A New Equating Method Through Latent Variables

Comparability of measurements is an important practice in different fields. In educational measurement, equating methods are used to achieve the goal of having comparable scores from different test forms. Equated scores are obtained using the equating transformation which maps the scores on the scale of one test form into their equivalents on the scale of another for the case of sum scores. Such transformation has been typically computed using continuous approximations of the score distributions, leading to equated scores that are not necessarily defined on the original discrete scale. Considering scores as ordinal random variables, we propose a latent variable formulation based on a flexible Bayesian nonparametric model to perform an equipercentile-like equating that is capable to produce equated scores on the original discrete scale. The performance of our model is assessed using simulated data under the equivalent groups equating design. The results show that the proposed method has better performance with respect to a discrete version of estimated equated scores from traditional equating methods.