A semiparametric additive regression model for longitudinal data

In previous work we have studied a nonparametric additive time-varying regr ession model for longitudinal data recorded at irregular intervals. The mod el allows the influence of each covariate to vary separately with time. For small datasets, however, only a limited number of covariates may be handle d in this way. In this paper, we introduce a semiparametric regression mode l for longitudinal data. The influence of some of the covariates varies non parametrically with time while the effect of the remaining covariates are c onstant. No smoothing is necessary in the estimation of the parametric term s of the model. Asymptotics are derived using martingale techniques for the cumulative regression functions, which are much easier to estimate and stu dy than the regression functions themselves, The approach is applied to lon gitudinal data from the Copenhagen Study Group for Liver Diseases (Schlicht ing et al., 1983).