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Equating methods is a family of statistical models and methods used to adjust scores on different test forms so that scores can be comparable and used interchangeably. These methods lie on functions to transform scores on two or more versions of a test. Most of the proposed approaches for the estimation of these functions are based on continuous approximations of the score distributions, as they are most of the time discrete functions.
Considering scores as ordinal random variables, we propose a flexible dependent Bayesian nonparametric model for test equating. The new approach both avoids continuous assumptions of the score distributions and it allows the use of covariates in the estimation of the score distribution functions, an approach not explored at all in the equating literature. Applications of the proposed model to real and simulated data under different sampling designs are discussed. Several methods are considered to evaluate the performance of our method and to compare it with current methods of equating. Results show that the proposal has better performance in almost all the aspect evaluated.
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