Partially Generalized Ridge Regression with Longitudinal Data

This paper considers the multicollinearity problem for longitudinal data in the framework of generalized partially linear model (GPLM). To overcome this problem, a new ridge estimation method is proposed while the nonparametric function in the partially part is approximated using splines. The proposed approach integrates ridge method into the generalized estimating equation method in order to account for both the correlation induced by repeatedly measuring an outcome on each individual over time and the potentially high degree of correlation among possible predictor variables. The asymptotic normality of the exhibited estimator is established. The performance of the proposed estimator is assessed through numerical studies.