My question is regarding the interpretation of the percent of deviance explained (and other $R^2$ anaologs or pseudo $R^2$ values for GLMs.
Is this a meaningful summary statistic for models other than Gaussian? That is, is it at least as meaningful/useful as the $R^2$ statistic in the typical OLS regression model. (We'll work under the assumption that $R^2$ is useful summary measure in an OLS framework).
Of course, percent of deviance explained is equivalent to the $R^2$ value if the link is Gaussian.
fit1<-glm( rating~1, data=attitude,family = gaussian) fit2<-glm( rating~complaints+privileges+learning+raises+critical+advance, data=attitude,family = gaussian) (deviance(fit1)-deviance(fit2))/deviance(fit1)
summary(lm( rating~complaints+privileges+learning+raises+critical+advance, data=attitude))
Multiple R-squared: 0.7326
Is there a similarly meaningful interpretation of the percent of deviance explained from models from other GLM families, like binomial (logit/probit) or poisson regression? Or, does the change in link function and the characteristics of the model/response affect the interpretation of this statistic?