Self-modeling Regression for Multivariate Curve Data

We present self-modeling regression models for flexible nonparametric modeling of multiple outcomes measured longitudinally. Based on penalized regression splines, the models borrow strength across multiple outcomes by specifying a global time profile, thereby yielding a means of dimension reduction and estimates of trend more precise than those based on univariate regressions. The proposed models represent nonparametric regression extensions to existing factor analytic models for a multivariate response recorded at a single timepoint, and are easily generalized to incorporate serial correlation above that captured by nonlinear effects over time. We illustrate the methods by applying them to data on the respiratory effects of residual oil fly ash inhalation in humans.