Smoothing spline analysis of variance for polychotomous response data

We consider the penalized likelihood method with smoothing spline ANOVA for estimating nonparametric functions to data involving a polychotomous response. The fitting procedure involves minimizing the penalized likelihood in a Reproducing Kernel Hilbert Space. One Step Block SOR-Newton-Raphson Algorithm is used to solve the minimization problem. Generalized Cross-Validation or unbiased risk estimation is used to empirically assess the amount of smoothing (which controls the bias and variance trade-off) at each one-step Block SOR-Newton-Raphson iteration. Under some regular smoothness conditions, the one-step Block SOR-Newton- Raphson will produce a sequence which converges to the minimizer of the penalized likelihood for the fixed smoothing parameters. Monte Carlo simulations are conducted to examine the performance of the algorithm. The method is applied to polychotomous data from the Wisconsin Epidemiological Study of Diabetic Retinopathy to estimate the risks of cause-specific mortality given several potential risk factors at the start of the study. Strategies to obtain smoothing spline estimates for large data sets with polychotomous response are also proposed in this thesis. Simulation studies are conducted to check the performance of the proposed method.