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

[D. Rizopoulos]

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

https://emcbiostatistics.shinyapps.io/Repeated_Measurements/

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.

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 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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