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

[David Duffy]

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.

Cheers, David Duffy.


-- 
| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v