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Latent class models for testing monotonicity and invariant item ordering for polytomous items
Article first published online: 8 JUN 2011
DOI: 10.1111/j.2044-8317.2011.02019.x
©2011 The British Psychological Society
Issue
British Journal of Mathematical and Statistical Psychology
Volume 65, Issue 2, pages 237–250, May 2012
Additional Information
How to Cite
Ligtvoet, R. and Vermunt, J. K. (2012), Latent class models for testing monotonicity and invariant item ordering for polytomous items. British Journal of Mathematical and Statistical Psychology, 65: 237–250. doi: 10.1111/j.2044-8317.2011.02019.x
Publication History
- Issue published online: 16 APR 2012
- Article first published online: 8 JUN 2011
- Received 21 July 2010; revised version received 4 May 2011
- Abstract
- Article
- References
- Cited By
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.