Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 337-354 |
| Number of pages | 18 |
| Journal | British Journal of Mathematical and Statistical Psychology |
| Volume | 64 |
| DOIs | |
| Publication status | Published - 2011 |
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Hessen, D. J. (2011). Loglinear representations of multivariate Bernoulli Rasch models. British Journal of Mathematical and Statistical Psychology, 64, 337-354. https://doi.org/10.1348/2044-8317.002000
Hessen, D.J. / Loglinear representations of multivariate Bernoulli Rasch models. In: British Journal of Mathematical and Statistical Psychology. 2011 ; Vol. 64. pp. 337-354.
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title = "Loglinear representations of multivariate Bernoulli Rasch models",
abstract = "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.",
author = "D.J. Hessen",
year = "2011",
doi = "10.1348/2044-8317.002000",
language = "English",
volume = "64",
pages = "337--354",
journal = "British Journal of Mathematical and Statistical Psychology",
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Hessen, DJ 2011, 'Loglinear representations of multivariate Bernoulli Rasch models', British Journal of Mathematical and Statistical Psychology, vol. 64, pp. 337-354. https://doi.org/10.1348/2044-8317.002000
Loglinear representations of multivariate Bernoulli Rasch models. / Hessen, D.J.
In: British Journal of Mathematical and Statistical Psychology, Vol. 64, 2011, p. 337-354.
Research output: Contribution to journal › Article › Academic › peer-review
TY - JOUR
T1 - Loglinear representations of multivariate Bernoulli Rasch models
AU - Hessen, D.J.
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
U2 - 10.1348/2044-8317.002000
DO - 10.1348/2044-8317.002000
M3 - Article
SN - 0007-1102
VL - 64
SP - 337
EP - 354
JO - British Journal of Mathematical and Statistical Psychology
JF - British Journal of Mathematical and Statistical Psychology
ER -
Hessen DJ. Loglinear representations of multivariate Bernoulli Rasch models. British Journal of Mathematical and Statistical Psychology. 2011;64:337-354. doi: 10.1348/2044-8317.002000
