[R-sig-ME] subject-specific interpetation two random effects

[ben pelzer]

Dear Dimitris,

Thanks for your response, that was really helpful and the estimates are now
as good as equal!

I thought the difference was caused by the subject-specific interpretation,
which for the interaction model "mab" is different than for the two
separate models, if I'm right ...

After reading your comment, I also tried linear models (using lme) for
males/females separately and for the two groups combined using interaction
(for linear models the subject-specific interpretation would not make a
difference). Again it appeared that allowing for correlation of the
intercepts for males and females leads to slightly different estimates of
the fixed effects, whereas no correlation leads to exactly the same fixed
effects as in the separate analyses.

Thanks for your help, and, of course, a happy and healthy 2023,

Ben.


On Thu, 29 Dec 2022 at 07:37, Dimitris Rizopoulos <d.rizopoulos using erasmusmc.nl>
wrote:

> The last model says that the random effects for males and females are
> correlated-you would need to assume independent random effects.
>
> Best,
> Dimitris
>
>
> ——
> Dimitris Rizopoulos
> Professor of Biostatistics
> Erasmus University Medical Center
> The Netherlands
> ------------------------------
> *From:* R-sig-mixed-models <r-sig-mixed-models-bounces using r-project.org> on
> behalf of ben pelzer <benpelzer using gmail.com>
> *Sent:* Wednesday, December 28, 2022 3:13:26 PM
> *To:* r-sig-mixed-models <r-sig-mixed-models using r-project.org>
> *Subject:* [R-sig-ME] subject-specific interpetation two random effects
>
>
>
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>
> Dear list,
>
> Sorry for cross-posting this question; I got no response on Cross
> Validated. Hope to get one here.
>
>
> I have two groups of pupils, males and females in a number of schools. So,
> two-level data, pupils nested in schools. For each gender group, a logistic
> model was estimated with a school-level predictor "type" of school. Next, a
> "complete" model was estimated for both gender groups simultaneously. Here
> is the syntax I used:
>
>
> library(GLMMadaptive)
>
>
> ma  <- mixed_model(y ~ 1+type, random=~ 1|school, family=binomial,
> data=maledata)
>
>
>
> mb  <- mixed_model(y ~ 1+type, random=~ 1|school, family=binomial,
> data=femaledata)
>
>
>
> mab <- mixed_model(y ~ 0+male+female+type:male+type:female,
>
>                    random=~ 0+male+female|school, family=binomial,
> data=completedata)
>
>
> The final model mab uses interaction terms and is specified without
> intercepts, so that its estimates can directly be compared with those of
> the separate group models ma and mb.
>
>
> I expected that the final "complete" model mab would give the same
> estimates for the effects of "type" as the separate models do. More in
> particular, that the regression coefficients of type:male and type:female
> in model mab would be equal to the coefficients of "type" in ma and mb,
> respectively.
>
>
> However, this is not (exactly) the case: the coefficients are relatively
> close, but clearly not equal. I first thought that these dissimilarities
> might be due to the number of quadrature points used by mixed_model. Hence,
> I chose larger values for nAGQ but this did not help: the dissimilarities
> persist, and all estimates hardly change. Also, no convergence problems
> exist, everything seems all right.
>
>
> Now my guess is that these differences are caused by the fact that the
> regression coefficients are subject-specific. That is, for model ma, the
> effect of "type" expresses the influence of schooltype for two schools with
> the same random school effect across male pupils. In contrast, the effect
> of "type" in model mab expresses the effect of schooltype for two schools
> with the same random school effect across male pupils and also across
> female pupils. So in mab, there are two random school effects, one for
> males and the other for females, which BOTH have to be equal. It toke me
> quite a while to realise this, and still I'm not completely sure. I would
> really appreciate it if someone could confirm my suspicion. Thanks!!!
>
>
> Ben.
>
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