A Note on Stochastic Ordering of the Latent Trait Using the Sum of Polytomous Item Scores
Source: Psychometrika, Volume 75, Number 2, June 2010 , pp. 272-279(8)
Abstract:In contrast to dichotomous item response theory (IRT) models, most well-known polytomous IRT models do not imply stochastic ordering of the latent trait by the total test score (SOL). This has been thought to make the ordering of respondents on the latent trait using the total test score questionable and throws doubt on the justifiability of using nonparametric polytomous IRT models for ordinal measurement. We show that a broad class of polytomous IRT models has a weaker form of SOL, denoted weak SOL, and argue that weak SOL justifies ordering respondents on the latent trait using the total test score and, therefore, the use of nonparametric polytomous IRT models for ordinal measurement.
Document Type: Research Article
Affiliations: 1: Department of Methodology and Statistics, Faculty of Social and Behavioral Sciences, Tilburg University, 5000 LE, Tilburg, The Netherlands, Email: firstname.lastname@example.org 2: London School of Economics, London, UK
Publication date: June 2010