Unlike their monotone counterparts, nonparametric unfolding response models, which assume the item response function is unimodal, have seen little attention in the psychometric literature. This paper studies the nonparametric behavior of unfolding models by building on the work of Post (1992). The paper provides rigorous justification for a class of nonparametric estimators of respondents’ latent attitudes by proving that the estimators consistently rank order the respondents. The paper also suggests an algorithm for the rank ordering of items along the attitudes scale. Finally, the methods are evaluated using simulated data.

This paper presents an approach for determining unidimensional scale estimates that are relatively insensitive to limited inconsistencies in paired comparisons data. The solution procedure, shown to be a minimum-cost network-flow problem, is presented in conjunction with a sensitivity diagnostic that assesses the influence of a single pairwise comparison on traditional Thurstone (ordinary least squares) scale estimates. When the diagnostic indicates some source of distortion in the data, the network technique appears to be more successful than Thurstone scaling in preserving the interval scale properties of the estimates.