, Volume 54, Issue 2, pp 181-202

Factor and ideal point analysis for interpersonally incomparable data

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Abstract

Interpersonally incomparable responses pose a significant problem for survey researchers. If the manifest responses of individuals differ from their underlying true responses by monotonic transformations which vary from person to person, then the covariances of the manifest responses tools such as factor analysis may yield incorrect results. Satisfactory results for interpersonally incomparable ordinal responses can be obtained by assuming that rankings are based upon a set of multivariate normal latent variables which satisfy the factor or ideal point models of choice. Two statistical methods based upon these assumptions are described; their statistical properties are explored; and their computational feasibility is demonstrated in some simulations. We conclude that is possible to develop methods for factor and ideal point analysis of interpersonally incomparable ordinal data.

This research was begun in the supportive enviroment of the Survey Research Center at the University of California, Berkeley. Financial support was provided by Percy Tannenbaum, Director of the Center, by Allan Sindler, Dean of the Graduate School of Public Policy at Berkeley, by the Data Center of Harvard University, and by the National Science Foundation through grant number SES-84-03056. Chris Achen, Doug Rivers, and members of the Harvard-MIT econometrics seminar provided useful comments.