[R-sig-ME] Anova()'s Wald chisquare test for predictors with df > 1 in a logistic GLMM

[Juho Kristian Ruohonen]

Hi,

I'm trying to figure out how the Wald chi-square test is performed for a
nominal predictor with more than two levels in the context of a logistic
GLMM. With fixed-effects logistic models, Anova() defaults to a
likelihood-ratio test, but since this requires refitting the model, it
would be too slow for a GLMM, thus Anova() performs Wald chi-square tests
instead. But how are they calculated for a multi-level nominal predictor?

My (un)educated guess is that for each level of the nominal variable, the
z-score is squared and the sum of these squares compared to the right-tail
probability of the chi-squared distribution with DF equal to the number of
levels of the predictor minus one. And indeed this square-the-z approach
seems to correctly reproduce the results of Anova() for predictors with a
single degree of freedom. But I can't make it reproduce the results of
Anova() for predictors with more than one level. Hence my question: how is
the test statistic calculated?

(My logistic GLMM was fit using glmer())

Best,

J

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