ISBN 978-951-22-8929-5 (printed version)

For decades, much research has been devoted to developing and comparing variable selection methods, but primarily for the classical case of independent observations. Existing variable-selection methods can be adapted to cluster-correlated observations, but some adaptation is required. For example, classical model fit statistics such as AIC and BIC are undefined if the likelihood function is unknown (Pan, 2001). Little research has been done on variable selection for generalized estimating equations (GEE, Liang and Zeger, 1986) and similar correlated data approaches. This thesis will review existing work on model selection for GEE and propose new model selection options for GEE, as well as for a more sophisticated marginal modeling approach based on quadratic inference functions (QIF, Qu, Lindsay, and Li, 2000), which has better asymptotic properties than classic GEE. The focus is on selection using continuous penalties such as LASSO (Tibshirani, 1996) or SCAD (Fan and Li, 2001) rather than the older discrete penalties such as AIC and BIC. The

The LASSO-Patternsearch algorithm is proposed as a two-step method to identify clusters or patterns of multiple risk factors for outcomes of interest in demographic and genomic studies. The predictor variables are dichotomous or can be coded as dichotomous. Many diseases are suspected of having multiple interacting risk factors acting in concert, and it is of much interest to uncover higher order interactions or risk patterns when they exist. The patterns considered here are those that arise naturally from the log linear expansion of the multivariate Bernoulli density. The method is designed for the case where there is a possibly very large number of candidate patterns but it is believed that only a relatively small number are important. A LASSO is used to greatly reduce the number of candidate patterns, using a novel computational algorithm that can handle an extremely large number of unknowns simultaneously. Then the patterns surviving the LASSO are further pruned in the framework of (parametric) generalized linear models. A novel tuning procedure based on the GACV for Bernoulli

Ridge-SimSel: A generalization of the variable selection method SimSel to

Recursive regularization for inferring gene networks from time-course gene expression profiles

DMS-0112069. Any opinions, findings, and conclusions or recommendations expressed in this material are

The LASSO-Patternsearch Algorithm and its variant the Grouped LASSO-Patternsearch Algorithm are proposed to efficiently identify patterns of multiple dichotomous risk factors for outcomes of interest in demographic and genomic studies. The patterns considered are those that arise naturally from the log linear expansion of the multivariate Bernoulli density. Both methods are designed for the case where there is a possibly very large number of candidate patterns but it is believed that only a relatively small number are important. In the LASSO-Patternsearch Algorithm, a LASSO is used to greatly reduce the number of candidate patterns, using a novel computational algorithm that can handle an extremely large number of unknowns simultaneously. The patterns surviving the LASSO are further pruned in the framework of (parametric) generalized linear models. A novel tuning procedure based on the GACV for Bernoulli outcomes, modified to act as a model selector, is used at both steps. We applied the method to myopia data from the population-based Beaver Dam Eye Study, exposing physiologically interesting interacting risk factors. We then

We propose a Bayesian stochastic search approach to selecting restrictions for Vector Autoregressive (VAR) models. For this purpose, we develop a Markov Chain Monte Carlo (MCMC) algorithm that visits high posterior probability restrictions on the elements of both the VAR regression coefficients and the error variance matrix. Numerical simulations show that stochastic search based on this algorithm can be effective at both selecting a satisfactory model and improving forecasting performance. To illustrate the potential of our approach, we apply our stochastic search to VAR modelling of inflation transmission from Producer Price Index (PPI) components to the Consumer