[R-sig-ME] predicted mean from GLMM lower than mean from GAM

[Jarrod Hadfield]

Hi,

If you take exp(log(1.14)+0.5*v) where v is the sum of the estimated  
variances do the two estimates then coincide? 1.14 in the GLMM is the  
predicted modal count (i.e. when the two random effects are zero) and  
exp(log(1.14)+0.5*v) is the predicted mean count (i.e. averaged over  
random effects).

Cheers,

Jarrod



Quoting Ben Bolker <bbolker at gmail.com> on Tue, 17 Jul 2012 20:57:55  
+0000 (UTC):

> benton <benton at ...> writes:
>
>> I fit a Poisson GLMM with only the intercept and two random effects, and
>> the predicted mean was 1.14. When I fit a generalized additive model
>> (GAM) with only the intercept, the predicted mean was 1.6. Does anyone
>> know why this is happening? I'm looking for a theoretical response, as
>> I've checked my code and there are no errors.
>>
>
>   A little more information/reproducible example would be helpful; it
> would be possible for me to invent a reproducible example for myself,
> but it would be easier (for me!) and more likely to answer your
> specific question if you provide the example.  Have you compared the
> Poisson GLMM prediction with a Poisson GLM (no random effects)
> prediction to make sure there's not some funky/surprising difference
> between the GAM (presumably you're using mgcv::gam()) and the GLMM
> (presumably you're using lme4::glmer()) ?  How are you deriving the
> predictions?  Are you definitely using the same family and link
> function for both models?  In general there can be important
> differences between the marginal (no-random-effects) and conditional
> (including-random-effects) predictions, but off the top of my head
> that should not apply to intercept-only models ...  See
> http://tinyurl.com/reproducible-000 for more info on reproducible
> examples ...
>
>   Ben Bolker
>
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>



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