On A-optimal Designs for Discrete Choice Experiments and Sensitivity Analysis for Computer Experiments.

摘要

The first part of this dissertation is on A-optimal designs for stated choice experiments. Stated choice experiments are widely used in areas such as marketing, planning, transportation, medical care, etc. In such studies, a set of n choice sets is presented to the subjects. Each choice set consists of two or more profiles. Subjects are asked to choose their favorite profile from each choice set. Therefore the outcomes of such studies are discrete and nonlinear models are usually used. The multinomial logit model (MNL) is one of the most frequently used models for stated choice experiments. There are discussions in literature about how to generate optimal designs with the MNL model but primarily with the assumption that all profiles are equally attractive.;In this dissertation, a new approach is proposed to generate A-optimal designs by the local linearization of the MNL model. Under the assumption that all options are equally attractive, this approach gives the same A-optimal designs as in the literature under the same setting but in a wider class of designs. This approach is also extendable to more general settings when profiles are unequally attractive.;The second part of this dissertation deals with sensitivity analysis for computer experiments. Sensitivity analysis is widely used for identifying influential input variables. Two approaches to evaluating sensitivity statistically are (1) estimating global sensitivity indices based on Sobol' variance decomposition, and (2) evaluating local sensitivity indices based on a gradient measure using a one-at-a-time sampling design. Although both approaches have been studied for (hyper-) rectangular input regions, they have not been considered carefully for the non-rectangular input region setting.;In this dissertation, a more flexible gradient-based method is proposed to evaluate sensitivity indices for non-rectangular regions. In addition, the use of variable-length gradients is introduced and the importance of the starting design is emphasized. It is shown by examples that the proposed method works well in both the standard and non-rectangular settings.