[R-sig-ME] R-sig-mixed-models Digest, Vol 183, Issue 17

[John Willoughby]

Dear Russ and Maarten,

Many thanks for the clarification on why I can't simply exponentiate the
intercept of a Poisson model with random effects and get the same result as
exponentiating
the intercept of a Poisson model without random effects.  I understand the
issue more clearly now.

Best,
John Willoughby



>
>
>    1. Re:  Poisson intercept-only multilevel model doesn't appear
>       to return the correct population mean (Lenth, Russell V)
>    2. Re:  Poisson intercept-only multilevel model doesn't appear
>       to return the correct population mean (Maarten Jung)
>    3. Post hoc on glmer for specific hypotheses (Timothy MacKenzie)
>    4. Re: Post hoc on glmer for specific hypotheses (Ben Bolker)
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Wed, 9 Mar 2022 14:15:13 +0000
> From: "Lenth, Russell V" <russell-lenth using uiowa.edu>
> To: John Willoughby <johnwillec using gmail.com>
> Cc: "r-sig-mixed-models using r-project.org"
>         <r-sig-mixed-models using r-project.org>
> Subject: Re: [R-sig-ME]  Poisson intercept-only multilevel model
>         doesn't appear to return the correct population mean
> Message-ID:
>         <
> DM6PR04MB4474A526398B5DCC8121DCFDF10A9 using DM6PR04MB4474.namprd04.prod.outlook.com
> >
>
> Content-Type: text/plain; charset="utf-8"
>
> This happens precisely because there is a random effect in the model
> 'glmm3.2'. We have a model that basically says that log Y is normally
> distributed with an estimate mean of 2.424. That implies that Y is
> lognormal, and therefore
>
>     E[Y] = exp(mu + sigma^2/2)
>
> If you use VarCorr(glmm3.2) to get the estimate of sigma^2, and add half
> of that before you exponentiate, you'll get a lot closer to the estimate
> you expect.
>
> Russ Lenth
>
> -----Original Message-----
>
>
>
>
> Message: 2
> Date: Wed, 9 Mar 2022 15:52:46 +0100
> From: Maarten Jung <jungmaarten using gmail.com>
> To: John Willoughby <johnwillec using gmail.com>
> Cc: r-sig-mixed-models using r-project.org
> Subject: Re: [R-sig-ME]  Poisson intercept-only multilevel model
>         doesn't appear to return the correct population mean
> Message-ID: <ec308b91-5069-42d3-0062-afe9f1873821 using gmail.com>
> Content-Type: text/plain; charset="utf-8"; Format="flowed"
>
> 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.
>
> Best,
> Maarten
>
>
>

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