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

[Dimitris Rizopoulos]

The last model says that the random effects for males and females are correlated-you would need to assume independent random effects.

Best,
Dimitris


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Dimitris Rizopoulos
Professor of Biostatistics
Erasmus University Medical Center
The Netherlands
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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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