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05-16-2013 01:32 PM

Hello all,

In advance, please let me thank whoever reads this entire post. I have been working very hard to understand and build this model, and stats are not my strength. Any assistance you can provide in answering these few remaining questions I have will be greatly appreciated.

I am using a mixed model poisson regression to model my data (because I have random effects), and have been working with another statistician to make sure that is the correct model. However, I still have a few BASIC but not completely resolved questions that I am hoping someone can help me with.

Mostly, I am not entirely certain what ALL of the model assumptions are. I KNOW that I need to check for **overdispersion**, and have been using the negative binomial model when that is the case. However, I am not sure what other assumptions I need to validate. Namely:

1) Do the model residuals need to be normally distributed?

2) I have read that for mixed models in general, the random effects are assumed to be randomly distributed. Is this true for poisson as well and **how is this assessed in SAS (I am using Proc GLIMMIX)? **I am not necessarily asking for complete code, just a general approach.

3) Assumptions of equal variance: Is this an assumption of this model ? (please read more detailed questions below)

a. Do I need to look for random scatter when I plot the overall model residuals against the linear predictor values.

b. Do I need to look for random scatter when I plot the residuals against the individual predictor values (for each independent variable.

c. If A and/or B are true, what can/should I do when I see a cone shaped pattern indicating homoscedasticity.

THANK YOU!!

Meghan

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05-17-2013 09:16 AM

1. One of the assumptions under a mixed model with a Poisson distribution (without explicit overdispersion fitting) is that the mean and variance are equal. Consequently, there is really no "residual" in the classic linear model sense. There is a deviation, but there is no IID residual term that you assume to be normally distributed.

2. Random effects are assumed to have N(**0, Sigma**) distributions. SAS does not test this. If you really want to get into distributional testing of random effects, I suggest you start with Bates and Pinheiro's work and then pursue all of this in one of the dozen or so R packages (which all seem to give different results) for generalized linear mixed models.

3. Recall that the variance and the mean are directly related, so cone-shaped plots of the deviance should be expected: As the mean increases, so does the variance. If you are concerned about equal variance amongst groups, this can be tested using the COVTEST option. For instance, if your code has:

random _residual_;

You could try:

random _residual_/group=<fixed_effect_of_interest>;

covtest homogeneity;

The results will tell you something important about the deviance by group.

I hope this attracts some comments from and . Their insights on this are really helpful.

Also, track down a copy of Walt Stroup's *Generalized Linear Mixed Models.* It will make the assumptions much clearer than what I did here.

Steve Denham

Message was edited by: Steve Denham