[R] Dispersion factor in GLM

[Johan Stenberg]

Dear all,

I have two questions concerning GLM (logistic regression) with
family=binomial.

1. A measure of the departure from the binomial assumption is given by
the
dispersion factor (= residual deviance / residual df). The data is
over-dispersed when the dispersion factor is significantly higher than 1
(Crawley, page 518). Is there any way to test if the dispersion factor
is significantly higher than 1? The residual deviance should be
chi2-distributed which should allow to test for the significance of the
departure...
See below to see how my syntax looks like.

2. How do you calculate the proportion of deviance explained by the
model (the equivalent of r2 in a standard regression) in R?

Kind regards

Johan Stenberg


> y<-cbind(para,unpara)
> model<-glm(y~log(larvae),binomial)
> summary(model)

Call:
glm(formula = y ~ log(larvae), family = binomial)

Deviance Residuals:
    Min       1Q   Median       3Q      Max
-2.0633  -1.6218  -0.1871   0.7907   2.7670

Coefficients:
            Estimate Std. Error z value Pr(>|z|)
(Intercept)   1.0025     0.7049   1.422  0.15499
log(larvae)  -1.0640     0.3870  -2.749  0.00597 **

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 35.981  on 12  degrees of freedom
Residual deviance: 27.298  on 11  degrees of freedom
AIC: 40.949

Number of Fisher Scoring iterations: 4

> anova(model,test="F")
Analysis of Deviance Table

Model: binomial, link: logit

Response: y

Terms added sequentially (first to last)


            Df Deviance Resid. Df Resid. Dev      F   Pr(>F)
NULL                           12     35.981
log(larvae)  1    8.683        11     27.298 8.6828 0.003212 **