Inferences with generalized partially linear single-index models for longitudinal data.

Abstract We study generalized partially linear single-index models for longitudinal data in this article. We propose a method to efficiently estimate both the parameters and the nonparametric single-index function in generalized partially linear single-index models when subjects are observed or measured over time. The proposed estimation approach is more flexible and more general in that we can model both categorical response and transformation-necessary response such as heavy-tailed variable with multiple covariates, especially when some covariates are parametrically correlated with the response and the others are nonparametrically correlated with the response. With minimal assumptions, we show that the semiparametric efficiency bound is reached for the parameter estimators. We also show that the asymptotic variance of the single-index function estimator is generally less than that of existing estimators. Furthermore, we provide Monte Carlo simulation results and an empirical data analysis that support our new method. Highlights • A new estimation method is proposed for generalized partially linear single-index models for longitudinal data. • The method is shown to be semiparametrically efficient. • Empirical results support the new method. [ABSTRACT FROM AUTHOR]