X=factor(c(rep("x1",4),rep("x2",4))) Y=factor(c(rep(c("y1","y1","y2","y2"),2))) Z=factor(c(rep(c("z1","z2"),4))) count=c(0,6,5,9,16,5,7,0) table=xtabs(count~X+Y+Z) ### Table 1 of X*Y list(Frequency=table,RowPct=prop.table(table[,,1],1)) chisq.test(table[,,1],correct=FALSE) ### Table 2 of X*Y list(Frequency=table,RowPct=prop.table(table[,,2],1)) chisq.test(table[,,2],correct=FALSE) ### Saturated Model model=glm(count~X+Y+Z+X*Y+X*Z+Y*Z+X*Y*Z,family=poisson(link=log)) summary(model) ### Complete Independence Model:(X,Y,Z) model=glm(count~X+Y+Z,family=poisson(link=log)) summary(model) ### Joint Independence Model:(XY,Z) model=glm(count~X+Y+Z+X*Y,family=poisson(link=log)) summary(model) ### Joint Independence Model:(XZ,Y) model=glm(count~X+Y+Z+X*Z,family=poisson(link=log)) summary(model) ### Joint Independence Model:(YZ,X) model=glm(count~X+Y+Z+Y*Z,family=poisson(link=log)) summary(model) ### Conditional Indepence Model:(XY,XZ) model=glm(count~X+Y+Z+X*Y+X*Z,family=poisson(link=log)) summary(model) ### Conditional Indepence Model:(XY,YZ) model=glm(count~X+Y+Z+X*Y+Y*Z,family=poisson(link=log)) summary(model) ### Conditional Indepence Model:(XZ,YZ) model=glm(count~X+Y+Z+X*Z+Y*Z,family=poisson(link=log)) summary(model) ### Homogeneous Association (XY,XZ,YZ) model=glm(count~X+Y+Z+X*Y+X*Z+Z*Y,family=poisson(link=log)) summary(model) ### Zero Margin,Bad Pattern of Zeros count=c(0,6,5,9,0,5,16,7) table=xtabs(count~X+Y+Z) ### Homogeneous Association (XY,XZ,YZ)with zero margin: (XY,XZ,YZ) model=glm(count~X+Y+Z+X*Y+X*Z+Z*Y,family=poisson(link=log)) summary(model) ### Delete Zero Values count=c(0,6,5,9,0,5,16,7) count=count[which(count!=0)] X=X[which(count!=0)] Y=Y[which(count!=0)] Z=Z[which(count!=0)] ### Homogeneous Association with zero margin: (XY,XZ,YZ) model=glm(count~X+Y+Z+X*Y+X*Z+Z*Y,family=poisson(link=log)) summary(model)