1 Glucose BloodPressure SkinThickness Insulin BMI
## 38 2 Glucose BloodPressure SkinThickness Insulin BMI
## 38 3 Glucose BloodPressure SkinThickness Insulin BMI
## 38 4 Glucose BloodPressure SkinThickness Insulin BMI
## 38 5 Glucose BloodPressure SkinThickness Insulin BMI
## 39 1 Glucose BloodPressure SkinThickness Insulin BMI
## 39 2 Glucose BloodPressure SkinThickness Insulin BMI
## 39 3 Glucose BloodPressure SkinThickness Insulin BMI
## 39 4 Glucose BloodPressure SkinThickness Insulin BMI
## 39 5 Glucose BloodPressure SkinThickness Insulin BMI
## 40 1 Glucose BloodPressure SkinThickness Insulin BMI
## 40 2 Glucose BloodPressure SkinThickness Insulin BMI
## 40 3 Glucose BloodPressure SkinThickness Insulin BMI
## 40 4 Glucose BloodPressure SkinThickness Insulin BMI
## 40 5 Glucose BloodPressure SkinThickness Insulin BMI
## 41 1 Glucose BloodPressure SkinThickness Insulin BMI
## 41 2 Glucose BloodPressure SkinThickness Insulin BMI
## 41 3 Glucose BloodPressure SkinThickness Insulin BMI
## 41 4 Glucose BloodPressure SkinThickness Insulin BMI
## 41 5 Glucose BloodPressure SkinThickness Insulin BMI
## 42 1 Glucose BloodPressure SkinThickness Insulin BMI
## 42 2 Glucose BloodPressure SkinThickness Insulin BMI
## 42 3 Glucose BloodPressure SkinThickness Insulin BMI
## 42 4 Glucose BloodPressure SkinThickness Insulin BMI
## 42 5 Glucose BloodPressure SkinThickness Insulin BMI
## 43 1 Glucose BloodPressure SkinThickness Insulin BMI
## 43 2 Glucose BloodPressure SkinThickness Insulin BMI
## 43 3 Glucose BloodPressure SkinThickness Insulin BMI
## 43 4 Glucose BloodPressure SkinThickness Insulin BMI
## 43 5 Glucose BloodPressure SkinThickness Insulin BMI
## 44 1 Glucose BloodPressure SkinThickness Insulin BMI
## 44 2 Glucose BloodPressure SkinThickness Insulin BMI
## 44 3 Glucose BloodPressure SkinThickness Insulin BMI
## 44 4 Glucose BloodPressure SkinThickness Insulin BMI
## 44 5 Glucose BloodPressure SkinThickness Insulin BMI
## 45 1 Glucose BloodPressure SkinThickness Insulin BMI
## 45 2 Glucose BloodPressure SkinThickness Insulin BMI
## 45 3 Glucose BloodPressure SkinThickness Insulin BMI
## 45 4 Glucose BloodPressure SkinThickness Insulin BMI
## 45 5 Glucose BloodPressure SkinThickness Insulin BMI
## 46 1 Glucose BloodPressure SkinThickness Insulin BMI
## 46 2 Glucose BloodPressure SkinThickness Insulin BMI
## 46 3 Glucose BloodPressure SkinThickness Insulin BMI
## 46 4 Glucose BloodPressure SkinThickness Insulin BMI
## 46 5 Glucose BloodPressure SkinThickness Insulin BMI
## 47 1 Glucose BloodPressure SkinThickness Insulin BMI
## 47 2 Glucose BloodPressure SkinThickness Insulin BMI
## 47 3 Glucose BloodPressure SkinThickness Insulin BMI
## 47 4 Glucose BloodPressure SkinThickness Insulin BMI
## 47 5 Glucose BloodPressure SkinThickness Insulin BMI
## 48 1 Glucose BloodPressure SkinThickness Insulin BMI
## 48 2 Glucose BloodPressure SkinThickness Insulin BMI
## 48 3 Glucose BloodPressure SkinThickness Insulin BMI
## 48 4 Glucose BloodPressure SkinThickness Insulin BMI
## 48 5 Glucose BloodPressure SkinThickness Insulin BMI
## 49 1 Glucose BloodPressure SkinThickness Insulin BMI
## 49 2 Glucose BloodPressure SkinThickness Insulin BMI
## 49 3 Glucose BloodPressure SkinThickness Insulin BMI
## 49 4 Glucose BloodPressure SkinThickness Insulin BMI
## 49 5 Glucose BloodPressure SkinThickness Insulin BMI
## 50 1 Glucose BloodPressure SkinThickness Insulin BMI
## 50 2 Glucose BloodPressure SkinThickness Insulin BMI
## 50 3 Glucose BloodPressure SkinThickness Insulin BMI
## 50 4 Glucose BloodPressure SkinThickness Insulin BMI
## 50 5 Glucose BloodPressure SkinThickness Insulin BMIsummary(tempData)## Class: mids
## Number of multiple imputations: 5
## Imputation methods:
## Glucose BloodPressure SkinThickness
## "pmm" "pmm" "pmm"
## Insulin BMI DiabetesPedigreeFunction
## "pmm" "pmm" ""
## Age
## ""
## PredictorMatrix:
## Glucose BloodPressure SkinThickness Insulin BMI
## Glucose 0 1 1 1 1
## BloodPressure 1 0 1 1 1
## SkinThickness 1 1 0 1 1
## Insulin 1 1 1 0 1
## BMI 1 1 1 1 0
## DiabetesPedigreeFunction 1 1 1 1 1
## DiabetesPedigreeFunction Age
## Glucose 1 1
## BloodPressure 1 1
## SkinThickness 1 1
## Insulin 1 1
## BMI 1 1
## DiabetesPedigreeFunction 0 1tempData$imp$Insulin## 1 2 3 4 5
## 1 480 130 237 175 140
## 2 55 42 16 66 23
## 3 579 168 185 192 70
## 6 94 68 79 180 18
## 8 56 326 140 205 215
## 10 63 115 170 220 58
## 11 100 82 120 105 48
## 12 225 168 321 300 680
## 13 220 130 170 284 100
## 16 75 152 94 120 48
## 18 81 192 83 158 258
## 22 88 114 182 44 120
## 23 207 543 510 207 280
## 24 44 82 215 120 63
## 27 130 485 171 328 120
## 30 44 142 182 183 105
## 31 75 106 129 200 96
## 34 40 45 40 55 76
## 35 142 74 94 64 176
## 37 165 140 167 135 128
## 38 258 90 105 120 105
## 39 73 180 135 57 94
## 42 167 204 88 182 165
## 43 76 76 76 110 49
## 45 132 193 155 135 540
## 46 200 846 145 375 744
## 47 144 29 29 193 284
## 48 49 45 66 45 66
## 49 125 94 110 160 87
## 50 65 115 148 160 110
## 56 45 45 45 95 66
## 59 190 328 325 495 140
## 61 60 45 37 54 49
## 62 220 167 480 165 180
## 63 49 15 66 45 49
## 65 119 180 96 190 215
## 66 77 66 65 90 90
## 67 78 165 156 160 82
## 68 44 120 85 105 215
## 73 200 88 88 160 180
## 75 40 55 88 60 66
## 76 110 126 180 84 191
## 77 49 37 15 45 49
## 78 180 90 196 72 48
## 79 250 60 110 167 100
## 80 83 116 325 125 100
## 81 74 182 50 74 105
## 82 55 36 37 55 49
## 84 48 58 116 54 77
## 85 330 240 128 240 155
## 87 160 120 148 165 120
## 90 18 265 71 100 88
## 91 45 66 40 40 45
## 94 83 156 170 480 60
## 97 92 92 90 70 16
## 101 474 321 156 90 300
## 102 171 240 240 310 96
## 103 78 258 25 105 265
## 105 54 116 81 92 87
## 107 76 45 15 45 66
## 114 42 41 74 70 40
## 116 60 167 29 237 480
## 117 105 74 150 335 92
## 118 49 66 140 82 54
## 119 86 54 152 50 90
## 122 175 175 74 145 56
## 124 176 108 170 130 110
## 125 176 130 110 63 191
## 130 77 100 100 130 94
## 132 270 160 122 128 220
## 134 51 36 54 70 84
## 139 92 106 94 291 106
## 141 85 142 112 140 94
## 142 120 148 125 142 278
## 144 196 63 105 75 183
## 146 36 56 87 258 88
## 147 76 76 49 37 15
## 149 144 171 272 135 284
## 150 84 41 50 49 36
## 152 105 68 100 105 64
## 155 249 207 207 14 846
## 156 175 175 168 495 140
## 161 194 160 140 130 140
## 164 152 126 48 210 75
## 165 170 130 285 275 83
## 167 193 135 127 325 165
## 168 130 215 105 89 94
## 169 178 120 125 74 215
## 171 88 54 192 110 66
## 173 84 66 56 70 70
## 177 45 49 43 90 71
## 179 135 545 210 210 130
## 180 150 110 130 130 182
## 181 60 66 36 54 45
## 184 49 95 55 36 66
## 185 480 220 220 135 110
## 186 207 392 392 14 207
## 191 105 265 278 165 92
## 193 440 272 485 168 105
## 194 130 545 140 146 168
## 195 71 37 43 258 82
## 197 192 36 36 100 64
## 201 160 120 71 64 81
## 202 165 165 240 165 88
## 203 114 110 114 175 165
## 206 56 48 83 215 71
## 208 171 237 171 321 144
## 210 192 120 130 200 495
## 211 40 55 49 54 55
## 212 480 228 210 130 193
## 213 114 185 225 130 100
## 219 49 76 53 18 38
## 220 120 77 165 230 106
## 222 100 342 284 255 140
## 223 200 160 148 600 112
## 227 25 50 278 120 210
## 228 168 225 156 185 300
## 231 194 370 130 182 130
## 234 190 92 105 63 148
## 236 225 90 510 120 120
## 238 375 579 185 680 300
## 239 231 272 130 67 140
## 240 115 53 84 105 66
## 241 16 84 64 54 82
## 243 83 220 125 360 360
## 246 185 579 175 130 293
## 247 99 176 170 150 270
## 250 135 50 36 120 90
## 251 63 74 105 115 188
## 252 85 112 78 105 176
## 254 100 85 48 85 71
## 256 140 142 77 180 99
## 257 94 50 115 77 215
## 258 50 71 110 148 196
## 262 285 160 250 165 140
## 263 115 56 72 265 56
## 264 165 96 145 132 110
## 265 140 94 110 61 402
## 267 240 194 250 168 144
## 268 480 182 140 125 29
## 269 48 48 78 78 258
## 270 144 160 110 146 125
## 271 190 200 110 75 130
## 273 63 82 215 285 105
## 275 116 99 89 415 160
## 277 81 116 94 105 100
## 279 57 78 182 63 215
## 281 194 127 126 130 284
## 284 120 130 171 140 284
## 285 258 100 152 200 278
## 295 485 155 440 495 168
## 300 120 125 81 600 145
## 301 225 540 342 465 225
## 304 77 180 415 110 215
## 305 83 275 29 293 110
## 311 37 40 106 85 60
## 315 105 85 63 140 188
## 318 156 135 579 277 185
## 320 225 156 90 207 392
## 322 158 160 148 130 156
## 323 285 85 89 190 326
## 325 142 94 105 130 165
## 328 579 156 185 293 478
## 331 158 110 94 140 105
## 333 375 180 100 846 145
## 334 265 48 115 87 36
## 337 140 105 115 170 180
## 338 110 148 105 165 96
## 340 130 120 90 180 325
## 343 32 54 54 215 66
## 344 180 99 176 106 180
## 345 92 135 99 75 190
## 348 64 57 74 74 79
## 350 54 480 440 250 106
## 351 88 72 56 57 59
## 352 145 63 110 145 275
## 353 66 45 66 45 15
## 355 90 210 180 92 76
## 356 342 193 126 474 168
## 358 130 180 145 275 122
## 362 387 210 140 478 168
## 363 48 160 48 110 90
## 364 96 237 100 185 140
## 367 215 129 63 200 215
## 368 77 32 48 36 49
## 379 168 114 168 321 140
## 382 54 32 105 210 74
## 387 56 188 180 77 85
## 388 115 78 91 130 192
## 392 168 240 321 225 168
## 395 100 272 325 175 495
## 398 150 156 167 88 220
## 399 45 76 36 60 37
## 400 249 159 846 846 846
## 401 57 94 258 116 92
## 402 150 140 330 126 140
## 404 76 37 66 42 37
## 405 474 135 114 510 156
## 407 120 215 74 74 120
## 408 54 66 115 105 66
## 409 543 325 375 274 744
## 411 92 180 196 160 105
## 417 77 77 56 48 75
## 418 318 480 135 130 370
## 419 37 76 45 42 45
## 424 183 142 99 74 78
## 427 88 192 95 54 76
## 431 90 125 50 72 70
## 434 145 74 63 480 94
## 435 46 59 55 90 32
## 436 127 165 110 130 146
## 437 240 360 240 480 125
## 438 228 330 228 96 29
## 439 64 40 70 44 55
## 440 156 91 115 105 160
## 441 180 114 321 495 240
## 444 114 130 120 120 190
## 445 285 326 176 75 110
## 452 335 140 122 88 205
## 454 87 119 72 130 120
## 456 465 680 156 293 185
## 457 167 146 96 105 171
## 462 45 66 49 66 66
## 464 42 42 18 74 49
## 465 50 92 75 83 105
## 469 110 178 170 106 129
## 471 127 293 100 127 293
## 472 60 275 83 130 140
## 473 235 140 140 77 200
## 474 140 140 220 110 220
## 475 99 57 50 110 130
## 476 205 155 275 190 88
## 480 130 152 148 168 167
## 482 120 110 106 99 145
## 485 127 387 245 130 284
## 489 48 43 115 86 84
## 490 293 325 192 274 280
## 492 71 46 44 90 23
## 493 258 25 105 116 90
## 495 60 37 95 60 76
## 496 342 150 271 495 168
## 497 182 152 63 110 54
## 502 46 66 48 43 88
## 503 36 191 89 293 125
## 505 56 56 91 184 210
## 506 66 55 55 55 45
## 510 132 120 89 110 176
## 511 55 64 66 92 64
## 513 49 140 52 120 74
## 514 43 44 65 23 115
## 518 106 166 58 135 122
## 519 76 44 43 58 55
## 523 94 130 94 215 54
## 524 335 135 194 83 60
## 525 220 115 160 200 285
## 526 76 36 23 38 42
## 530 190 114 196 78 91
## 532 188 285 92 190 63
## 534 41 32 85 115 64
## 536 194 205 140 74 130
## 537 66 210 65 94 180
## 538 49 45 49 60 45
## 543 37 50 48 156 88
## 550 255 67 168 478 300
## 551 78 100 129 160 91
## 553 115 57 36 130 94
## 557 54 78 110 160 56
## 558 114 120 91 22 78
## 559 129 53 230 105 99
## 560 76 41 49 82 23
## 561 106 205 204 110 205
## 565 106 76 23 54 82
## 571 95 71 55 18 66
## 572 63 100 74 50 120
## 578 115 79 210 130 140
## 579 205 83 200 240 200
## 580 579 375 207 274 280
## 581 310 370 342 310 130
## 582 100 36 175 175 90
## 583 112 200 142 88 96
## 584 87 57 135 50 120
## 586 52 76 100 74 53
## 587 480 194 127 210 293
## 588 180 77 105 56 59
## 590 45 66 45 66 45
## 591 75 180 83 402 105
## 593 95 61 335 250 160
## 597 60 58 44 56 37
## 599 120 168 194 277 185
## 601 50 92 48 25 59
## 602 52 77 115 57 67
## 603 188 215 270 270 120
## 605 156 140 271 304 180
## 606 275 155 135 200 200
## 614 192 120 100 100 56
## 616 36 105 56 182 88
## 617 110 105 57 116 54
## 619 68 23 135 285 99
## 620 130 74 140 215 190
## 622 23 125 88 52 85
## 623 293 130 465 265 249
## 625 64 68 160 105 196
## 627 106 105 285 94 148
## 628 130 105 156 155 155
## 629 63 155 130 130 122
## 630 82 88 73 115 41
## 631 160 119 74 106 105
## 633 44 79 278 75 94
## 635 77 18 46 36 71
## 636 81 114 100 50 156
## 637 265 120 78 145 192
## 642 210 53 145 155 230
## 643 165 125 480 387 146
## 644 100 49 76 94 54
## 650 114 54 158 105 90
## 654 96 326 105 83 105
## 659 200 105 120 335 96
## 661 100 310 318 321 485
## 662 744 14 744 274 274
## 665 63 285 275 64 207
## 667 29 100 128 125 318
## 668 135 110 130 120 91
## 672 72 86 66 87 76
## 675 71 110 91 148 87
## 676 280 293 145 249 846
## 677 168 146 250 168 168
## 678 78 65 180 36 258
## 679 291 190 110 135 230
## 682 194 90 300 168 474
## 684 155 75 79 600 200
## 685 291 110 77 150 110
## 687 270 63 130 115 120
## 688 175 132 50 74 182
## 691 56 258 36 115 65
## 692 193 193 194 155 100
## 695 46 49 94 58 60
## 698 140 48 48 92 51
## 700 190 110 100 140 95
## 702 145 96 22 480 230
## 703 168 168 231 120 114
## 704 130 128 220 150 360
## 706 49 106 76 82 55
## 707 132 278 176 200 105
## 709 328 144 155 225 175
## 713 182 285 135 140 146
## 715 94 105 71 78 88
## 718 38 52 44 64 90
## 720 115 71 67 110 48
## 721 36 40 55 71 37
## 725 196 100 71 74 325
## 726 56 85 120 106 110
## 728 240 275 61 135 135
## 729 474 370 190 105 237
## 730 88 56 182 64 56
## 732 74 18 105 44 115
## 735 70 265 56 110 68
## 736 152 120 57 115 152
## 738 49 66 49 36 66
## 740 81 112 148 188 105
## 744 166 88 135 146 130
## 747 342 180 284 194 293
## 750 210 180 245 240 125
## 751 167 335 318 130 100
## 753 68 90 120 120 79
## 755 126 310 126 125 144
## 757 63 230 480 167 88
## 758 83 220 335 165 330
## 759 94 120 110 78 116
## 760 159 130 130 744 249
## 762 277 495 680 192 70
## 763 70 71 23 115 60
## 765 402 152 152 115 99
## 767 130 130 88 165 100
## 768 16 82 265 92 100tempData$method## Glucose BloodPressure SkinThickness
## "pmm" "pmm" "pmm"
## Insulin BMI DiabetesPedigreeFunction
## "pmm" "pmm" ""
## Age
## ""completedData <- complete(tempData,1)
Outcome <- diabetes$Outcome ##The missing values have been replaced with the imputed values in the first of the five datasets.
magenta points (imputed) - blue ones (observed)
xyplot(Insulin~ BMI + BloodPressure + Glucose,
data = completedData, scales = "free", layout = c(2, 2),
auto.key = list(x = .6, y = .7, corner = c(0, 0)))
xyplot(Glucose ~Insulin+BMI+BloodPressure,data=completedData,pch=18,cex=.75,
auto.key = list(x = .6, y = .7, corner = c(-0.5, 4)))
xyplot(data=completedData,SkinThickness ~Glucose+BMI+BloodPressure,pch=18,cex=.75)
xyplot(data=completedData,BloodPressure ~Glucose+BMI+Insulin,pch=18,cex=0.75)
##—————- The density of the imputed data for each imputed dataset is showed in magenta while the density of the observed data is showed in blue. Again, under our previous assumptions we expect the distributions to be similar. ##—————
densityplot(completedData$Glucose)
modelFit1 <- with(completedData,lm(Insulin~ Glucose+BMI+Age+BloodPressure))
summary(modelFit1)##
## Call:
## lm(formula = Insulin ~ Glucose + BMI + Age + BloodPressure)
##
## Residuals:
## Min 1Q Median 3Q Max
## -319.39 -49.07 -13.86 31.44 531.75
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -117.51914 23.08886 -5.090 4.52e-07 ***
## Glucose 2.27724 0.11366 20.035 < 2e-16 ***
## BMI 2.09257 0.50304 4.160 3.55e-05 ***
## Age 0.06167 0.29996 0.206 0.837171
## BloodPressure -1.08759 0.29402 -3.699 0.000232 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 89.69 on 763 degrees of freedom
## Multiple R-squared: 0.3928, Adjusted R-squared: 0.3896
## F-statistic: 123.4 on 4 and 763 DF, p-value: < 2.2e-16Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.
# compare classical and robust covariance estimates
covEllipses(completedData[,2:7], Outcome)
covEllipses(completedData[,2:7], Outcome, fill=TRUE, pooled=FALSE,
col=c("blue", "red", "darkgreen"), variables=1:5)
diab.boxm <- boxM(completedData[,2:7], Outcome)
plot(diab.boxm, cex.lab=1.5)
Preparing dataset for regression analysis
First : combine the completedData set with outcome
complete <- completedData
complete$Outcome <- Outcome
summary(complete)## Glucose BloodPressure SkinThickness Insulin
## Min. : 44.0 Min. : 24.00 Min. : 7.00 Min. : 14.0
## 1st Qu.: 99.0 1st Qu.: 64.00 1st Qu.:20.00 1st Qu.: 74.0
## Median :117.0 Median : 72.00 Median :29.00 Median :120.0
## Mean :121.5 Mean : 72.35 Mean :28.77 Mean :150.4
## 3rd Qu.:140.2 3rd Qu.: 80.00 3rd Qu.:36.00 3rd Qu.:188.5
## Max. :199.0 Max. :122.00 Max. :99.00 Max. :846.0
## BMI DiabetesPedigreeFunction Age Outcome
## Min. :18.20 Min. :0.0780 Min. :21.00 False:500
## 1st Qu.:27.50 1st Qu.:0.2437 1st Qu.:24.00 True :268
## Median :32.05 Median :0.3725 Median :29.00
## Mean :32.42 Mean :0.4719 Mean :33.24
## 3rd Qu.:36.60 3rd Qu.:0.6262 3rd Qu.:41.00
## Max. :67.10 Max. :2.4200 Max. :81.00For convenience sake we will use a 70/30 split, using 70% of the data as the training set and the remaining 30% for the testing set.
set.seed(3456)
index <- createDataPartition(complete$Outcome, p = .7,
list = FALSE,
times = 1)
train <- complete[ index,]
test <- complete[-index,]
head(train)## Glucose BloodPressure SkinThickness Insulin BMI
## 3 183 64 14 579 23.3
## 4 89 66 23 94 28.1
## 6 116 74 19 94 25.6
## 7 78 50 32 88 31.0
## 8 115 70 45 56 35.3
## 9 197 70 45 543 30.5
## DiabetesPedigreeFunction Age Outcome
## 3 0.672 32 True
## 4 0.167 21 False
## 6 0.201 30 False
## 7 0.248 26 True
## 8 0.134 29 False
## 9 0.158 53 Truehead(test)## Glucose BloodPressure SkinThickness Insulin BMI
## 1 148 72 35 480 33.6
## 2 85 66 29 55 26.6
## 5 137 40 35 168 43.1
## 11 110 92 36 100 37.6
## 13 139 80 22 220 27.1
## 16 100 80 24 75 30.0
## DiabetesPedigreeFunction Age Outcome
## 1 0.627 50 True
## 2 0.351 31 False
## 5 2.288 33 True
## 11 0.191 30 False
## 13 1.441 57 False
## 16 0.484 32 TrueNormalize the data. Categorical variables are automatically ignored
prep <- train %>%
preProcess(method = c("center", "scale"))
# Transform the data using the estimated parameters
train_prep <- prep %>% predict(train)
test_prep <- prep %>% predict(test)LDA
library(MASS)##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## selectmodel_lda <- lda(Outcome~., data = train)
model_lda## Call:
## lda(Outcome ~ ., data = train)
##
## Prior probabilities of groups:
## False True
## 0.6505576 0.3494424
##
## Group means:
## Glucose BloodPressure SkinThickness Insulin BMI
## False 109.7286 71.21429 27.28571 123.7686 30.88400
## True 142.8883 75.15426 32.15426 197.5532 35.28191
## DiabetesPedigreeFunction Age
## False 0.4349457 30.67714
## True 0.5311277 36.20745
##
## Coefficients of linear discriminants:
## LD1
## Glucose 0.034099001
## BloodPressure -0.010371262
## SkinThickness -0.005636507
## Insulin -0.001693631
## BMI 0.072542298
## DiabetesPedigreeFunction 0.437085722
## Age 0.024375131plot(model_lda)
library(klaR)
partimat(Outcome ~ Glucose+Insulin+BloodPressure+BMI, data=train, method="lda")
Prediction
predictions <- model_lda %>% predict(test_prep)
summary(predictions)## Length Class Mode
## class 230 factor numeric
## posterior 460 -none- numeric
## x 230 -none- numericfitControl <- trainControl(## 10-fold CV
method = "repeatedcv",
number = 10,
## repeated ten times
repeats = 10)
set.seed(825)
gbm_fit <- train(Outcome ~ ., data = train,
method = "gbm",
trControl = fitControl,
## This last option is actually one
## for gbm() that passes through
verbose = FALSE)
gbm_fit## Stochastic Gradient Boosting
##
## 538 samples
## 7 predictor
## 2 classes: 'False', 'True'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 10 times)
## Summary of sample sizes: 484, 484, 484, 485, 484, 484, ...
## Resampling results across tuning parameters:
##
## interaction.depth n.trees Accuracy Kappa
## 1 50 0.7753040 0.4803382
## 1 100 0.7717890 0.4772438
## 1 150 0.7646995 0.4633156
## 2 50 0.7650908 0.4639867
## 2 100 0.7578477 0.4509521
## 2 150 0.7474249 0.4277235
## 3 50 0.7661740 0.4671532
## 3 100 0.7548358 0.4445688
## 3 150 0.7477813 0.4302643
##
## Tuning parameter 'shrinkage' was held constant at a value of 0.1
##
## Tuning parameter 'n.minobsinnode' was held constant at a value of 10
## Accuracy was used to select the optimal model using the largest value.
## The final values used for the model were n.trees = 50, interaction.depth
## = 1, shrinkage = 0.1 and n.minobsinnode = 10.# predict the outcome on a test set
gbm_pred <- predict(gbm_fit, test)
# compare predicted outcome and true outcome
confusionMatrix(gbm_pred, test$Outcome)## Confusion Matrix and Statistics
##
## Reference
## Prediction False True
## False 131 38
## True 19 42
##
## Accuracy : 0.7522
## 95% CI : (0.6912, 0.8066)
## No Information Rate : 0.6522
## P-Value [Acc > NIR] : 0.0007075
##
## Kappa : 0.4217
##
## Mcnemar's Test P-Value : 0.0171182
##
## Sensitivity : 0.8733
## Specificity : 0.5250
## Pos Pred Value : 0.7751
## Neg Pred Value : 0.6885
## Prevalence : 0.6522
## Detection Rate : 0.5696
## Detection Prevalence : 0.7348
## Balanced Accuracy : 0.6992
##
## 'Positive' Class : False
## Random Forest
# repeating fitcontrol function
library(naivebayes)## naivebayes 0.9.6 loaded##
## Attaching package: 'naivebayes'## The following object is masked from 'package:data.table':
##
## tablesfitControl <- trainControl(## 10-fold CV
method = "repeatedcv",
number = 10,
## repeated ten times
repeats = 10)
# fit a random forest model
library(randomForest)
rf_fit <- train(Outcome ~ .,
data = train,
method = "rf",
trControl = fitControl,
verbose = FALSE)
rf_fit## Random Forest
##
## 538 samples
## 7 predictor
## 2 classes: 'False', 'True'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 10 times)
## Summary of sample sizes: 484, 484, 484, 484, 485, 484, ...
## Resampling results across tuning parameters:
##
## mtry Accuracy Kappa
## 2 0.7451188 0.4216633
## 4 0.7460657 0.4265525
## 7 0.7442278 0.4244386
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was mtry = 4.# predict the outcome on a test set
rf_pred <- predict(rf_fit, test)
# compare predicted outcome and true outcome
confusionMatrix(rf_pred, test$Outcome)## Confusion Matrix and Statistics
##
## Reference
## Prediction False True
## False 125 37
## True 25 43
##
## Accuracy : 0.7304
## 95% CI : (0.6682, 0.7866)
## No Information Rate : 0.6522
## P-Value [Acc > NIR] : 0.006878
##
## Kappa : 0.3843
##
## Mcnemar's Test P-Value : 0.162413
##
## Sensitivity : 0.8333
## Specificity : 0.5375
## Pos Pred Value : 0.7716
## Neg Pred Value : 0.6324
## Prevalence : 0.6522
## Detection Rate : 0.5435
## Detection Prevalence : 0.7043
## Balanced Accuracy : 0.6854
##
## 'Positive' Class : False
## Bootstrap Bootstrap resampling involves taking random samples from the dataset (with re-selection) against which to evaluate the model. In aggregate, the results provide an indication of the variance of the models performance. Typically, large number of resampling iterations are performed (thousands or tends of thousands). ##LDA
The following example uses a bootstrap with 100 resamples to prepare a Linear Discrinimant Analysis model.
library(MASS)
fitControl <- trainControl(method = "boot", number = 100)
set.seed(825)
# train the model
lda_fit <- train(Outcome ~ ., data = train,
method = "lda",
trControl = fitControl,
verbose = FALSE)
lda_fit## Linear Discriminant Analysis
##
## 538 samples
## 7 predictor
## 2 classes: 'False', 'True'
##
## No pre-processing
## Resampling: Bootstrapped (100 reps)
## Summary of sample sizes: 538, 538, 538, 538, 538, 538, ...
## Resampling results:
##
## Accuracy Kappa
## 0.7701148 0.4704893# predict the outcome on a test set
lda_pred <- predict(lda_fit, test)
# compare predicted outcome and true outcome
confusionMatrix(lda_pred, test$Outcome)## Confusion Matrix and Statistics
##
## Reference
## Prediction False True
## False 127 36
## True 23 44
##
## Accuracy : 0.7435
## 95% CI : (0.6819, 0.7986)
## No Information Rate : 0.6522
## P-Value [Acc > NIR] : 0.001872
##
## Kappa : 0.4123
##
## Mcnemar's Test P-Value : 0.118225
##
## Sensitivity : 0.8467
## Specificity : 0.5500
## Pos Pred Value : 0.7791
## Neg Pred Value : 0.6567
## Prevalence : 0.6522
## Detection Rate : 0.5522
## Detection Prevalence : 0.7087
## Balanced Accuracy : 0.6983
##
## 'Positive' Class : False
##