Comparing the Robustness of PROX Estimation to Maximum Likelihood Estimators with Fixed Item Parameters

Abstract

This study examines the robustness and comparability of a non-iterative estimation method (PROX) with more common estimation methods using the binary Rasch model when item parameters are known. A simulation was conducted with R to manipulate the person ability distribution, item difficulty distribution, number of items, and sample size. Comparisons between PROX, joint maximum likelihood estimation (JMLE), marginal maximum likelihood estimation, and expected a posteriori estimation in terms of recovery of person parameters were made in terms of correlations with simulated person parameters, bias, MAD, and RMSE. Results indicate that in typical conditions, PROX is at least as good as other methods, and in more extreme conditions, it performs worse than JMLE alone for person parameter recovery. Future avenues of investigation are also discussed.