A nonparametric dynamic additive regression model for longitudinal data

Abstract

In this work we study additive dynamic regression models for longitudinal data. These models provide a flexible and nonparametric method for investigating the time-dynamics of longitudinal data. The methodology is aimed at data where measurements are recorded at random time points. We model the conditional mean of responses given the full internal history and possibly time-varying covariates. We derive the asymptotic distribution for a new nonparametric least squares estimator of the cumulative time-varying regression functions. Based on the asymptotic results, confidence bands may be computed and inference about time-varying coefficients may be drawn. We propose two estimators of the cumulative regression function. One estimator that involves smoothing and one that does not. The latter, however, has twice the variance as the smoothing based estimator. Goodness of fit of the model is considered using martingale residuals. Finally, we also discuss how partly-conditional mean models in which the mean of the response is regressed onto selected time-varying covariates may be analysed in the same framework. We apply the methods to longitudinal data on height development for cystic fibrosis patients.