[R-sig-ME] Poisson intercept-only multilevel model doesn't appear to return the correct population mean

Maarten Jung jungm@@rten @end|ng |rom gm@||@com
Wed Mar 9 15:52:46 CET 2022

Dear John,

> Why would including random intercepts for plot change the grand mean
> (exponentiated) from
> 44.24 to 11.29? Note that this only happens with the multilevel Poisson
> regression and not the
> multilevel Gaussian. I suspect I'm missing something, but I'll be 
> darned if
> I can figure out what.
In generalized linear mixed models the fixed population effects in the 
marginal and conditional model are in general different (taking the 
expectation of a nonlinear function of a random variable is not the same 
as taking the expectation of that random variable first and then 
applying the nonlinear function).
In particular, for the log-linear Poisson random intercept model, the 
amount by which the intercept terms will differ depends on the random 
effects variance.


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