Kernel Poisson Regression for Longitudinal Data

Abstract

An estimating procedure is introduced for the nonlinear mixed-effect Poisson regression, for longitudinal study, where data from different subjects are independent whereas data from same subject are correlated. The proposed procedure provides the estimates of the mean function of the response variables, where the canonical parameter is related to the input vector in a nonlinear form. The generalized cross validation function is introduced to choose optimal hyper-parameters in the procedure. Experimental results are then presented, which indicate the performance of the proposed estimating procedure.

Keywords

• Canonical parameter;
• Generalized cross validation function;
• Kernel trick;
• Longitudinal data;
• Mixed effects model;
• Penalized negative log-likelihood;
• Poisson regression