Physical Sciences and Mathematics Commons^™

Random Regression Models Based On The Elliptically Contoured Distribution Assumptions With Applications To Longitudinal Data, Alfred A. Bartolucci, Shimin Zheng, Sejong Bae, Karan P. Singh

Shimin Zheng

We generalize Lyles et al.’s (2000) random regression models for longitudinal data, accounting for both undetectable values and informative drop-outs in the distribution assumptions. Our models are constructed on the generalized multivariate theory which is based on the Elliptically Contoured Distribution (ECD). The estimation of the fixed parameters in the random regression models are invariant under the normal or the ECD assumptions. For the Human Immunodeficiency Virus Epidemiology Research Study data, ECD models fit the data better than classical normal models according to the Akaike (1974) Information Criterion. We also note that both univariate distributions of the random intercept and …