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When running a GLMM in R with family=gaussian and link=identity, it's easy enough to test whether normality and homoscedasticity of the residuals have been achieved (qqnorm plots and shapiro-wilks tests for normality and residuals vs. fitted plots for homoscedasticity). But what process should I use to test assumptions have been met when using a non-gaussian family and a non-identity link?

I'm mostly interested in how to test to see if the residuals are consistent with an inverse gaussian family and log-link, but how to assess for a gamma distribution might also be useful.

Here is a histogram of my GLMM residuals when I used an inverse gaussian family and log-link in case it helps at all: http://i.imgur.com/PlK5Q33.png

From what I've found, it sounds like qqPlot from the car package might be useful, but I'm not sure how to go about choosing shape parameters and such like. As well, that only accounts for the distribution I specified..not the link function.

Thanks in advance!

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  • $\begingroup$ if you can find an answer that applies to GLMs, it should also apply reasonably well to GLMMs, because if you condition on the conditional modes ("random effects"/"BLUPs"), GLMMs are the same as GLMs. So you're really looking for adequacy-of-link (Pregibon 1980) and adequacy-of-distribution (Augustin et al. Comp Stat & Data Analysis 2012) tests/plots that can easily be implemented for GLMMs. $\endgroup$ – Ben Bolker Sep 30 '14 at 20:37
  • $\begingroup$ one other possibility is to create parametric bootstrap/posterior predictive simulations of residual distributions and compare them against yours. $\endgroup$ – Ben Bolker Sep 30 '14 at 20:37
  • $\begingroup$ Ben's suggestion is implemented in cran.r-project.org/web/packages/DHARMa/index.html $\endgroup$ – Florian Hartig Jan 9 '17 at 20:24

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