[R] lmer and mixed effects logistic regression

[Spencer Graves]

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Rick Bilonick wrote:
> On Fri, 2006-06-23 at 21:38 -0700, Spencer Graves wrote:
>> 	  Permit me to try to repeat what I said earlier a little more clearly: 
>>   When the outcomes are constant for each subject, either all 0's or all 
>> 1's, the maximum likelihood estimate of the between-subject variance in 
>> Inf.  Any software that returns a different answer is wrong. This is NOT 
>> a criticism of 'lmer' or SAS NLMIXED:  This is a sufficiently rare, 
>> extreme case that the software does not test for it and doesn't handle 
>> it well when it occurs.  Adding other explanatory variables to the model 
>> only makes this problem worse, because anything that will produce 
>> complete separation for each subject will produce this kind of 
>> instability.
>>
>> 	 Consider the following:
>>
>> library(lme4)
>> DF <- data.frame(y=c(0,0, 0,1, 1,1),
>>                   Subj=rep(letters[1:3], each=2),
>>                   x=rep(c(-1, 1), 3))
>> fit1 <- lmer(y~1+(1|Subj), data=DF, family=binomial)
>>
>> # 'lmer' works fine here, because the outcomes from
>> # 1 of the 3 subjects is not constant.
>>
>>  > fit.x <- lmer(y~x+(1|Subj), data=DF, family=binomial)
>> Warning message:
>> IRLS iterations for PQL did not converge
>>
>> 	  The addition of 'x' to the model now allows complete separation for 
>> each subject.  We see this in the result:
>>
>> Generalized linear mixed model fit using PQL
>> <snip>
>> Random effects:
>>   Groups Name        Variance   Std.Dev.
>>   Subj   (Intercept) 3.5357e+20 1.8803e+10
>> number of obs: 6, groups: Subj, 3
>>
>> Estimated scale (compare to 1)  9.9414e-09
>>
>> Fixed effects:
>>                 Estimate  Std. Error    z value Pr(>|z|)
>> (Intercept) -5.4172e-05  1.0856e+10  -4.99e-15        1
>> x            8.6474e+01  2.7397e+07 3.1563e-06        1
>>
>> 	  Note that the subject variance is 3.5e20, the estimate for x is 86 
>> wit a standard error of 2.7e7.  All three of these numbers are reaching 
>> for Inf;  lmer quit before it got there.
>>
>> 	  Does this make any sense, or are we still misunderstanding one another?
>>
>> 	  Hope this helps.
>> 	  Spencer Graves
>>
> Yes, thanks, it's clear. I had created a new data set that has each
> subject with just one observation and randomly sampled one observation
> from each subject with two observations (they are right and left eyes).
> I'm not sure why lmer gives small estimated variances for the random
> effects when it should be infinite. 

SG:  If lmer gave me small estimated variances for the random effects, I 
would check very carefully my model, as I would believe I probably have 
specified something incorrectly.

I ran NLMIXED on the original data
> set with several explanatory factors and the variance component was in
> the thousands.
> 
> I guess the moral is before you do any computations you have to make
> sure the procedure makes sense for the data.
> 
> Rick B.
>