Computational Methods for Mixed-Effects Models Douglas M. Bates, U. of Wisconsin - Madison Abstract This research extends current computational methods and software implementations for the estimation of parameters in mixed-effects models. There is a special emphasis on extensions to models where there are several levels of random effects nested within each other. Another emphasis is on models where the within-subject response depends nonlinearly on the parameters of interest. The primary implementation is in the S computer language and complements current graphical and analytical methods available in that language. When a response is measured on several occasions for each of several "subjects" or experimental units, the resulting data are called repeated-measures data. If the data on each experimental unit are collected over time, they are also known as longitudinal data. A statistical model for such data will usually incorporate both fixed effects, parameters that describe the typical behaviour in the population from which the experimental units are selected, and random effects, quantaties that describe the variation within the population. Models with both fixed effects and random effects are called mixed-effects models. This research provides new computational methods for fitting mixed-effects models to observed data. The new methods are suitable for use with parallel computers and with other high performance computing environments. This is important because some of the applications of mixed-effects models in manufacturing (evaluation of integrated circuit designs) and biotechnology (modelling of genetic effects in animal breeding) involve fitting complicated models to thousands and sometime millions of observations; a task that pushes the limits of current computers.
