Walker, S.G. and Karabatsos, G. (2009) Coherent psychometric modeling with Bayesian nonparametrics. British Journal of Mathematical and Statistical Psychology, 62 . pp. 1-20. ISSN 0007-1102.
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In this paper we argue that model selection, as commonly practised in psychometrics, violates certain principles of coherence. On the other hand, we show that Bayesian nonparametrics provides a coherent basis for model selection, through the use of a 'nonparametric' prior distribution that has a large support on the space of sampling distributions. We illustrate model selection under the Bayesian nonparametric approach, through the analysis of real questionnaire data. Also, we present ways to use the Bayesian nonparametric framework to define very flexible psychometric models, through the specification of a nonparametric prior distribution that supports all distribution functions for the inverse link, including the standard logistic distribution functions. The Bayesian nonparametric approach provides a coherent method for model selection that can be applied to any statistical model, including psychometric models. Moreover, under a 'non-informative' choice of nonparametric prior, the Bayesian nonparametric approach is easy to apply, and selects the model that maximizes the log likelihood. Thus, under this choice of prior, the approach can be extended to non-Bayesian settings where the parameters of the competing models are estimated by likelihood maximization, and it can be used with any psychometric software package that routinely reports the model log likelihood.
|Uncontrolled keywords:||MAXIMUM-LIKELIHOOD; EM ALGORITHM; DISTRIBUTIONS; INFERENCE|
|Subjects:||Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics|
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics|
|Depositing User:||Stephen Walker|
|Date Deposited:||29 Jun 2011 13:37|
|Last Modified:||05 Dec 2011 15:13|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/23912 (The current URI for this page, for reference purposes)|
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