A Single Ideal Point Model for Market Structure Analysis

Abstract

Computing unsegmented product maps from preference data by means of single ideal point models is commonly thought to be impossible because of indeterminacy problems. The authors show that this mathematical indeterminacy can be overcome by incorporating dependent sampling assumptions into a probabilistic multidimensional scaling (MDS) model. As a result, product space maps can be estimated for single markets from preference data alone. If desired, dissimilarity data can be combined with preference data to produce jointly estimated product space maps. The authors illustrate the advantages of the proposed approach with real and simulated data. They also make comparisons to both internal and external deterministic models. The results are favorable.