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On two threads, here and here, it suggests that random effects in GLMMs can be omitted if their variance approximates 0. This raises the question, below which level of variance can you reasonably omit a random effect from a GLMM? Would it be reasonable to omit a random effect that has a variance of <1, <2, are there any rules of thumb?

I am analysing some data from a randomised controlled trial. Several of the random effects in the GLMMs I have build have variance values less than 1, for example 0.2 or 0.7. Would it be reasonable to omit these random effects as their variance approaches 0?

See here also, the singularity section.

kjetil b halvorsen
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Pat Taggart
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  • That is not my reading of the two linked pages. Rather, they try to explain *why* you may bet a variance estimate of 0. My perception is that random effects that are part of the experimental design should not be removed, ever. Studies of observational data with random effects seem to be more comfortable with removing random effects "if they are small". I'm not aware of rules of thumb for "small" (and then only for standardised responses). – Carsten May 08 '20 at 13:20
  • Thanks for your help. The second answer in the first thread says that when the random effect variance is zero 'There is not enough additional subject-level variation to warrant adding an additional subject-level random effect to explain all the observed variation'. – Pat Taggart May 08 '20 at 22:51
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    Also see - https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#singular-models-random-effect-variances-estimated-as-zero-or-correlations-estimated-as---1 - singularity section says -> see next comment – Pat Taggart May 08 '20 at 22:53
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    'If a variance component is zero, dropping it from the model will have no effect on any of the estimated quantities (although it will affect the AIC, as the variance parameter is counted even though it has no effect). Pasch, Bolker, and Phelps (2013) gives one example where random effects were dropped because the variance components were consistently estimated as zero. Conversely, if one chooses for philosophical grounds to retain these parameters, it won’t change any of the answers.' – Pat Taggart May 08 '20 at 22:54

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