# Is the percent of total deviance explained a useful model summary? [duplicate]

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)
data=attitude,family = gaussian)

(deviance(fit1)-deviance(fit2))/deviance(fit1)


 0.732602

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?

• Is this: ats.ucla.edu/stat/mult_pkg/faq/general/psuedo_rsquareds.htm helpful, or do you mean something else? – gung - Reinstate Monica Jan 4 '12 at 20:04
• Indeed. The deviance R^2 from my question is the same as McFadden's measure. My question is really about interpretation of the deviance R^2 for non-Gaussian models. With a normal link it corresponds to SSR/SST and thus has a clean and neat interpretation. Is this true of other families? Do the results depend on the link used and the characteristics of the response? – Brett Jan 4 '12 at 20:47
• Walking down another path, I stumbled onto a very clear answer to my question in by @probabilityislogic in the thread at: stats.stackexchange.com/questions/3559/… – Brett Jan 6 '12 at 16:58
• Could you re-post your comment as an answer to your own question if it covers everything you wanted? Then you can accept your answer, and this won't appear as an unanswered question. – Corone Feb 2 '13 at 12:06
• The general deviance based R2, 1-residual deviance/null deviance, applies to any GLM with any family & link function. McFadden's was originally defined for logistic regression (where the log-likelihood of a saturated model=0) and in that case the above formula is correct, but the generically correct version would be 1-residual deviance/null deviance, see stats.stackexchange.com/questions/359906/… – Tom Wenseleers Jun 14 '19 at 23:12