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## ANCOVA with a Binary Response Variable

In our next example the binary response variable is parasite infection (infected or not) and the explanatory variables are weight and age (continuous) and sex (categorical). We begin with data inspection:

```infection<-read.table("c:\\temp\\infection.txt,header=T)
attach(infection)
names(infection)

[1]  "infected"  "age"  "weight"  "sex"

par(mfrow=c(1,2))
plot(infected,weight,xlab="Infection",ylab="Weight")
plot(infected,age,xlab="Infection",ylab="Age")```

Infected individuals are substantially lighter than uninfected individuals, and occur in a much narrower range of ages. To see the relationship between infection and gender (both categori cal variables) we can use table:

```table(infected,sex)

table(infected,sex)
sex
infected    female    male
absent        17      47
present        11       6```

This indicates that the infection is much more prevalent in females (11/28) than in males (6/53).

We now proceed, as usual, to fit a maximal model with different slopes for each level of the categorical variable:

```model<-glm(infected~age*weight*sex,family=binomial)
summary(model) Coefficients: Estimate Std.Error z value Pr(>|z|) (Intercept) -0.109124 1.375388 -0.079 0.937 age 0.024128 0.020874 1.156 0.248 weight -0.074156 0.147678 -0.502 0.616 sexmale -5.969109 4.278066 -1.395 0.163 age:weight -0.001977 0.002006 -0.985 0.325 age:sexmale 0.038086 0.041325 0.922 0.357 weight:sexmale 0.213830 ...```

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