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

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  • Francesco Bartolucci
  • Fulvia Pennoni

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. Copyright 2007, Oxford University Press.

Suggested Citation

  • Francesco Bartolucci & Fulvia Pennoni, 2007. "On the approximation of the quadratic exponential distribution in a latent variable context," Biometrika, Biometrika Trust, vol. 94(3), pages 745-754.
    • Handle: RePEc:oup:biomet:v:94:y:2007:i:3:p:745-754
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    File URL: http://hdl.handle.net/10.1093/biomet/asm045
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    Cited by:

    1. Bartolucci, Francesco & Nigro, Valentina, 2012. "Pseudo conditional maximum likelihood estimation of the dynamic logit model for binary panel data," Journal of Econometrics, Elsevier, vol. 170(1), pages 102-116.
    2. Francesco Bartolucci & Francesco Valentini & Claudia Pigini, 2023. "Recursive Computation of the Conditional Probability Function of the Quadratic Exponential Model for Binary Panel Data," Computational Economics, Springer;Society for Computational Economics, vol. 61(2), pages 529-557, February.

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