Limited information estimation and testing of Thurstonian models for preference data

Abstract

Thurstonian models provide a rich representation of choice behavior that does not assume that stimuli are judged independently of each other, and they have an appealing substantive interpretation. These models can be seen as multivariate standard normal models that have been discretized using a set of thresholds and that impose certain restrictions on these thresholds and on the inter-correlations among the underlying normal variates. In this paper we provide a unified framework for modeling preference data under Thurstonian assumptions and we propose a limited information estimation and testing framework for it. Although these methods have a long tradition in psychometrics, until recently only their application to rating data has been considered. Here we shall give an overview of how these methods can be readily applied to fit not only rating data, but also paired comparison and ranking data. The limited information methods discussed here are appealing because they are extremely fast, they are able to estimate models essentially of any size, they can easily accommodate external information about the stimuli and/or respondents, and in simulations they have been found to be very robust to data sparseness.