[R] zero random effect sizes with binomial lmer

[Andrew Robinson]

According to pp 197-198 of MASS 4, the Hauck-Donner phenomenon refers
to cases when the Wald approximations and the likelihood ratio tests
have different p values because of the former underestimating the the
change in log-likelihood on setting \beta_i = 0.

This seems quite different to me than the phenomenon that Daniel is
reporting, and that I believe I saw previously (post:
http://tolstoy.newcastle.edu.au/R/e2/help/06/12/6903.html
)

I tried an earlier version of R, on a different platform, and got
quite different results.  Sadly, the *earlier* results are the ones
that make sense.

eg:

> sessionInfo()
R version 2.4.1 Patched (2006-12-30 r40330) 
i386-unknown-freebsd6.1 

locale:
C

attached base packages:
[1] "stats"     "graphics"  "grDevices" "utils"   "datasets"  "methods"  
[7] "base"     

other attached packages:
       lme4      Matrix     lattice 
"0.9975-10"  "0.9975-6"   "0.14-16" 
> ranef(lmer(Reaction ~ Days + (1|Subject), sleepstudy,
       family=Gamma(link="log")))
An object of class "ranef.lmer"
[[1]]
      (Intercept)
308  6.817268e-10
309 -1.369242e-09
310 -1.122033e-09
330  1.164825e-10
331  2.096848e-10
332  1.494418e-10
333  3.042078e-10
334 -6.276876e-11
335 -7.556428e-10
337  1.263863e-09
349 -3.984973e-10
350  2.107439e-10
351 -1.230185e-10
352  6.409427e-10
369  1.224258e-10
370 -1.528146e-10
371 -5.310404e-11
372  3.228682e-10



> sessionInfo()
Version 2.3.1 (2006-06-01) 
i386-pc-mingw32 

attached base packages:
[1] "methods"   "stats"   "graphics"  "grDevices" "utils" "datasets" 
[7] "base"     

other attached packages:
      lme4     Matrix    lattice 
 "0.995-2" "0.995-20"   "0.13-8" 
> ranef(lmer(Reaction ~ Days + (1|Subject), sleepstudy,
+        family=Gamma(link="log")))
An object of class "ranef.lmer"
[[1]]
     (Intercept)
308  0.128473227
309 -0.294234827
310 -0.232009186
330  0.029091372
331  0.046196655
332  0.035400265
333  0.063273674
334 -0.004238362
335 -0.147285458
337  0.220381662
349 -0.070565390
350  0.046822487
351 -0.015994000
352  0.121461879
369  0.030457370
370 -0.021387277
371 -0.002494534
372  0.066650443

> 



Cheers,

Andrew




On Mon, Jan 01, 2007 at 06:09:12PM +0000, Dieter Menne wrote:
> Daniel Ezra Johnson <johnson4 <at> babel.ling.upenn.edu> writes:
> 
> > 
> > I am fitting models to the responses to a questionnaire that has
> > seven yes/no questions (Item). For each combination of Subject and
> > Item, the variable Response is coded as 0 or 1.
> > 
> > I want to include random effects for both Subject and Item. While I
> > understand that the datasets are fairly small, and there are a lot of
> > invariant subjects, I do not understand something that is happening
> > here, and in comparing other subsets of the data.
> > 
> > In the data below, which has been adjusted to show this phenomenon
> > clearly, the Subject random effect variance is comparable for A
> > (1.63) and B (1.712), but the Item random effect variance comes out
> > as 0.109 for B and essentially zero for A (5.00e-10).
> ...
> 
> Check the list archives for quite a few postings of Professor Brian Ripley on
> the subject of Hauk-Donner.
> 
> 
> Dieter
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

-- 
Andrew Robinson  
Department of Mathematics and Statistics            Tel: +61-3-8344-9763
University of Melbourne, VIC 3010 Australia         Fax: +61-3-8344-4599
http://www.ms.unimelb.edu.au/~andrewpr
http://blogs.mbs.edu/fishing-in-the-bay/