[R-sig-ME] Using residuals to test for random effect

[Max Reuter]

Dear list members,

I have run a GLMM on behavioural data from a species of fly. We investigate the rate with which females do or do not accept mates (a binomial response) depending on whether the males are relatives or not (a fixed treatment effect). Females come from 21 different genetic lines and the line is included as a random effect.

To test whether female behaviour has a genetic component I would like to assess whether including the random line effect significantly improves the model fit. For a Gaussian model, this can be done using the likelihood-ratio tests implemented in the package RLRsim, but this does not seem to work for a binomial model. As a solution, this post (https://stat.ethz.ch/pipermail/r-sig-mixed-models/2010q3/004338.html) suggested to effectively 'gaussianise' the problem. This could be done by first running a  glm with the fixed effect only, take its deviance residuals and use those as the dependent variable in a gaussian lmer with the intercept as fixed effect as well as the random effect. The significance of the random effect in this model can then be analysed using RLRsim.

I have done this and found my random line effect to be significant. This result, however, only holds if I use the deviance residuals (as suggested by the post mentioned above) or Pearson residuals. For other types of residuals the line effect does not improve the model fit.

I have read Davison and Snell and have some understanding of what the different types of residuals represent, but I still have trouble to get a feeling for how the choice of residuals affects the test above. Any help would be greatly appreciated!

Many thanks and best regards, Max






___________________________________________________________
Max Reuter
				         
Research Department of Genetics, Evolution and Environment
Faculty of Life Sciences
University College London
4 Stephenson Way
London NW1 2HE, UK

Phone: +44-20-76795095 (internal 25095)

Lab: http://www.homepages.ucl.ac.uk/~ucbtmre/Labsite/
Department: http://www.ucl.ac.uk/gee