# November 19, 2024

setwd("~/Class/MATH5910/Fall2024/R")

### Example 1
### See slides (no R)


### Example 2

ex2data<-read.table('ex2data.txt',header=T)
ex2.glm<-glm(CHD~Age, family=binomial, data=ex2data)
summary(ex2.glm)

1/(1+exp(-(-5.30945+0.11092*50)))
1/(1+exp(-(-5.30945+0.11092*55)))
1/(1+exp(-(-5.30945+0.11092*45)))

predict(ex2.glm,type = "response")
1/(1+exp(-(-5.30945+0.11092*20)))
1/(1+exp(-(-5.30945+0.11092*69)))
predict(ex2.glm)
predict(ex2.glm,newdata=data.frame(Age=50),type = "response")
predict(ex2.glm,newdata=data.frame(Age=seq(1,100)),type = "response")
plot(predict(ex2.glm,newdata=data.frame(Age=seq(1,100)),type = "response"),type='l')
?predict.glm

anova(ex2.glm)
anova(ex2.glm, test='Chisq')


### Example 3

xy.data<-read.table("xy.data.txt",header=T)
xy.data
xy.table<-table(xy.data)
xy.table
(xy.table[1,1]*xy.table[2,2])/(xy.table[1,2]*xy.table[2,1])
chisq.test(xy.table)
xy.glm<-glm(factor(y)~factor(x),family=binomial,data=xy.data)
summary(xy.glm)
anova(xy.glm, test='Chisq')


### Example 4

ex4data<-read.table('ex4data.txt',header=T)
ex4data

ex4.glm<-glm(Y~X1*X2,family=binomial,data=ex4data)
summary(ex4.glm)
anova(ex4.glm, test='Chisq')

summary(glm(Y~X1,family=binomial,data=ex4data))
summary(glm(Y~X1+X2,family=binomial,data=ex4data))


### Example 5

#ex4.glm<-glm(Y~X1*X2,family=binomial,data=ex4data)
summary(ex4.glm)
anova(ex4.glm, test='Chisq')

ex4.glm1<-glm(Y~X1*X2,family=binomial(link="logit"),data=ex4data)
summary(ex4.glm1)
anova(ex4.glm1, test='Chisq')

ex4.glm2<-glm(Y~X1*X2,family=binomial(link="probit"), data=ex4data)
summary(ex4.glm2)
anova(ex4.glm2, test='Chisq')

ex4.glm3<-glm(Y~X1*X2,family=binomial(link="cloglog"), data=ex4data)
summary(ex4.glm3)
anova(ex4.glm3, test='Chisq')


### Example 6

?glm

counts <- c(18,17,15,20,10,20,25,13,12)
outcome <- gl(3,1,9)
treatment <- gl(3,3)
data.frame(treatment, outcome, counts)

glm.D93 <- glm(counts ~ outcome + treatment, family = poisson())
anova(glm.D93)

summary(glm.D93)


### Example 7

library(alr4)

galapagos
?galapagos

summary(galapagos)
plot(galapagos)

gala.a.poi<-glm(NS~Area, family=poisson, data=galapagos)
summary(gala.a.poi)

gala.e.poi<-glm(NS~Elevation, family=poisson, data=galapagos)
summary(gala.e.poi)

gala.ae.poi<-glm(NS~Area+Elevation, family=poisson, data=galapagos)
summary(gala.ae.poi)

gala.ane.poi<-glm(NS~Area+Anear+Elevation, family=poisson, data=galapagos)
summary(gala.ane.poi)

gala.ade.poi<-glm(NS~Area+Dist+Elevation, family=poisson, data=galapagos)
summary(gala.ade.poi)

# Bad practice...

gala.all.poi<-glm(NS~., family=poisson, data=galapagos)
summary(gala.all.poi)
step(gala.all.poi)

gala.poi<-glm(NS~., family=poisson, data=galapagos[complete.cases(galapagos),])
summary(gala.poi)
gala.poi.step<-step(gala.poi)
summary(gala.poi.step)
anova(gala.poi.step)