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## Analysing Schoener's Lizards as Proportion Data

```names(new.lizards)

[1]  "Ao"  "Ag"  "sun"  "height"  "perch"  "time"```

The response variable is a two-column object containing the counts of the two species:

`y<-cbind(Ao,Ag)`

We begin by fitting the saturated model with all possible interactions:

`model1<-glm(y~sun*height*perch*time,binomial)`

Since there are no nuisance variables, we can use step directly to begin the model simplification (compare this with p. 560 with a log-linear model of the same data):

```model2<-step(model1)

Start: AIC= 102.82
y ~ sun * height * perch * time```
```Df    Deviance AIC
- sun:height:perch:time   1   2.180e-10 100.82
<none>              3.582e-10 102.82```

Out goes the four-way interaction (with a sigh of relief):

```Step: AIC= 100.82
Df   Deviance      AIC
- sun:height:time        2      0.442   97.266
- sun:perch:time         2      0.810   97.634
- height:perch:time      2      3.222  100.046
<none>                       2.18e-10  100.824
- sun:height:perch       1     2.709   101.533```

Next, we wave goodbye to three of the three-way interactions

```Step: AIC= 97.27
Df  Deviance      AIC
- sun:perch:time         2     1.071   93.896
<none>                         0.442   97.266
- height:perch:time      2     4.648   97.472
- sun:height:perch       1     3.111   97.936
Step: AIC= 93.9
Df  Deviance      AIC
- sun:time               2     3.340   92.165
<none>                         1.071   93.896
- sun:height:perch       1    3.302   94.126
- height:perch:time      2     5.791   94.615```

and the two-way interaction of sun by time

```Step: AIC= 92.16
Df  Deviance       AIC
<none>                 3.340    92.165
- sun:height:perch     1     5.827    92.651
- height:perch:time    2     8.542    93.366

summary(model2) Call: glm(formu la = y ~ sun + height + ...```

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