A Bayesian Nonparametric Latent Approach for Score Distributions in Test Equating

Abstract

Equating is a family of statistical models and methods used to adjust scores on different test forms so that they can be comparable and used interchangeably. Equated scores are obtained estimating the equating transformation function, which maps the scores on the scale of one test form into their equivalents on the scale of other one. All the statistical models that have been proposed for estimating this function are based on continuous approximations of the score distributions, leading to equated scores lying on a continuous scale even though score scales are usually subsets of the integer numbers (e.g., the total number of correct answers). In this article, we develop a new equating method from which equated scores defined on the original discrete scale are obtained. Considering scores as ordinal random variables, we propose a continuous latent variable formulation to perform an equipercentile-like equating based on a Bayesian nonparametric model for score distributions. The proposed model is applied to simulated and real data collected under an equivalent group design. Some methods to assess the performance of our model are also discussed. Compared with discrete versions of equated scored obtained from traditional equating methods, the results show that the proposed method has better performance.