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# Proc Glim​mix : Calculate intraclass correlatio​n (ICC) for Generalized linear mixed model (Poisson)

Hello,

I would like to compute intraclass correlation using Proc Glimmix for a generalized linear mixed modelling (Poisson) with 1 fixed effect (intervention) and 1 random effect (cluster).

I model proportions with the Poisson model, defining log(n) in the offset term :

class CLUSTER INTERVENTION;

model NEVENTS = INTERVENTION / link=log dist=poisson s offset=logn ;

random intercept / subject=CLUSTER G solution

I understand that the residual variance is the 'Estimate' listed in the "Covariance Parameter Estimates" table (or in the G matrix with only 1 row) but I have maybe some misunderstanding.
I can't find the common variance in order to estimate the ICC for this model: does it correspond to the 'Estimate' per cluster in the "Solution for random effects" ?
The ICC could then be calculated with ( common variance / common variance + residual variance ) but I'm not sure this is appropriate here.

I thought maybe others with more knowledge in GLMM and GLIMMIX may be able to enlighten me.

Regards,

Jude

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## Re: Proc Glim​mix : Calculate intraclass correlatio​n (ICC) for Generalized linear mixed model (Pois

You are specifying a Poisson distribution. There is no residual variance term with a Poisson, by definition. The variance estimate you are seeing is the cluster variance. If you fitted the model without a random effect term, you would not get any variance terms in the output.

The variance of the Poisson conditional distribution that you are using is given by the mean. There would be a different mean for each level of intervention.

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Posts: 2

## Re: Proc Glim​mix : Calculate intraclass correlatio​n (ICC) for Generalized linear mixed model (Pois

To be sure to understand well, does it mean that I can't compute ICC with this distribution? Or is there a way to quantify the degree of similarity in the responses of individuals from the same cluster for the outcome (nevents) ?
Thanks again,

Jude

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