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I'm doing a neg binomial glmm in glmmADMB. The random effects are not quite normally distributed (see attached images). How concerned about this do I need to be? If this is too much of a violation, are there other options for analyzing longitudinal data?

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    $\begingroup$ How do you conclude these values are inconsistent with normality? Your sample size is ten; there will usually be lumpiness and curvature in the Q-Q plot. I just now looked at ten Q-Q plots of simulated normals at that sample size and three of the ten looked less normal than that. (I don't think your values are normal - they never are with real data - I just think you have no basis in that plot on which to think that they aren't) $\endgroup$ – Glen_b -Reinstate Monica Apr 18 '13 at 0:07
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I do not know the scale of your other predictors and your response but it seems to be that your random effects are almost zero anyway.

Your plot is also not enough to convince me that they are not normally distributed; doing a qqplot with 10 random points produces very similar pictures. For example, look at this R script:

par(mfrow=c(4,4))
plot (i in 1:16) qqnorm(rnorm(10))

and compare the output of some runs.

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  • $\begingroup$ Yes, you're right. It is possible to generate a similar looking plot with random data drawn from a normal distribution. $\endgroup$ – Stephen 123 Apr 17 '13 at 12:55
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When you draw a random sample from a normal distribution, there is no guarantee that the sample will be normally distributed when the sample is small. My experience with samples of less than 30 is not to expect the sample to meet all the strict criteria of normality.

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