Conservative robust estimation methods do not appear to be currently available in the standard mixed model methods for R, where by conservative robust estimation I mean methods which work almost as well as the methods based on assumptions of normality when the assumption of normality *IS* satisfied.
We are considering adding such a conservative robust estimation option for the random effects to our AD Model Builder mixed model package, glmmADMB, for R, and perhaps extending it to do robust estimation for linear mixed models at the same time. An obvious candidate is to assume something like a mixture of normals. I have tested this in a simple linear mixed model using 5% contamination with a normal with 3 times the standard deviation, which seems to be a common assumption. Simulation results indicate that when the random effects are normally distributed this estimator is about 3% less efficient, while when the random effects are contaminated with 5% outliers the estimator is about 23% more efficient, where by 23% more efficient I mean that one would have to use a sample size about 23% larger to obtain the same size confidence limits for the parameters. Question? I wonder if there are other distributions besides a mixture or normals. which might be preferable. Three things to keep in mind are: 1.) It should be likelihood based so that the standard likelihood based tests are applicable. 2.) It should work well when the random effects are normally distributed so that things that are already fixed don't get broke. 3.) In order to implement the method efficiently it is necessary to be able to produce code for calculating the inverse of the cumulative distribution function. This enables one to extend methods based one the Laplace approximation for the random effects (i.e. the Laplace approximation itself, adaptive Gaussian integration, adaptive importance sampling) to the new distribution. Dave -- David A. Fournier P.O. Box 2040, Sidney, B.C. V8l 3S3 Canada Phone/FAX 250-655-3364 http://otter-rsch.com ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html