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Loglinear representations of multivariate Bernoulli Rasch models
Article first published online: 7 DEC 2010
DOI: 10.1348/2044-8317.002000
©2010 The British Psychological Society
Issue
British Journal of Mathematical and Statistical Psychology
Volume 64, Issue 2, pages 337–354, May 2011
Additional Information
How to Cite
Hessen, D. J. (2011), Loglinear representations of multivariate Bernoulli Rasch models. British Journal of Mathematical and Statistical Psychology, 64: 337–354. doi: 10.1348/2044-8317.002000
Publication History
- Issue published online: 15 APR 2011
- Article first published online: 7 DEC 2010
- Received 26 January 2010; revised version received 21 July 2010
- Abstract
- Article
- References
- Cited By
In this paper, the extended Rasch model for dichotomously scored items is derived from the general multivariate Bernoulli distribution. The necessary and sufficient conditions for the multivariate Bernoulli distribution to be equal to the extended Rasch model provide a new loglinear representation of the extended Rasch model. Conditions are also given under which the extended Rasch model is equal to the random effects Rasch model, and it is shown under what conditions the extended Rasch model is equal to a random effects Rasch model in which the underlying variable has a normal distribution. In addition, alternative models for the construction of likelihood ratio tests are proposed. One of these alternative models is Haberman's extended interaction model. Furthermore, it is shown how both the SPSS and SAS programs can be used to estimate and test loglinear representations of extended Rasch models.