Alternative Goodness-of-fit Measure (Reading: Faraway (2006, 1st ed.), section 2.9)

    We now use the Bliss insect data studied in the previous lab,  to demonstrate how to calculate the Perason's X² statistic:

> bliss <- read.table("bliss.txt")

> modl <- glm(cbind(dead,alive) ~ conc, family=binomial, data=bliss)

> sum(residuals(modl,type="pearson")^2)

The Perason's X² statistic is typically close in size to the deviance:

> deviance(modl)

As can be seen, there is little difference here between the X² and the deviance.

    For the Bliss insect data, the generalized R² can be calculated by:

> (1-exp((modl$dev-modl$null)/150))/(1-exp(-modl$null/150))

Notice that

• the generalized R² is very close to 1, which indicates this is a very good fit.

• in the calculation of the generalized R², we have use K=150 as there are 5 covariate classes (i.e., k=5) each with 30 Bernoulli observations (i.e., n_i=30 for i=1,...,k).