Latent and Manifest Monotonicity in Item Response Models

By Brian W. Junker, Klaas Sijtsma. 2000

124 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/3e49c99970457d5f2fed79c2b66edc33014e8504

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In Computer Networks and Communications

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Nonparametric Item Response Theory in Action: An Overview of the Special Issue (2001, methodology): “…program provides a straightforward use of nonparametric regression as an exploratory tool for assessing IRF monotonicity for each item response variable Xj , using as a proxy for θ either the total score, X+ = ∑j Xj (Ramsay, 1991), or the rest-score, Rj = X+ − Xj (Junker & Sijtsma, 2000).”
Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables (2007, methodology): “rest-scores comes from studies on the shape of item response functions, model fit, dierential item functioning, and identification of incorrectly coded responses ( Junker and Sijtsma 2000 ).”
Paradoxical Results in Multidimensional Item Response Theory (2009, background): “Monotone response functions are considered in Junker and Sijtsma (2000) and Antal (2007); nonmonotone response functions can clearly be seen to produce paradoxical results.”
Cognitive Assessment Models with Few Assumptions, and Connections with Nonparametric Item Response Theory (2001, background): “No sample violations of manifest monotonicity (Junker & Sijtsma, 2000) were found.”
Mokken Scale Analysis in R (2007, background): “Manifest monotonicity is an observable property of the test data, and defined as P(Xj ≥ x|R−j = s) ≥ P(Xj ≥ x|R−j = r) for all j, x, s > r. (3) Junker and Sijtsma (2000) showed that for dichotomous items latent monotonicity implies manifest monotonicity.”
New Developments in Mokken Scale Analysis in R (2012, background): “…of R j (r; s = 0; : : : ; [J 1] m), then manifest monotonicity is de ned as P(Xj xjR(j) = s) P(Xj xjR(j) = r) for all j; x; s > r: For dichotomous items, latent monotonicity implies manifest monotonicity, but for polytomous items, some counterexamples have been found (Junker and Sijtsma 2000).”