[R-sig-ME] how reliable are inferences drawn from binomial modelsfor small datasets fitted with lme4?

[Roger Levy]

On Jul 5, 2009, at 10:38 PM, David Duffy wrote:

> On Sun, 5 Jul 2009, Roger Levy wrote:
>
>> This post may be of interest in light of the recent discussion of  
>> PQL versus Laplace-approximated likelihood.  I'm facing an  
>> interestingly challenging analysis of a relatively small (190- 
>> observation) binary-response dataset with a single two-level  
>> treatment and two crossed random factors (call them F1 and F2).   
>> The question of current interest is whether I can infer a  
>> difference in fixed effect of treatment ...  [SNIP]
>
> Although F1 has an effect, F2 doesn't seem as impressive:
>
> For Response, Tarone score test for extrabinomial variance gives
> F1 3.86 (P=0.0493), F2 0.54 (P=0.4616).
>
> So it seems reasonable just to ignore F2.  Then the conditional  
> logistic regression stratifying on F1 is nicely significant:
>
> clogit(Response ~ Treatment + strata(F1), method="exact", data = x)
>
>           coef exp(coef) se(coef)    z     p
> Treatment2 2.73      15.3     1.10 2.49 0.013
>
> Likelihood ratio test=10.9  on 1 df, p=0.000957  n= 190
>
> (and equivalent score test 9.054, P=0.0026).
>
> The conditional logistic should be fairly robust, and at least
> gives some kind of benchmark for other models.

Dear David,

Many thanks for your input -- I'm not familiar with the Tarone score  
test (looking around -- is this Tarone 1979, Biometrika?) or with  
stratified conditional logistic models.  Could you perhaps give me  
pointers to R code for the former, and references for both?

Best & many thanks again.

Roger

--

Roger Levy                      Email: rlevy at ling.ucsd.edu
Assistant Professor             Phone: 858-534-7219
Department of Linguistics       Fax:   858-534-4789
UC San Diego                    Web:   http://ling.ucsd.edu/~rlevy