The statistical design of adaptive preference modeling: A logit approach

The goal of this dissertation is to develop an approach for individual adaptive preference modeling which emphasizes statistical as well as psychological considerations. An algorithm is developed which is based on the D-optimality criterion applied to the binary logit model in an attempt to obtain the most information possible from each response. It is intended for use in an adaptive interview phase in which paired comparison preference data are collected from a respondent.;Theoretical and numerical D-optimality results for specific two-, three- and four-point designs suggest that the balanced symmetric two-point design with choice probabilities.176 and.824 is best. The algorithm, however, does not involve specifying a constant difference in utility between alternatives paired for respondent evaluation. Rather, the design point which maximizes the improvement of the overall design, as measured by the D-optimal criterion, is selected, as the next pair to be evaluated.;The proposed adaptive algorithm is compared to other sequential approaches, Johnson's heuristic (pairing alternatives as nearly equal in utility as possible for respondent evaluation) and random selection, via a simulation study. Data were generated for various parameter patters and error levels. The proposed algorithm was found to significantly outperform both approaches in terms of estimation accuracy. Under conditions of low error, the proposed algorithm outperformed both Johnson's heuristic and random selection in predictive efficiency; under conditions of high error it again outperformed Johnson's heuristic.;The proposed adaptive algorithm is also compared to both traditional (nonadaptive) methods and the aforementioned sequential approaches using data on students' expressed preferences for apartment alternatives. The results indicate that the proposed algorithm yields individual level models with reasonably good predictive power when compared to nonadaptive methods. As compared to the sequential approaches, the proposed algorithm was found to be equivalent to Johnson's heuristic in terms of estimation quality and predictive efficiency, and significantly better than random selection. These results appear to encourage the use of such an adaptive algorithm in light of the potential reduction in data requirements without significant loss in predictive accuracy.