Is there a way to get the null deviance and df for a generalized linear mixed model fit with glmer()? Is there a reason that this is not included in the summary() output, the way that it is with a glm() object?

CodePudding user response：

You can compute the null deviance by re-fitting the model with an intercept term only, e.g.

gm1 <- glmer(cbind(incidence, size - incidence) ~ period   (1 | herd),
                   data = cbpp, family = binomial)
gm0 <- update(gm1, . ~ 1   (1|herd))
deviance(gm1)  ## 73.47
deviance(gm0)  ## 92.42 (null deviance)

• I'm not sure what you mean by the "null df" for the GLMM; the 'denominator degree of freedom' measure of effective sample size that works perfectly for balanced ANOVAs and questionably for linear mixed models [via inclusion/exclusion, Satterthwaite, Kenward-Roger, etc.] is hard to define for GLMMs.
• I can think of a couple of reasons that lme4 doesn't automatically do this computation for you:
  • it could be an expensive re-fit (even for GLMs it does require refitting the model, see here for the code in glm that does it)
  • it's less obvious for GLMMs what the appropriate null model for comparison is. Do you remove both random and fixed effects and reduce the model to a GLM? Do you keep all of the random effects, or only intercept-level random effects, or some other mixture depending on the context of the question? Making the user do it themselves forces them to make this choice.

(That said, I don't believe that omitting the null deviance was an explicit choice.)

If you do choose to discard all of the random effects (i.e. comparing to deviance(glm(cbind(incidence, size - incidence) ~ period, data =cbpp, family = binomial)) in the example above, you should be able to do a meaningful comparison with a glmer fit, but there are some subtleties: you might want to read the section on Deviance and log-likelihood of GLMMs in ?deviance.merMod.