I agree that the model is not fitting the Lesaffre data well, but my point was to show that glmmADMB is numerically stable. Numerical stability is obviously a nice property, but becomes particularly important when one wants to do parametric bootstrappin, which I think is needed for these kinds of models to assess bias in parameter estimates. glmmADMB produces the exact parameter values that maximizes the Laplace approximation for this dataset. Another story is that the Laplace approximation is inaccurate here, as can be shown by using other likelihood approximations. hans
Douglas Bates wrote:
Ah yes, that example. It is also given as the 'toenail' data set in the 'mlmus' package of data sets from the book "Multilevel and Longitudinal Modeling Using Stata" by Sophia Rabe-Hesketh and Anders Skrondal (Stata Press, 2005). It is not surprising that it is difficult to fit such a model to these data because the data do not look like they come from such a model. You did not include the estimates of the variance of the random effects in your output. It is very large and very poorly determined. If you check the distribution of the posterior modes of the random effects (for linear mixed models these are called the BLUPs - Best Linear Unbiased Predictors - and you could call them BLUPs here too except for the fact that they are not linear and they are not unbiased and there isn't a clear sense in which they are "best") it is clearly not a Gaussian distribution with mean zero. I enclose a density plot. You can see that it is bimodal and the larger of the two peaks is for a negative value. These are the random effects for those subjects that had no positive responses - 163 out of the 294 subjects.
sum(with(lesaffre, tapply(y, subject, mean)) == 0)
[1] 163 There is no information to estimate the random effects for these subjects other than "make it as large and negative as possible". It is pointless to estimate the fixed effects for such a clearly inappropriate model. lattice package.