A Dependent Bayesian Nonparametric Model for Test Equating
Equating methods utilize functions to transform scores on two or more versions of a test, so that they can be compared and used interchangeably. In common practice, traditional methods of equating use parametric models where, apart from the test scores themselves, no additional information is used for the estimation of the equating transformation. We propose a flexible Bayesian nonparametric model for test equating which allows the use of covariates in the estimation of the score distribution functions that lead to the equating transformation. A major feature of this approach is that the complete shape of the score distribution may change as a function of the covariates. As a consequence, the form of the equating transformation can change according to covariate values. We discuss applications of the proposed model to real and simulated data. We conclude that our method has good performance compared to alternative approaches.
KeywordsScore Distribution Dirichlet Process Test Equate Dirichlet Process Mixture High Probability Density
The first author acknowledges partial support of Fondecyt 11110044 and Anillo SOC1107 grants. The second author was partially funded by Fondecyt 3130400 grant. The third author was partially funded by Fondecyt grant 1100010.
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