There has recently been some discussion of GLMMs on this list. Unfortunately, I deleted the messages so that this is from memory. The original question was about doing a homework problem concerning mixed logistic regression in R for a course based on SAS. Clearly, the R function to use is my glmm because it uses essentially the same algorithm as SAS (the SAS Gauss-Hermite used an adaptive method that can reduce the number of quadrature points for the same precision). Although I have made available this function, I never recommend its use because I think this type of model is very artificial, except possibly in some animal breeding situations. I have never been able to understand why GLMMs, with their normal mixing distribution, are popular. If someone must use mixed logistic regression in this sense, I strongly recommend using a specialized program such as Sabre or Egret for a variety of reasons. At least two points came up in the discussion that I would like to address: approximations and restrictions. Restrictions The main restrictions to glmm come from glm itself: 1) linear regression and 2) exponential family conditional distribution plus 3) the fact that the normal mixing distribution is imposed on them. The latter is typical of the sort of general models that statisticians love to develop that have no real mechanistic interpretation. Troels pointed out that I have more general functions available that lift these restrictions. gnlmm removes the two imposed by glm. Any nonlinear model can be fitted with a wide variety of conditional distributions. However, the mixing distribution is still normal and in addition, in nonlinear models, a random "intercept" may often be unnatural. However, I also have gnlmix which removes all restrictions. It has nonlinear regression with a wide variety of conditional distributions where any one nonlinear parameter can be random with a mixing distribution chosen from a wide selection. Romberg integration is used so that it is essentially exact, if rather slow. It would be simple to extend it to say two nonlinear random parameters but time would quickly become rather exhorbitant. Approximations When discussing GLMMs using Gauss-Hermite integration, the question of approximations is essentially a red herring. No matter the number of quadrature points, the likelihood is always exact (as exact as any likelihood can be on a digital computer). It is a finite mixture. The approximation question arises in the sense that this finite mixture is more or less close to a Gaussian mixing distribution, which is a completely artificial choice in the first place. It is quite possible for the model with very few quadrature points to fit better than one with sufficient for a very close approximation to the normal mixing distribution, indicating that normal mixing is not a good choice. It is false to say that the properties of this approximation, in the latter sense are unknown. GLMMs using Gauss-Hermite go back at least to an unpublished tech report by Don Pierce in the mid 70s and the published paper by John Hinde in 1982. Since then, there is a vast literature on the subject of the approximation in the second sense above, especially for the model in question, mixed logistic regression, including work by Alan Agresti, Murray Aitkin, David Brillinger, Bruce Lindsay, etc. (There is also another literature on approximations replacing Gauss-Hermite, such as Breslow and Clayton.) The most recent published reference that I am aware of is earlier this year, but I have refereed others that are not yet in print. 15 to 20 quadrature points gives an extremely close numerical approximation to the normal mixing distribution for most data sets, for what that is worth. Jim -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._