Optimal designs for generalized linear models
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Generalized linear models with factors are widely used in many areas, such as public health, financial and psychology. Models that are often used include models with factorial effects. Selecting optimal designs for such models is a very challenging problem. There have been several results in this area, which are focused on algorithms. Models that we considered are generalized linear models with both factorial effects and one covariate. The factorial effects include both main effects and interactions. Then the optimal design problem is to choose both factor combinations and the corresponding covariate. There are several results about optimal designs under generalized linear models, which include the complete class approach by Yang and Stufken (2009) and the use of efficient algorithms. The research in this dissertation, which includes three different parts, builds on those results. In the first part, we develop a theoretical result about optimal designs under models with main effects and one covariate. Available results focus primarily on the full factorial in the factors. Hence we propose optimal designs under fractional factorial settings. In the second part we consider optimal designs under generalized linear models with main effects, interactions between factors, and one covariate. There are very few results for this topic. We extend our results from main effects models to models with interactions. Finally, in the third part, we propose an algorithm to search for optimal designs. It works for generalized linear models with factorial effects and one covariate and a variety of optimality criteria.