# [R-sig-ME] 答复: Non-normal random effect in glmm

Chen Chun talischen at hotmail.com
Wed Oct 12 16:30:36 CEST 2016

```Dear all,

I am applying a mixed model with binomial distribution on a very large data set (around 400000 samples) with binary outcome (very few event, around 4%).  Some respondents but not all are repeated measured over the years, that's why a mixed model is applied. The model can be written as :

mod <- glmer(response ~ AGE + SEX...+ YEAR + (1 | respondentID), family=binomial, data=dat)

The distribution of the random effect (ID) from the model output shows an obvious non-normal distribution: a large proportion of close to zero values and very few large values around 10. I am wondering if in this case the glmm model is still valid?  if not valid, what kind of alternative model can I try? Can someone give some suggestion?

A consequent problem is when I calculate the explained variance from the model:
VarF <- var(as.vector(fixef(mod ) %*% t(mod @pp\$X)))
VarF/(VarF + VarCorr(mod )\$respondentID + (pi^2)/3)

the variance of the fixed effect (VarF) from the model is only 1.6, while the variance of the random effect (VarCorr(mod )\$respondentID) is 149. Due to the non-normal distribution, the variance of the random effect is very large as compared to the fixed effect. Does this imply that the model performs bad? Or I should compute conditional R square?

To summarize, my questions are:

1) What's the influence in estimation of the fixed effect and its explained variance (R squared) when the random effect does not follow a normal distribution? If the influence is large, any suggestions to solve it?

2) In a more general sense, how to comment a model where a large amount of variation comes from the random effects?

Thanks

Regards,
Chun

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