FOUNDATION FOR NONLINEAR MODELS WITH THRESHOLDS FOR LONGITUDINAL DATA

Threshold models first appeared in the literature nearly half a century ago. Threshold segments have been added to many commonly used forms of models from linear models and generalized linear models through mixed models for the analysis of cross-sectional data. Nonlinear models with thresholds for cross-sectional data are less prevalent in the literature. Nonlinear models with thresholds for longitudinal data are new. The historical developments leading to this point are reviewed as a means of introducing terms necessary for discussing features of these newer models. Nonlinear models for longitudinal data with thresholds are presented and discussed.

Keywords:

• Mean model
• Variance model
• Two-stage model
• Population-averaged inference
• Subject-specific inference

Acknowledgments

The author thanks her advisor, Dr. Chris Gennings, and members of her doctoral committee, Dr. W. Hans Carter and Dr. Vernon Chinchilli, for their valuable suggestions to the work performed on the nonlinear models with thresholds for longitudinal data. Work on the population-averaged model for the toxicity experiment was partially funded by U.S.EPA-NCEA (Cincinnati) Cooperative agreement #CR822671-01-0, Chemical Mixtures Risk Assessment. The author also thanks Dr. Stephen O'Keefe, Medical College of the Virginia Commonwealth University, for the use of his data for the subject-specific model.