Flexible Semi- And Non-Parametric Modelling and Prognosis for Discrete Outcomes

This thesis presents new models and estimation techniques based on the generalized linear model framework. In Chapter 1 the GAMBoost procedure for estimation of generalized additive models is developed. Based on boosting and gradient descent in function space it generalizes the notion of repeated fitting of residuals to exponential family responses. By using a flexible number of updates for each covariate the selection of smoothing parameters is reduced to the selection of the number of boosting steps. The latter is chosen based on approximate effective degrees of freedom. The resulting procedure shows good performance for a wide variety of examples with binary and Poisson response data. A considerable advantage compared to other procedures is found for a large number of covariates and a low level of information. An application to real data is presented. In Chapter 2 a flexible model for discrete time survival data is developed that allows for non-linear covariate effects that vary over time. For estimation an iterative two-step procedure based on Fisher scoring is given. A simulation study with various levels of complexity underlying the data compares the performance of adequate models to the performance of models that are too restrictive, too flexible or that provide the wrong kind of flexibility. It is shown that effective degrees of freedom work well as a basis for selection of smoothing parameters as well as for model selection. An example with real data is given. In Chapter 3 a technique for classification with binary response data is developed based on logistic regression. It uses local models with local selection of predictors for reduction of complexity and penalized estimation for numerical stability. Standard simulated data examples are used to evaluate components of the algorithm such as the kernel for local weight calculation, and to compare the performance to other procedures. It is found that the procedure is competitive for a wide range of examples and that selection of predictors is crucial for local quadratic models while being regulated rather well for local linear models. Good performance can also be seen for real data examples.