A Comparison of Two Approaches for Constructing Exact Designs for Mixed Binary and Continuous Responses

Abstract

This thesis is concerned with experimental designs for studies a controllable independent variable X, a continuous response variable Y and a binary response variable Z. It is known that judiciously selected design allows experimenters to collect informative data for making precise and valid statistical inferences with minimum cost. However, for the complex set- ting that this thesis consider, designs that yield a high expected estimation precision may still possess a high probability of having non-estimable parameters, especially when the sample size is small. Such an observation has been reported in some previous works on the separation issue for, e.g., the logistic regression. Therefore, when selecting a study design, it is important to consider both the expected variances of the parameter estimates, and the probability for having non-estimable parameters. A comparison of two approaches for constructing designs for the previously mentioned setting with a mixed responses model is presented in this work. The two design approaches are the locally A-optimal design approach, and a penalized A-optimal design approach that involves the optimization of A-optimality criterion plus the penalty term to reduce the chance of including designs points that have a high probability to make some parameters non-estimable.