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

[David Duffy]

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.