# 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)


[1] 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? Jan 4, 2012 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? Jan 4, 2012 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/… Jan 6, 2012 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. Feb 2, 2013 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/… Jun 14, 2019 at 23:12