GLM.md

Generalized linear models (GLM)

Dataset

donner

crab

Note

Inclass assignment #2 (Due 9/18 11:59PM).

Create a PDF report using RMarkdown/knitr. Give the title of the report as "Last_name.First_name.inclass2.pdf." Then upload both RMD (5 points) and PDF (5 points) files in the D2L:Assessments: Assignments:inclass2.

Hand in the hard copy of the PDF file by Next Monday in class (extra 1 point).

1. Write a function called, NegLogLik, which computes the binomial negative log likelihood for binary outcome variable.

NegLoglik=function(X,y,b){
eta=X%*%b
p=exp(eta)/(1+exp(eta))
Loglik=sum(ifelse(y==1,log(p),log(1-p)))
return(-Loglik)
}

2. Consider donner dataset. Estimate coefficients for age and sex with survive being outcome variable using the optim function. Compare with the results with the estimates obtained by the glm function in R.

donner=read.table(Choose.file()) ## choose donner.txt
survive=donner[,3]
age=donner[,1]
sex=donner[,2]
colnames(donner)=c("age","sex","survive")
head(donner)

b.ini=c(0,0,0)
X=cbind(1,age,sex)
y=survive
optim(fn=NegLoglik, X=X, y=y, par=b.ini)  #By default `optim` searches for parameters, which minimize the function `fn`.


model=glm(survive~age+sex, data=donner, family=binomial("logit"))
summary(model)$coefficients

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