[R-sig-ME] lmer (binomial) and mcmcsamp

[Douglas Bates]

On Dec 4, 2007 1:55 AM, Dieter Menne <dieter.menne at menne-biomed.de> wrote:
> Douglas,
>
> I am using the latest CRAN version; details see below.
>
> I tried to run mcmcsamp on a problem of the form
>
> The model is
>
>  lmer(RespB~Treat+Gender+(1|Pat),family=binomial)
>
>
> Results look ok, in reasonable agreement with method="PQL", and in good
> agreement with Göran's glmmML.
>
> Running mcmcsamp() gave strange results. See
>
> http://www.menne-biomed.de/uni/mcmc20000.pdf
> http://www.menne-biomed.de/uni/mcmc2000.pdf
>
> I cannot get rid of the occasional stuck flat segments in between, even if I run
> several times. Is this
>
> -- Expected behavior, do your homework
> -- Somewhat fishy; don't trust the results
> -- Ill posed problem
> -- Well known issue with current lmer
> -- ...
>
> Dieter

This is a known issue with the current lmer and you should not trust
the results.

The problem is that I use a Metropolis-Hastings update for the fixed
effects and the random effects together, conditional on the variance
components.  In awkward cases the approximate distribution from which
the sample is drawn is not a good approximation to the conditional
distribution of these parameters and the proposed step keeps getting
rejected.

I believe the solution is to separate the fixed effects from the
random effects but that is difficult to do in the formulation for the
0.99875 series.  This was one of the reasons for changing the internal
representation in the 0.999375 series (the development version) but I
am still encountering difficulties in some of the code design for that
series.  I thought I had the penalized iteratively reweighted least
squares algorithm for determining the conditional modes working but
then I tried it on a difficult example and found that it isn't working
as well as I thought it was.

I am working on it.  It is just taking considerably longer than I
thought it would.

> #------------------------------
> Generalized linear mixed model fit using Laplace
> Formula: form
>    Data: x
>  Family: binomial(logit link)
>  AIC BIC logLik deviance
>  340 356   -166      332
> Random effects:
>  Groups Name        Variance Std.Dev.
>  Pat    (Intercept) 2.15     1.47
> number of obs: 426, groups: Pat, 20
>
> Estimated scale (compare to  1 )  0.859
>
> Fixed effects:
>             Estimate Std. Error z value Pr(>|z|)
> (Intercept)   -1.809      0.497   -3.64  0.00027 ***
> TreatFOS      -0.267      0.290   -0.92  0.35775
> Genderm       -0.775      0.778   -0.99  0.31975
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Correlation of Fixed Effects:
>          (Intr) TrtFOS
> TreatFOS -0.274
> Genderm  -0.593  0.009
>
>
> Package: lme4
> Version: 0.99875-9
> Date: 2007-10-14
> Built: R 2.6.0; i386-pc-mingw32; 2007-10-15 12:22:16; windows
>
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>