[R-sig-ME] Choice of distribution for random effects

[J.D. Haltigan]

Hi:

Is there clear best practice or guidance when it comes to choosing the
distribution of random effects where multiple choices exist (e.g.,
gaussian, gamma, etc.)? I ask in the context of extending some analyses
from an RCT in which the outcome is symptomatic seropositivity (so a
count). The random effects I am modeling are village cluster [union] (it's
a cluster randomized trial). I get different results (significance-wise)
depending on whether I choose a normal or gamma distribution for the random
effects.

The basic model (proportional outcome) is:

lme4_5_B = glmer(posXsymp~ treatment+proper_mask_base+prop_resp_ill_base_2
+ pairID + (1 | union), family = "poisson", nAGQ=0, data = bdata.raw3)#lme4
package using glmer


HGLM2_5_A = hglm2(posXsymp~ treatment+proper_mask_base+prop_resp_ill_base_2
+ pairID + (1 | union), family =poisson (link = log), rand.family
=Gamma(link=log),
                  data = bdata.raw3)#HGLM package using hglm2

Does, for example, the choice of distribution for the fixed effects portion
of the model inform the choice for the random effects?

Thank you for any insights.

Best regards,
J.D.

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