Assingment 3- MultipleLogisticRegression
Sayli Gharat
29 July 2017
Problem Definition :
The objective is to predict whether a patient has diabetes based on diagnostic measurements.
Data Description:
This dataset is from the National Institute of Diabetes and Digestive and Kidney Diseases. Several constraints were placed on the selection of these instances from a larger database. In particular, all patients here are females at least 21 years old of Pima Indian heritage.
Attributes: Patient ID: serial number for the patient Pregnancies: Number of times pregnant Glucose: Plasma glucose concentration a 2 hours in an oral glucose tolerance test BloodPressure: Diastolic blood pressure (mm Hg) SkinThickness: Triceps skin fold thickness (mm) Insulin: 2-Hour serum insulin (mu U/ml) BMI: Body mass index (weight in kg/(height in m)^2) DiabetesPedigreeFunction: Diabetes pedigree function Age: Age (years) Outcome: Class variable (0 or 1)
Working Directory
setwd("D:/R-BA/R-Scripts")set-up
Loading Libraries
library(tidyr)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(ggplot2)
library(corrgram)
library(gridExtra)##
## Attaching package: 'gridExtra'## The following object is masked from 'package:dplyr':
##
## combinelibrary(caret)## Loading required package: latticelibrary(pscl)## Loading required package: MASS##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## select## Classes and Methods for R developed in the## Political Science Computational Laboratory## Department of Political Science## Stanford University## Simon Jackman## hurdle and zeroinfl functions by Achim ZeileisFunctions
reading the file Train Data Diabetes.csv
dfrTrainDiabetesData <- read.csv("./data/Train Data Diabetes.csv", header=T, stringsAsFactors=F)
intRowCount <- nrow(dfrTrainDiabetesData)
print(intRowCount)## [1] 700head(dfrTrainDiabetesData,20)## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 1 0 148 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
## 7 3 78 50 32 88 31.0
## 8 10 115 0 0 0 35.3
## 9 2 197 70 45 543 30.5
## 10 8 125 96 0 0 0.0
## 11 4 110 92 0 0 37.6
## 12 10 168 74 0 0 38.0
## 13 10 139 80 0 0 27.1
## 14 1 189 60 23 846 30.1
## 15 5 166 72 19 175 25.8
## 16 7 100 0 0 0 30.0
## 17 0 118 84 47 230 45.8
## 18 7 107 74 0 0 29.6
## 19 1 103 30 38 83 43.3
## 20 1 115 70 30 96 34.6
## DiabetesPedigreeFunction Age Outcome
## 1 0.627 50 1
## 2 0.351 31 0
## 3 0.672 32 1
## 4 0.167 21 0
## 5 2.288 33 1
## 6 0.201 30 0
## 7 0.248 26 1
## 8 0.134 29 0
## 9 0.158 53 1
## 10 0.232 54 1
## 11 0.191 30 0
## 12 0.537 34 1
## 13 1.441 57 0
## 14 0.398 59 1
## 15 0.587 51 1
## 16 0.484 32 1
## 17 0.551 31 1
## 18 0.254 31 1
## 19 0.183 33 0
## 20 0.529 32 1Observation Only numeric data is seen
Missing Data
#sum(is.na(dfrModel$Age))
lapply(dfrTrainDiabetesData, FUN=detect_na)## $Pregnancies
## [1] 0
##
## $Glucose
## [1] 0
##
## $BloodPressure
## [1] 0
##
## $SkinThickness
## [1] 0
##
## $Insulin
## [1] 0
##
## $BMI
## [1] 0
##
## $DiabetesPedigreeFunction
## [1] 0
##
## $Age
## [1] 0
##
## $Outcome
## [1] 0Observation No missing data is seen in any of the columns
Outliers Data
#detect_outliers(dfrModel$Age)
lapply(dfrTrainDiabetesData, FUN=detect_outliers)## $Pregnancies
## integer(0)
##
## $Glucose
## integer(0)
##
## $BloodPressure
## [1] 0 0 0 0 0 0 122 0 0 0 0 0 0 0 0 0 0
## [18] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##
## $SkinThickness
## integer(0)
##
## $Insulin
## [1] 543 846 495 485 495 478 744 680 545 465 579 474 480 600 540 480
##
## $BMI
## [1] 0.0 0.0 0.0 0.0 0.0 67.1 0.0 0.0 0.0 0.0 0.0
##
## $DiabetesPedigreeFunction
## [1] 2.288 1.893 1.781 2.329 2.137 1.731 2.420 1.699 1.698
##
## $Age
## [1] 81
##
## $Outcome
## integer(0)Visualizing the outliers
displaygraph <- function(inp, na.rm=TRUE) {
TrainDiabetesPlot <- ggplot(dfrTrainDiabetesData, aes(x="", y=inp)) +
geom_boxplot(aes(fill=inp), color="blue") +
labs(title="Outliers in TrainDiabetesData")
TrainDiabetesPlot
}lapply(dfrTrainDiabetesData, FUN= displaygraph)## $Pregnancies
##
## $Glucose
##
## $BloodPressure
##
## $SkinThickness
##
## $Insulin
##
## $BMI
##
## $DiabetesPedigreeFunction
##
## $Age
##
## $Outcome
Correlation
vctCorr = numeric(0)
for (i in names(dfrTrainDiabetesData)){
cor.result <- cor(as.numeric(dfrTrainDiabetesData$Outcome), as.numeric(dfrTrainDiabetesData[,i]))
vctCorr <- c(vctCorr, cor.result)
}
dfrCorr <- vctCorr
names(dfrCorr) <- names(dfrTrainDiabetesData)
dfrCorr## Pregnancies Glucose BloodPressure
## 0.22408577 0.45928020 0.06019258
## SkinThickness Insulin BMI
## 0.08740524 0.14592233 0.30659734
## DiabetesPedigreeFunction Age Outcome
## 0.17053194 0.22699018 1.00000000Data For Visualization
dfrGraph <- gather(dfrTrainDiabetesData, variable, value, -Outcome)
head(dfrGraph)## Outcome variable value
## 1 1 Pregnancies 0
## 2 0 Pregnancies 1
## 3 1 Pregnancies 8
## 4 0 Pregnancies 1
## 5 1 Pregnancies 0
## 6 0 Pregnancies 5Data Visualization
ggplot(dfrGraph) +
geom_jitter(aes(value,Outcome, colour=variable)) +
facet_wrap(~variable, scales="free_x") +
labs(title="Relation Of Outcome With Other Features")
Summary
lapply(dfrTrainDiabetesData, FUN=summary)## $Pregnancies
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 1.000 3.000 3.819 6.000 17.000
##
## $Glucose
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 99.0 116.5 120.5 140.2 199.0
##
## $BloodPressure
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 63.50 72.00 68.88 80.00 122.00
##
## $SkinThickness
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 0.00 23.00 20.38 32.00 99.00
##
## $Insulin
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 0.00 36.50 79.88 126.50 846.00
##
## $BMI
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 27.00 32.00 31.89 36.50 67.10
##
## $DiabetesPedigreeFunction
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0780 0.2400 0.3755 0.4760 0.6370 2.4200
##
## $Age
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 21.00 24.00 29.00 33.12 40.00 81.00
##
## $Outcome
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.0000 0.0000 0.3443 1.0000 1.0000Observation
Find Best Multi Logistic Model with R Squared values
Choose the best logistic model by using step().
stpModel=step(glm(data=dfrTrainDiabetesData, formula=Outcome~., family=binomial), trace=0, steps=100)
summary(stpModel)##
## Call:
## glm(formula = Outcome ~ Pregnancies + Glucose + BloodPressure +
## BMI + DiabetesPedigreeFunction, family = binomial, data = dfrTrainDiabetesData)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.7483 -0.7330 -0.4109 0.7159 2.8968
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -8.001307 0.712745 -11.226 < 2e-16 ***
## Pregnancies 0.154737 0.029182 5.302 1.14e-07 ***
## Glucose 0.033491 0.003518 9.520 < 2e-16 ***
## BloodPressure -0.012340 0.005243 -2.353 0.01860 *
## BMI 0.090916 0.014952 6.080 1.20e-09 ***
## DiabetesPedigreeFunction 0.886659 0.304068 2.916 0.00355 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 901.37 on 699 degrees of freedom
## Residual deviance: 660.13 on 694 degrees of freedom
## AIC: 672.13
##
## Number of Fisher Scoring iterations: 5pR2(stpModel)## llh llhNull G2 McFadden r2ML
## -330.0664745 -450.6861271 241.2393052 0.2676356 0.2915158
## r2CU
## 0.4025970Observation
Best results given by Outcome ~ Pregnancies + Glucose + BMI
Make Final Multi Linear Model
# make model
mgmModel <- glm(data=dfrTrainDiabetesData, formula=Outcome~Pregnancies+Glucose+BMI, family=binomial(link="logit"))
# print summary
summary(mgmModel)##
## Call:
## glm(formula = Outcome ~ Pregnancies + Glucose + BMI, family = binomial(link = "logit"),
## data = dfrTrainDiabetesData)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.1642 -0.7279 -0.4250 0.7684 2.8207
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -8.177774 0.670401 -12.198 < 2e-16 ***
## Pregnancies 0.136706 0.028022 4.879 1.07e-06 ***
## Glucose 0.033024 0.003431 9.624 < 2e-16 ***
## BMI 0.087133 0.014476 6.019 1.75e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 901.37 on 699 degrees of freedom
## Residual deviance: 674.54 on 696 degrees of freedom
## AIC: 682.54
##
## Number of Fisher Scoring iterations: 5pR2(mgmModel)## llh llhNull G2 McFadden r2ML
## -337.2698365 -450.6861271 226.8325814 0.2516525 0.2767834
## r2CU
## 0.3822509Confusion Matrix
prdVal <- predict(mgmModel, type='response')
prdBln <- ifelse(prdVal > 0.5, 1, 0)
cnfmtrx <- table(prd=prdBln, act=dfrTrainDiabetesData$Outcome)
confusionMatrix(cnfmtrx)## Confusion Matrix and Statistics
##
## act
## prd 0 1
## 0 403 107
## 1 56 134
##
## Accuracy : 0.7671
## 95% CI : (0.734, 0.798)
## No Information Rate : 0.6557
## P-Value [Acc > NIR] : 9.981e-11
##
## Kappa : 0.457
## Mcnemar's Test P-Value : 8.992e-05
##
## Sensitivity : 0.8780
## Specificity : 0.5560
## Pos Pred Value : 0.7902
## Neg Pred Value : 0.7053
## Prevalence : 0.6557
## Detection Rate : 0.5757
## Detection Prevalence : 0.7286
## Balanced Accuracy : 0.7170
##
## 'Positive' Class : 0
## Regression Data
dfrPlot <- mutate(dfrTrainDiabetesData, PrdVal=prdVal, POutcome=prdBln)
head(dfrPlot)## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 1 0 148 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
## DiabetesPedigreeFunction Age Outcome PrdVal POutcome
## 1 0.627 50 1 0.41034201 0
## 2 0.351 31 0 0.05135422 0
## 3 0.672 32 1 0.72898218 1
## 4 0.167 21 0 0.06577407 0
## 5 2.288 33 1 0.52546528 1
## 6 0.201 30 0 0.19265441 0Regression Visulaization
#dfrPlot
ggplot(dfrPlot, aes(x=PrdVal, y=POutcome)) +
geom_point(shape=19, colour="blue", fill="blue") +
geom_smooth(method="gam", formula=y~s(log(x)), se=FALSE) +
labs(title="Binomial Regression Curve") +
labs(x="") +
labs(y="")
ROC Visulaization
#rocplot(logistic.model,diag=TRUE,pred.prob.labels=FALSE,prob.label.digits=3,AUC=TRUE)
#rocplot(mgmModel)Test Data
dfrTests <- read.csv("./data/Test Data Diabetes.csv", header=T, stringsAsFactors=F)
head(dfrTests)## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 1 0 122 76 27 200 35.9
## 2 6 125 78 31 0 27.6
## 3 1 168 88 29 0 35.0
## 4 2 129 0 0 0 38.5
## 5 4 110 76 20 100 28.4
## 6 6 80 80 36 0 39.8
## DiabetesPedigreeFunction Age
## 1 0.483 26
## 2 0.565 49
## 3 0.905 52
## 4 0.304 41
## 5 0.118 27
## 6 0.177 28Observation
Test Data successfully created.
Predict
resVal <- predict(mgmModel, dfrTests, type="response")
prdSur <- ifelse(resVal > 0.5, 1, 0)
prdSur <- as.factor(prdSur)
levels(prdSur) <- c("Diabetic", "Non-Diabetic")
dfrTests <- mutate(dfrTests, Result=resVal, Outcome=prdSur)
dfrTests ## Pregnancies Glucose BloodPressure SkinThickness Insulin BMI
## 1 0 122 76 27 200 35.9
## 2 6 125 78 31 0 27.6
## 3 1 168 88 29 0 35.0
## 4 2 129 0 0 0 38.5
## 5 4 110 76 20 100 28.4
## 6 6 80 80 36 0 39.8
## 7 10 115 0 0 0 0.0
## 8 2 127 46 21 335 34.4
## 9 9 164 78 0 0 32.8
## 10 2 93 64 32 160 38.0
## 11 3 158 64 13 387 31.2
## 12 5 126 78 27 22 29.6
## 13 10 129 62 36 0 41.2
## 14 0 134 58 20 291 26.4
## 15 3 102 74 0 0 29.5
## 16 7 187 50 33 392 33.9
## 17 3 173 78 39 185 33.8
## 18 10 94 72 18 0 23.1
## 19 1 108 60 46 178 35.5
## 20 5 97 76 27 0 35.6
## 21 4 83 86 19 0 29.3
## 22 1 114 66 36 200 38.1
## 23 1 149 68 29 127 29.3
## 24 5 117 86 30 105 39.1
## 25 1 111 94 0 0 32.8
## 26 4 112 78 40 0 39.4
## 27 1 116 78 29 180 36.1
## 28 0 141 84 26 0 32.4
## 29 2 175 88 0 0 22.9
## 30 2 92 52 0 0 30.1
## 31 3 130 78 23 79 28.4
## 32 8 120 86 0 0 28.4
## 33 2 174 88 37 120 44.5
## 34 2 106 56 27 165 29.0
## 35 2 105 75 0 0 23.3
## 36 4 95 60 32 0 35.4
## 37 0 126 86 27 120 27.4
## 38 8 65 72 23 0 32.0
## 39 2 99 60 17 160 36.6
## 40 1 102 74 0 0 39.5
## 41 11 120 80 37 150 42.3
## 42 3 102 44 20 94 30.8
## 43 1 109 58 18 116 28.5
## 44 9 140 94 0 0 32.7
## 45 13 153 88 37 140 40.6
## 46 12 100 84 33 105 30.0
## 47 1 147 94 41 0 49.3
## 48 1 81 74 41 57 46.3
## 49 3 187 70 22 200 36.4
## 50 6 162 62 0 0 24.3
## 51 4 136 70 0 0 31.2
## 52 1 121 78 39 74 39.0
## 53 3 108 62 24 0 26.0
## 54 0 181 88 44 510 43.3
## 55 8 154 78 32 0 32.4
## 56 1 128 88 39 110 36.5
## 57 7 137 90 41 0 32.0
## 58 0 123 72 0 0 36.3
## 59 1 106 76 0 0 37.5
## 60 6 190 92 0 0 35.5
## 61 2 88 58 26 16 28.4
## 62 9 170 74 31 0 44.0
## 63 9 89 62 0 0 22.5
## 64 10 101 76 48 180 32.9
## 65 2 122 70 27 0 36.8
## 66 5 121 72 23 112 26.2
## 67 1 126 60 0 0 30.1
## 68 1 93 70 31 0 30.4
## DiabetesPedigreeFunction Age Result Outcome
## 1 0.483 26 0.26487765 Diabetic
## 2 0.565 49 0.30477416 Diabetic
## 3 0.905 52 0.63567019 Non-Diabetic
## 4 0.304 41 0.42809131 Diabetic
## 5 0.118 27 0.17891277 Diabetic
## 6 0.177 28 0.22309499 Diabetic
## 7 0.261 30 0.04684399 Diabetic
## 8 0.176 22 0.32895027 Diabetic
## 9 0.148 45 0.79025778 Non-Diabetic
## 10 0.674 23 0.17915652 Diabetic
## 11 0.295 24 0.54207196 Non-Diabetic
## 12 0.439 40 0.31993261 Diabetic
## 13 0.441 38 0.73870819 Non-Diabetic
## 14 0.352 21 0.18965614 Diabetic
## 15 0.121 32 0.13838338 Diabetic
## 16 0.826 34 0.87084669 Non-Diabetic
## 17 0.970 31 0.70901244 Non-Diabetic
## 18 0.595 56 0.15529198 Diabetic
## 19 0.415 24 0.20080802 Diabetic
## 20 0.378 52 0.23344176 Diabetic
## 21 0.317 34 0.08810797 Diabetic
## 22 0.289 21 0.27756710 Diabetic
## 23 0.349 42 0.36181523 Diabetic
## 24 0.251 42 0.44434841 Diabetic
## 25 0.265 45 0.17983889 Diabetic
## 26 0.236 38 0.37772434 Diabetic
## 27 0.496 25 0.25639702 Diabetic
## 28 0.433 22 0.33219383 Diabetic
## 29 0.326 22 0.46759131 Diabetic
## 30 0.141 22 0.09591609 Diabetic
## 31 0.323 34 0.26894978 Diabetic
## 32 0.259 22 0.34374102 Diabetic
## 33 0.646 24 0.84803028 Non-Diabetic
## 34 0.426 22 0.13273854 Diabetic
## 35 0.560 53 0.08266761 Diabetic
## 36 0.284 28 0.19636678 Diabetic
## 37 0.515 21 0.16392563 Diabetic
## 38 0.600 42 0.10439604 Diabetic
## 39 0.453 21 0.19063102 Diabetic
## 40 0.293 42 0.22603039 Diabetic
## 41 0.785 48 0.72603579 Non-Diabetic
## 42 0.400 26 0.15245049 Diabetic
## 43 0.219 22 0.12366633 Diabetic
## 44 0.734 45 0.62836083 Non-Diabetic
## 45 1.174 39 0.89931884 Non-Diabetic
## 46 0.488 46 0.34957467 Diabetic
## 47 0.358 27 0.75196514 Non-Diabetic
## 48 1.096 32 0.20885164 Diabetic
## 49 0.408 36 0.82913007 Non-Diabetic
## 50 0.178 50 0.52739308 Non-Diabetic
## 51 1.182 22 0.39624524 Diabetic
## 52 0.261 28 0.34367173 Diabetic
## 53 0.223 25 0.12613154 Diabetic
## 54 0.222 26 0.82812990 Non-Diabetic
## 55 0.443 45 0.69522905 Non-Diabetic
## 56 1.057 37 0.34668583 Diabetic
## 57 0.391 39 0.52291242 Non-Diabetic
## 58 0.258 52 0.27830365 Diabetic
## 59 0.197 26 0.21873840 Diabetic
## 60 0.278 66 0.88186852 Non-Diabetic
## 61 0.766 22 0.07421535 Diabetic
## 62 0.403 43 0.92417792 Non-Diabetic
## 63 0.142 33 0.11427590 Diabetic
## 64 0.171 63 0.35237604 Diabetic
## 65 0.340 27 0.33873490 Diabetic
## 66 0.245 30 0.22873744 Diabetic
## 67 0.349 47 0.22143228 Diabetic
## 68 0.315 23 0.08939939 Diabetic