Generating Dichotomous Item Scores with the Four‐Parameter Beta Compound Binomial Model

Abstract

A Monte Carlo simulation technique for generating dichotomous item scores is presented that implements (a) a psychometric model with different explicit assumptions than traditional parametric item response theory (IRT) models, and (b) item characteristic curves without restrictive assumptions concerning mathematical form. The four‐parameter beta compound‐binomial (4PBCB) strong true score model (with two‐term approximation to the compound binomial) is used to estimate and generate the true score distribution. The nonparametric item‐true score step functions are estimated by classical item difficulties conditional on proportion‐correct total score. The technique performed very well in replicating inter‐item correlations, item statistics (point‐biserial correlation coefficients and item proportion‐correct difficulties), first four moments of total score distribution, and coefficient alpha of three real data sets consisting of educational achievement test scores. The technique replicated real data (including subsamples of differing proficiency) as well as the three‐parameter logistic (3PL) IRT model (and much better than the 1PL model) and is therefore a promising alternative simulation technique. This 4PBCB technique may be particularly useful as a more neutral simulation procedure for comparing methods that use different IRT models.