[R] Fitting binomial lmer-model, high deviance and low logLik

[Ivar Herfindal]

Hello

I have a problem when fitting a mixed generalised linear model with the 
lmer-function in the Matrix package, version 0.98-7. I have a respons 
variable (sfox) that is 1 or 0, whether a roe deer fawn is killed or not 
by red fox. This is expected to be related to e.g. the density of red 
fox (roefoxratio) or other variables. In addition, we account for family 
effects by adding the mother (fam) of the fawns as random factor. I want 
to use AIC to select the best model (if no other model selection 
criterias are suggested).

the syntax looks like this:
 > mod <- lmer(sfox ~ roefoxratio + (1|fam), data=manu2, family=binomial)

The output looks ok, except that the deviance is extremely high 
(1.798e+308).

 > mod
Generalized linear mixed model fit using PQL
Formula: sfox ~ roefoxratio + (1 | fam)
    Data: manu2
  Family: binomial(logit link)
            AIC           BIC         logLik      deviance
  1.797693e+308 1.797693e+308 -8.988466e+307 1.797693e+308
Random effects:
      Groups        Name    Variance    Std.Dev.
         fam (Intercept)      17.149      4.1412
# of obs: 128, groups: fam, 58

Estimated scale (compare to 1)  0.5940245

Fixed effects:
             Estimate Std. Error  z value Pr(>|z|)
(Intercept) -2.60841    1.06110 -2.45820  0.01396 *
roefoxratio  0.51677    0.63866  0.80915  0.41843

I suspect this may be due to a local maximum in the ML-fitting, since:

 > mod at logLik
'log Lik.' -8.988466e+307 (df=4)

However,

 > mod at deviance
       ML     REML
295.4233 295.4562

So, my first question is what this second deviance value represent. I 
have tried to figure out from the lmer-syntax 
(https://svn.r-project.org/R-packages/trunk/Matrix/R/lmer.R)
but I must admit I have problems with this.

Second, if the very high deviance is due to local maximum, is there a 
general procedure to overcome this problem? I have tried to alter the 
tolerance in the control-parameters. However, I need a very high 
tolerance value in order to get a more reasonable deviance, e.g.

 > mod <- lmer(sfox ~ roefoxratio + (1|fam), data=manu2, 
family=binomial, 
control=list(tolerance=sqrt(sqrt(sqrt(sqrt(.Machine$double.eps))))))
 > mod
Generalized linear mixed model fit using PQL
Formula: sfox ~ roefoxratio + (1 | fam)
    Data: manu2
  Family: binomial(logit link)
       AIC      BIC    logLik deviance
  130.2166 141.6247 -61.10829 122.2166
Random effects:
      Groups        Name    Variance    Std.Dev.
         fam (Intercept)      15.457      3.9316
# of obs: 128, groups: fam, 58

Estimated scale (compare to 1)  0.5954664

Fixed effects:
             Estimate Std. Error  z value Pr(>|z|)
(Intercept) -2.55690    0.98895 -2.58548 0.009724 **
roefoxratio  0.50968    0.59810  0.85216 0.394127

The tolerance value in this model represent 0.1051 on my machine. Does 
anyone have an advice how to handle such problems? I find the tolerance 
needed to achieve reasonable deviances rather high, and makes me not too 
confident about the estimates and the model. Using the other methods, 
("Laplace" or "AGQ") did not help.

My system is windows 2000,
 > version
          _
platform i386-pc-mingw32
arch     i386
os       mingw32
system   i386, mingw32
status
major    2
minor    2.0
year     2005
month    10
day      06
svn rev  35749
language R

Thanks

Ivar Herfindal

By the way, great thanks to all persons contributing to this package 
(and other), it makes my research more easy (and fun).