Two-level linear paired comparison models: Estimation and identifiability issues

The method of paired comparisons became popular in psychological research with Thurstone's [Psychometrika 65 (1927) 233] demonstration that attitudes can be scaled along a one-dimensional continuum. Despite a large number of applications of this method over the years, it has been noted only recently that paired comparison data do not only contain information about item mean differences but are also useful for studying how individuals differ in their evaluative judgments. We show that a mixed-effects, generalized linear model is well-suited for investigating such individuals differences and present a Monte Carlo EM algorithm for parameter estimation. In addition, we discuss identification issues in the specifications of different covariance structures because they impose important constraints on the interpretation of model parameters. An extensive analysis of a value study employing ordinal paired comparison illustrates the proposed statistical framework.