Evaluation of Item Fit With Output From the EM Algorithm: RMSD Index Based on Posterior Expectations.

Abstract

In item response theory modeling, item fit analysis using posterior expectations, otherwise known as pseudocounts, has many advantages. They are readily obtained from the E-step output of the Bock-Aitkin Expectation-Maximization (EM) algorithm and continue to function as a basis of evaluating model fit, even when missing data are present. This paper aimed to improve the interpretability of the root mean squared deviation (RMSD) index based on posterior expectations. In Study 1, we assessed its performance using two approaches. First, we employed the poor person's posterior predictive model checking (PP-PPMC) to compute their significance levels. The resulting Type I error was generally controlled below the nominal level, but power noticeably declined with smaller sample sizes and shorter test lengths. Second, we used receiver operating characteristic (ROC) curve analysis (±) to empirically determine the reference values (cutoff thresholds) that achieve an optimal balance between false-positive and true-positive rates. Importantly, we identified optimal reference values for each combination of sample size and test length in the simulation conditions. The cutoff threshold approach outperformed the PP-PPMC approach with greater gains in true-positive rates than losses from the inflated false-positive rates. In Study 2, we extended the cutoff threshold approach to conditions with larger sample sizes and longer test lengths. Moreover, we evaluated the performance of the optimized cutoff thresholds under varying levels of data missingness. Finally, we employed response surface analysis (±) to develop a prediction model that generalizes the way the reference values vary with sample size and test length. Overall, this study demonstrates the application of the PP-PPMC for item fit diagnostics and implements a practical frequentist approach to empirically derive reference values. Using our prediction model, practitioners can compute the reference values of RMSD that are tailored to their dataset's sample size and test length.