[R-sig-ME] Precision about the glmer model for Bernoulli variables

D. Rizopoulos d@r|zopou|o@ @end|ng |rom er@@mu@mc@n|
Wed Apr 29 08:41:39 CEST 2020

Mixed models can assume negative correlations when you include something more than random intercepts. Check


Chapter 3, Section 3.3 -> Select random intercepts & random slopes, and make the correlation between the intercepts and slopes negative. When including quadratic random slopes even get more negative correlations.


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 David Duffy <David.Duffy using qimrberghofer.edu.au>
Sent: Wednesday, April 29, 2020 8:23:03 AM
To: Vaida, Florin <fvaida using health.ucsd.edu>; John Maindonald <john.maindonald using anu.edu.au>
Cc: r-sig-mixed-models using r-project.org <r-sig-mixed-models using r-project.org>
Subject: Re: [R-sig-ME] Precision about the glmer model for Bernoulli variables

Hi Florin.

> ...but negative correlations do not correspond to a mixed-effects model specification.  (I thought Geert
> Molenberghs had a paper to this point but I can't find it now.)

Hopefully still vaguely R-related - in the case of meta-analyses of correlations, the observed correlation for a given, say, sub-study can be negative, and _some_ mixed models will inappropriately truncate this contribution at zero, leading to inflated estimates for the global parameters. This comes up when meta-analysing heritability, where the genetic model (as you have pointed out) contrains this to be non-negative for a single trait.

Because of the computational difficulties, many geneticists still fit linear-normal mixed models to binary data (eg genome-wide association studies of large datasets eg UK Biobank), and don't usually get burnt. The "better" alternative for this has been PQL, implemented in several R packages.

Cheers, David Duffy.

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