Structural equation modeling of approval voting data

The method of approval voting is a commonly used voting procedure in which each judge selects a subset of the alternatives. By postulating that the random utilities associated with the choice options in approval voting elections follow a multivariate normal distribution under the Thurstonian framework, Regenwetter, Ho, and Tsetlin (2007) attempted to integrate the normative theories and individual variabilities in modeling social behavior. However, their approach is limited to only three alternatives, due to computational intractability as the number of alternatives increases. In this article, we reparameterize extensions of their models under the structural equation modeling framework and propose the use of limited information methods for estimating model parameters. As a result, we are able to extend their previous approach to the analysis of approval voting data with any number of alternatives. Two applications are presented to illustrate the usefulness of such an approach.