Accuracy of the Rasch rating scale person estimates using maximum likelihood approach with skewed distributions: A Markov chain Monte Carlo simulation analysis

Abstract

The performance of the maximum likelihood estimator when estimating the person parameter in the Rasch rating scale model (RRSM) is addressed in this article. The main focus of this study is to examine the accuracy of person parameter estimates in the model under the condition of skewed distributions. The Markov Chain Monte Carlo (MCMC) simulation analysis with 1000 iterations were carried out based on different sample sizes, the number of items, and skewness values. The accuracy of the maximum likelihood estimator in estimating the person parameter was compared using the root mean square error (RMSE) and mean absolute error (MAE). The results from the simulation analysis revealed that, in comparison to the normal distribution, the performance of the maximum likelihood estimator with positively and negatively skewed datasets tends to be poor with larger RMSE and MAE. Even though the findings of this study successfully showed that both positively and negatively skewed datasets resulted in less accurate estimation of the person parameter in the RRSM when the maximum likelihood estimation (MLE) approach is used, but there is still a great need for further studies to this preliminary investigation.