# [R] Dispersion factor in GLM

From: Johan Stenberg <jstenberg_at_ice.mpg.de>
Date: Wed 16 Mar 2005 - 06:26:15 EST

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)

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

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 **

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