Bayesian Nonparametric Estimation of Test Equating Functions with Covariates JorgeGonz´alez a,b,1, , Andr´ es F. Barrientos a , Fernando A. Quintana a a Department of Statistics, Pontificia Universidad Cat´olica de Chile, Chile b Measurement Center MIDE UC, Pontificia Universidad Cat´olica de Chile, Chile Abstract Equating is an important step in the process of collecting, analyzing, and reporting test scores in any program of assessment. Methods of equating uti- lize functions to transform scores on two or more versions of a test, so that they can be compared and used interchangeably. In common practice, tradi- tional methods of equating use either parametric or semi-parametric models where, apart from the test scores themselves, no additional information is used to estimate the equating transformation function. 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 is proposed. A major feature of this approach is that the complete shape of the scores distribution may change as a function of the covariates. As a consequence, the form of the equating transformation can change according to covariate values. Applications of the proposed model to real and simulated data are discussed and compared to other current methods Email address: jgonzale@mat.puc.cl (JorgeGonz´alez) URL: www.mat.puc.cl/~jgonzale (JorgeGonz´alez) 1 Faculty of Mathematics, Av. Vicu˜ na Mackenna 4860, Casilla 306, Correo 22, Santiago, Chile. Phone: +56223545467, Fax: +56225525916 Preprint submitted to CSDA March 8, 2015 This paper is published. Please cite it as: González, J., Barrientos, A. F., & Quintana, F. A. (2015). Bayesian Nonparametric Estimation of Test Equating Functions with Covariate. Computational Statistics and Data Analysis, 89, 222-244.