R Short Course Session 5

Transcription

1 R Short Course Session 5 Daniel Zhao, PhD Sixia Chen, PhD Department of Biostatistics and Epidemiology College of Public Health, OUHSC 11/20/2015

2 Outline Linear Regression Fit linear regression and check results Examine normality, independence and heteroscedasticity Examine outliers and influence points Examine collinearity Model selection procedure Model comparisons

3 Outline (2) Logistic Regression Fit logistic model and check results Odds ratio and confidence intervals Model selection procedure Goodness of fit test

4 Linear Regression Fitting linear regression of y vs x: lm(y~x,data=,weights=,singular.ok=true) Example: Input data is Prestige dataset in R package car Variables: education, income, women, prestige, census and type

5 Linear Regression (2) summary(prestige)

6 pairs(prestige) Linear Regression (3)

7 Fit linear regression reg1<lm(prestige~education+log2(income)+women, data=prestige)

8 summary(reg1) Check the results

9 attributes(reg1) Check the results (2)

10 Check the results (3) reg1$coefficients reg1$df.residual

11 Examine Normality QQ plot for studentized residuals: qqplot(reg1, main="qq Plot") Distribution of studentized residuals library(mass) sresid <- studres(reg1) hist(sresid, freq=false,main="distribution of Studentized Residuals") xfit<-seq(min(sresid),max(sresid),length=40) yfit<-dnorm(xfit) lines(xfit, yfit)

12 Examine Normality (2)

13 Examine Normality (3) shapiro.test(reg1$residuals) ad.test(reg1$residuals)

14 Plots: Examine Independence

15 Examine Independence (2) Durbin Watson Test: durbinwatsontest(reg1)

16 Plots: Examine heteroscedasticity

17 Examine heteroscedasticity (2) Goldfeld-Quandt test: gqtest(reg1). Note that we need to install R package lmtest Non-constant error variance test: ncvtest(reg1)

18 Examine Outliers outliertest(reg1) # Bonferonni p-value for most extreme obs lm.influence(reg1) # Calculate diagonal hat matrix and the influence of each point on regression coefficient and standard deviation estimation

19 Examine Outliers (2) lm.influence(reg1)$hat #calculate leverage lm.influence(reg1)$hat[lm.influence(reg1)$hat >3*(3+1)/102] #Identify high leverage cases

20 Examine influence points influence.measures(reg1) # calculate DFFITS, COOK S D, DFBETAS and Covariance ratios

21 Examine influence points (2) Cook s D plot (identify D values>4/(n-k-1)): cutoff<-4/((nrow(prestige)- length(reg1$coefficients)-2)) plot(reg1, which=4, cook.levels=cutoff) Influence Plot: influenceplot(reg1, id.method="identify", main="influence Plot", sub="circle size is proportial to Cook's Distance" )

22 Cook s D plot

23 Influence Plot

24 Examine Colinearity Variance inflation factors: vif(reg1) Problem? sqrt(vif(reg1)) > 2

25 Examine Colinearity (2) Added variable plots: avplots(reg1)

26 Model Selection Procedures step(object=,scope=list(lower=,upper=),directi on=c( both, backward, forward ), steps=1000,k=2, ) #object is an object representing a model #scope defines the range of models examined in the stepwise search #direction controls the mode of stepwise search

27 Model Selection Procedures (2) edu2<-education^2 loginc2<-log2(income)^2 edulogin<-education*log2(income) reg2<lm(prestige~education+edu2+log2(income)+lo ginc2+edulogin+women,data=prestige) step(reg2,direction='both')

28 Model Selection Procedures (3)

29 anova(reg1,reg2) Model Comparisons

30 Logistic Regression Input data: plasma in package HSAUR Variables: Fibrinogen: the fibrinogen level in the blood Globulin: the globulin level in the blood ESR: the erythrocyte sedimentation rate, either less or greater 20 mm /hour

31 Logistic Regression (2) plasma data: head(plasma) Objective: fit logistic regression by using ESR as dependent variable and other two as independent variables

32 Logistic Regression (3) glm(formula, data =,family=,weights=,intercept=, ) #formula is y~x type #data is the input dataset #family can be gussian, binomial or others #weights specifies weighted or unweighted analysis #intercept is logical (Do we need intercept or not?)

33 Fit logistic model fit<glm(esr~fibrinogen+globulin,data=plasma,fa mily=binomial('logit'))

34 summary(fit) Fit logistic model (2)

35 attributes(fit) Fit logistic model (3)

36 Logistic regression plot attach(plasma) ESR2<-rep(1,dim(plasma)[1]) ESR2[ESR=='ESR > 20']<-0 fit<glm(esr2~fibrinogen,data=plasma,family=binomi al('logit')) plot(fibrinogen, ESR2) lines(fibrinogen[order(fibrinogen)],fit$fitted.value s[order(fibrinogen)])

37 Logistic regression plot (2)

38 Odds ratio and confidence intervals Calculate Odds ratio: exp(coef(fit)) Calculate variance covariance for coefficients: vcov(fit)

39 Odds ratio and confidence intervals (2) Confidence interval for coefficient: confint.default(fit) Confidence interval for Odds ratio: exp(confint.default(fit))

40 Model selection fit2<glm(esr2~fibrinogen+globulin,data=plasma,fa mily=binomial('logit')) step(fit2)

41 Model selection (2)

42 Hosmer-Lemeshow goodness of fit test hoslem.test(x,y,g=10) in R package ResourceSelection #x is a numeric vector of observations, binary (0/1) #y is expected values #g is number of bins to use to calculate quantiles

43 Example hoslem.test(esr2,fit2$fitted.values)

44 Questions Contact and