Joseph Coveney wrote:
>>Sorry, Jay, about my misreading.
De nada.
>>Resampling certainly is an alternative.
It would be interesting to see how the bootstrap compares in a study like
David's under those potential outcomes in which summary measures would not
be expected to fare so well, e.g., binomial expectations in the neighborhood
of 0 of 50 or 50 of 50.>>
The fundamental problem is that with a binary DV this skewed, there's just not a lot of information to be had, ergo a larger sample is necessary.
>>I share your suspicions about mixed models in small samples, Messrs. Kenward
and Roger notwithstanding.
Simulations I did in my dissertation on the Bradley-Terry-Luce model with random effects---which is a mixed logistic regression with constraints on the covariance matrix of random effects---suggest that for a small level 1 (number of subjects) or level 2 (number of objects) N, the mixed model was no better in terms of MSE than ignoring the mixing in favor of assuming independence. While the mixed models had lower bias, their variance was correspondingly larger. Only when the sample size got fairly large (200 subjects, 8 objects, giving a total of 28 observations per subject, which is larger than most choice experiments) were mixed models clearly better. With continuous responses things are better, but still relatively bad with a highly skewed response.
Jay
<<winmail.dat>>
