Fitting Longitudinal Mixed Effects Logistic Models in S-Plus

Statistical models in which both fixed and random effects enter nonlinearly are becoming increasingly popular. These models have a wide variety of applications in many areas such as agriculture, forestry, biology, ecology, biomedicine, sociology, economics, pharmacokinetics, and other areas. Mixed effect models are flexible models to analyze grouped data including longitudinal data, repeated measures data, and multivariate multilevel data. One of the most common applications is nonlinear growth data. In this study, tree growth data set from forestry is used for nonlinear mixed-effects analysis. Nonlinear mixed-effects models involve both fixed effects and random effects. The process of model building for nonlinear mixed-effects models is to determine which parameters should be random effects and which should be purely fixed effects, as well as procedures for determining random effects variance-covariance matrices (e.g. diagonal matrices) to reduce the number of the parameters in the model. Autocorrelation structure was considered for explaining the dependency among repeated measurements within the each individual. Information criterion statistics (AIC, BIC and likelihood ratio test) are used for comparing different structures of the random effects components. These methods are illustrated using the nonlinear mixed-effects methods in S-Plus software.