A Note on Stochastic Ordering of the Latent Trait Using the Sum of Polytomous Item Scores

By L. A. van der Ark, Wicher P. Bergsma. 2010

46 citations recorded by the source corpus.

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.

Subfields: Computer Networks and Communications, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ef7ca1ebad93a1f92dd464052ca20cdd524cfe79

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In Computer Networks and Communications

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

New Developments in Mokken Scale Analysis in R (2012, background): “For polytomous items, the monotone homogeneity model implies weak SOL; that is, P( > ajX+ > K) P( > ajX+ K) for all a and for all K (Van der Ark and Bergsma 2010).”
Using Conditional Association to Identify Locally Independent Item Sets (2016, background): “For polytomous items, a weaker form of the stochastical ordering of persons holds (Van der Ark & Bergsma, 2010).”