# Question 1: X <-paste("X",1:3,sep="") Y <-paste("Y",1:3,sep="") Z <-paste("Z",1:3,sep="") data.mat <- cbind(expand.grid(Row=X,Col=Y,Level=Z),count=rep(100,27)) (tbl <-tapply(data.mat$count,data.mat[,1:3], sum) ) fit.1 <- glm(count~ (Row + Col + Level)^3, family="poisson", data=data.mat) summary(fit.1) # Question 2: x <-paste(0:1,sep="") y <-paste(0:1,sep="") z <-paste(0:1,sep="") (data.mat <- cbind(expand.grid(Y=y,X=x,Z=z),count=c(5,10,10,20,10,20,5,10))) (tbl <-tapply(data.mat$count,data.mat[,1:3], sum) ) tbl[1,,] tbl[2,,] apply(tbl,c(2,3),sum) fit.1 <- glm(count ~ X*Z*Y, family="poisson", data=data.mat) summary(fit.1) anova(fit.1) # Question 4 ( tbl <- cbind(expand.grid(Umb=0:1,Acc=0:1,Wth=c("Sharav","Pleasant","Rain")), counts = c(168, 17, 36, 4, 11, 32, 13, 17, 41, 6, 16, 4)) ) fitUW.AW <- glm(counts ~ Umb*Wth + Acc*Wth, family="poisson",data=tbl) summary(fitUW.AW) model.matrix(fitUW.AW) cbind(tbl,model.matrix(fitUW.AW)) fitUW.AW$y round(fitUW.AW$fit,2) fitUW.AW$dev sum(fitUW.AW$coef[c(1,2,3,5,6,8)]) (lin.est <- sum(model.matrix(fitUW.AW)[8,] * fitUW.AW$coef)) exp(lin.est) # ( Excerscise 5-a actually refers to observation number 12!!) summary(fitUW.AW) - 2 * sum(fitUW.AW$y*log(fitUW.AW$fit / fitUW.AW$y)) - 2 * sum(log(dpois(fitUW.AW$y,fitUW.AW$fit))) + 2*9 # AIC sum(log(dpois(fitUW.AW$y,fitUW.AW$fit))) sum(fitUW.AW$y*log(fitUW.AW$fit)) - sum(fitUW.AW$fit) - sum(log(factorial(fitUW.AW$y))) sum(fitUW.AW$fit) sum(fitUW.AW$y)