Modeling Repeated Count Data: Some Extensions of the Rasch Poisson Counts Model

Marijtje A. J. van Duijn and Margo G. H. Jansen

Journal of Educational and Behavioral Statistics, 1995, vol. 20, issue 3, 241-258

Abstract: We consider data that can be summarized as an N × K table of counts—for example, test data obtained by administering K tests to N subjects. The cell entries y ij are assumed to be conditionally independent Poisson-distributed random variables, given the NK Poisson intensity parameters μ ij . The Rasch Poisson Counts Model (RPCM) postulates that the intensity parameters are products of test difficulty and subject ability parameters. We expand the RPCM by assuming that the subject parameters are random variables having a common gamma distribution with fixed unknown parameters and that the vectors of test difficulty parameters per subject follow a common Dirichlet distribution with fixed unknown parameters. Further, we show how additional structures can be imposed on the test parameters, modeling a within-subjects design. Methods for testing the fit and estimating the parameters of these models are presented and illustrated with the analysis of two empirical data sets.

Keywords: Poisson distribution; gamma distribution; multinomial distribution; Dirichlet distribution; overdispersion; interaction; repeated count data (search for similar items in EconPapers)
Date: 1995
References: Add references at CitEc
Citations:

Downloads: (external link)
https://journals.sagepub.com/doi/10.3102/10769986020003241 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:20:y:1995:i:3:p:241-258

DOI: 10.3102/10769986020003241

Access Statistics for this article

More articles in Journal of Educational and Behavioral Statistics
Bibliographic data for series maintained by SAGE Publications ().