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Latent class models for testing monotonicity and invariant item ordering for polytomous items
Author(s) -
Ligtvoet Rudy,
Vermunt Jeroen K.
Publication year - 2012
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.2011.02019.x
Subject(s) - polytomous rasch model , monotonic function , mathematics , invariant (physics) , class (philosophy) , econometrics , item response theory , statistics , computer science , artificial intelligence , psychometrics , mathematical analysis , mathematical physics
Two assumptions that are relevant to many applications using item response theory are the assumptions of monotonicity (M) and invariant item ordering (IIO). A latent class model is proposed for ordinal items with inequality constraints on the class‐specific item means. This model is used as a tool for testing for violations of M and IIO. A Gibbs sampling scheme is used for estimating the model parameters. It is shown that the deviance information criterion can be used as an overall test of M and IIO, while posterior predictive checks can be used to test these assumptions at the item level. A real data application illustrates a model‐fitting strategy for detecting items that violate M and IIO.