HW1
Kunal Dolas
1/25/2021
####Q1:Fit a model with Class as the outcome and all of the covariates as predictors, then reduce the model using the step function. Report your final model and the deviance. Can you use the deviance to tell if the final model fits the data?
library(faraway)
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──## ✓ ggplot2 3.3.3 ✓ purrr 0.3.4
## ✓ tibble 3.0.6 ✓ dplyr 1.0.3
## ✓ tidyr 1.1.2 ✓ stringr 1.4.0
## ✓ readr 1.4.0 ✓ forcats 0.5.1## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()library(ggplot2)
library(pROC)## Type 'citation("pROC")' for a citation.##
## Attaching package: 'pROC'## The following objects are masked from 'package:stats':
##
## cov, smooth, varlibrary(ResourceSelection)## ResourceSelection 0.3-5 2019-07-22data(wbca)
wbca## Class Adhes BNucl Chrom Epith Mitos NNucl Thick UShap USize
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## 582 1 1 1 3 2 1 1 5 3 1
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## 639 1 1 1 2 2 1 1 5 1 1
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## 658 1 1 1 1 2 1 1 4 4 1
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## 672 1 1 1 1 2 8 1 1 1 1
## 673 1 3 1 1 2 1 1 1 1 1
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## 680 0 4 4 10 3 1 6 4 6 8
## 681 0 5 5 10 4 1 4 4 8 8wbcam <- na.omit(wbca)
lmod <- glm(Class ~ Adhes+BNucl+Chrom+Epith+Mitos+NNucl+Thick+UShap+USize, family = binomial, data=wbcam)
summary(lmod)##
## Call:
## glm(formula = Class ~ Adhes + BNucl + Chrom + Epith + Mitos +
## NNucl + Thick + UShap + USize, family = binomial, data = wbcam)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.48282 -0.01179 0.04739 0.09678 3.06425
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 11.16678 1.41491 7.892 2.97e-15 ***
## Adhes -0.39681 0.13384 -2.965 0.00303 **
## BNucl -0.41478 0.10230 -4.055 5.02e-05 ***
## Chrom -0.56456 0.18728 -3.014 0.00257 **
## Epith -0.06440 0.16595 -0.388 0.69795
## Mitos -0.65713 0.36764 -1.787 0.07387 .
## NNucl -0.28659 0.12620 -2.271 0.02315 *
## Thick -0.62675 0.15890 -3.944 8.01e-05 ***
## UShap -0.28011 0.25235 -1.110 0.26699
## USize 0.05718 0.23271 0.246 0.80589
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 881.388 on 680 degrees of freedom
## Residual deviance: 89.464 on 671 degrees of freedom
## AIC: 109.46
##
## Number of Fisher Scoring iterations: 8lmodr <- step(lmod)## Start: AIC=109.46
## Class ~ Adhes + BNucl + Chrom + Epith + Mitos + NNucl + Thick +
## UShap + USize
##
## Df Deviance AIC
## - USize 1 89.523 107.52
## - Epith 1 89.613 107.61
## - UShap 1 90.627 108.63
## <none> 89.464 109.46
## - Mitos 1 93.551 111.55
## - NNucl 1 95.204 113.20
## - Adhes 1 98.844 116.84
## - Chrom 1 99.841 117.84
## - BNucl 1 109.000 127.00
## - Thick 1 110.239 128.24
##
## Step: AIC=107.52
## Class ~ Adhes + BNucl + Chrom + Epith + Mitos + NNucl + Thick +
## UShap
##
## Df Deviance AIC
## - Epith 1 89.662 105.66
## - UShap 1 91.355 107.36
## <none> 89.523 107.52
## - Mitos 1 93.552 109.55
## - NNucl 1 95.231 111.23
## - Adhes 1 99.042 115.04
## - Chrom 1 100.153 116.15
## - BNucl 1 109.064 125.06
## - Thick 1 110.465 126.47
##
## Step: AIC=105.66
## Class ~ Adhes + BNucl + Chrom + Mitos + NNucl + Thick + UShap
##
## Df Deviance AIC
## <none> 89.662 105.66
## - UShap 1 91.884 105.88
## - Mitos 1 93.714 107.71
## - NNucl 1 95.853 109.85
## - Adhes 1 100.126 114.13
## - Chrom 1 100.844 114.84
## - BNucl 1 109.762 123.76
## - Thick 1 110.632 124.63summary(lmodr)##
## Call:
## glm(formula = Class ~ Adhes + BNucl + Chrom + Mitos + NNucl +
## Thick + UShap, family = binomial, data = wbcam)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.44161 -0.01119 0.04962 0.09741 3.08205
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 11.0333 1.3632 8.094 5.79e-16 ***
## Adhes -0.3984 0.1294 -3.080 0.00207 **
## BNucl -0.4192 0.1020 -4.111 3.93e-05 ***
## Chrom -0.5679 0.1840 -3.085 0.00203 **
## Mitos -0.6456 0.3634 -1.777 0.07561 .
## NNucl -0.2915 0.1236 -2.358 0.01837 *
## Thick -0.6216 0.1579 -3.937 8.27e-05 ***
## UShap -0.2541 0.1785 -1.423 0.15461
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 881.388 on 680 degrees of freedom
## Residual deviance: 89.662 on 673 degrees of freedom
## AIC: 105.66
##
## Number of Fisher Scoring iterations: 8sumary(lmodr)## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 11.03333 1.36320 8.0937 5.788e-16
## Adhes -0.39843 0.12935 -3.0802 0.002069
## BNucl -0.41920 0.10196 -4.1114 3.933e-05
## Chrom -0.56785 0.18405 -3.0854 0.002033
## Mitos -0.64561 0.36337 -1.7767 0.075611
## NNucl -0.29153 0.12363 -2.3580 0.018372
## Thick -0.62163 0.15791 -3.9366 8.266e-05
## UShap -0.25407 0.17849 -1.4234 0.154614
##
## n = 681 p = 8
## Deviance = 89.66176 Null Deviance = 881.38820 (Difference = 791.72644)###Just the defiance is not enough for binomial regression to tell if the final model fits the data. We can use it as a chi square test to compare nested models.
###Q2.Use the Hosmer-Lemeshow test to determine if the final model fits the data.
library("varhandle")
actual=as.data.frame(to.dummy(wbcam$Class,"yes"))
actual=actual$yes.Yes
hoslem.test(wbcam$Class, fitted(lmodr), g=10)##
## Hosmer and Lemeshow goodness of fit (GOF) test
##
## data: wbcam$Class, fitted(lmodr)
## X-squared = 4.155, df = 8, p-value = 0.8429#####Q3. Plot the ROC curve for the final model. What is the area under the curve and what does it say about the predictive strength of your model? Explain why area under the curve is a useful measure for characterizing the success of your predictive model.
gmod<-glm(Class ~ Adhes+BNucl+Chrom+Epith+Mitos+NNucl+Thick+UShap+USize, family = binomial, data=wbcam)
prob<- predict(gmod, type="response")
g<-roc(Class~prob, data=na.omit(wbca))## Setting levels: control = 0, case = 1## Setting direction: controls < casesplot(g)
auc(g)## Area under the curve: 0.9974## The Value of AUC is 0.9974 suggesting good fit of model.
####Area under curve is an indication of a probability fro an observation to predict the response correctly and therefore can be used to test the accuracy of the model. The value of .8-0.9 of AUC indicates good prediction by the model.