*Hi all,

it is counterintuitive to me that adding a random effect to a GLMM should
lead to a drop in the likelihood of the fitted model for, after all, one
can give the new random effect vanishingly small variance which should lead
to the same likelihood as before. But this is what I have encountered. I
regret that the output below is not self contained but if needed I could
follow-up offline with additional files.

The factor "box" is nested inside the factor "tree" and the factor "gap" is
crossed with both of these. This is a binomial GLMM with 0/1 response.

> f0128bit = lmer(fincr ~ icfac + (1|gap) + (1|box)+ (1|gap:box) +
(1|tree), family = binomial)
> summary(f0128bit)
Generalized linear mixed model fit by the Laplace approximation
Formula: fincr ~ icfac + (1 | gap) + (1 | box) + (1 | gap:box) + (1 |
tree)
 AIC   BIC logLik deviance
 687 732.4 -335.5      671
Random effects:
 Groups  Name        Variance Std.Dev.
 gap:box (Intercept) 0.000000 0.00000
 box     (Intercept) 0.082784 0.28772
 gap     (Intercept) 0.122614 0.35016
 tree    (Intercept) 0.505608 0.71106
Number of obs: 2160, groups: gap:box, 1080; box, 40; gap, 27; tree, 20

Fixed effects:
            Estimate Std. Error z value Pr(>|z|)
(Intercept)  -3.4348     0.2315 -14.835  < 2e-16 ***
icfacmale     1.4535     0.2738   5.308 1.11e-07 ***
icfacfem     -2.5740     0.7480  -3.441 0.000579 ***
icfacmix      0.2935     1.1049   0.266 0.790517
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
          (Intr) icfcml icfcfm
icfacmale -0.357
icfacfem  -0.114  0.122
icfacmix  -0.065  0.066  0.032
> anova(f0128bit,f0128bi)
Data:
Models:
f0128bi: fincr ~ icfac + (1 | gap) + (1 | box) + (1 | gap:box)
f0128bit: fincr ~ icfac + (1 | gap) + (1 | box) + (1 | gap:box) + (1 |
f0128bit:     tree)
         Df    AIC    BIC  logLik Chisq Chi Df Pr(>Chisq)
f0128bi   7 615.73 655.48 -300.87
f0128bit  8 687.01 732.43 -335.51     0      1          1

Any suggestions gratefully received.

Murray*
-- 
Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
Email: maj@waikato.ac.nz    majorgensen@ihug.co.nz      Fax 7 838 4155
Phone  +64 7 838 4773 wk    Home +64 7 825 0441   Mobile 021 0200 8350

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