Following Cox Wermuth (1994, 2002), we show that the distribution of a set of binary observable variables, induced by a certain discrete latent variable model, may be approximated by a quadratic exponential distribution. This discrete latent variable model is equivalent to the latent-class version of the two-parameter logistic model of Birnbaum (1968), which may be seen as a generalized version of the Rasch model (Rasch, 1960, 196). On the basis of this result, we develop an approximate maximum likelihood estimator of the item parameters of the two-parameter logistic model which is very simply implemented. The proposed approach is illustrated through an example based on a dataset on educational assessment. © 2007 Biometrika Trust.

Bartolucci, F., Pennoni, F. (2007). On the approximation of the quadratic exponential distribution in a latent variable context. BIOMETRIKA, 94(3), 745-754 [10.1093/biomet/asm045].

On the approximation of the quadratic exponential distribution in a latent variable context

PENNONI, FULVIA
2007

Abstract

Following Cox Wermuth (1994, 2002), we show that the distribution of a set of binary observable variables, induced by a certain discrete latent variable model, may be approximated by a quadratic exponential distribution. This discrete latent variable model is equivalent to the latent-class version of the two-parameter logistic model of Birnbaum (1968), which may be seen as a generalized version of the Rasch model (Rasch, 1960, 196). On the basis of this result, we develop an approximate maximum likelihood estimator of the item parameters of the two-parameter logistic model which is very simply implemented. The proposed approach is illustrated through an example based on a dataset on educational assessment. © 2007 Biometrika Trust.
Articolo in rivista - Articolo scientifico
Approximate maximum likelihood; Estimation; Item response theory; Rasch model; Two-parameter logistic model
English
745
754
Bartolucci, F., Pennoni, F. (2007). On the approximation of the quadratic exponential distribution in a latent variable context. BIOMETRIKA, 94(3), 745-754 [10.1093/biomet/asm045].
Bartolucci, F; Pennoni, F
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/7178
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