Rasch Rating Scale Item Estimates using Maximum Likelihood Approach: Effects of Sample Size on the Accuracy and Bias of the Estimates

Abstract

The main purpose of this study is to evaluate and compare the accuracy and bias of the item estimates in the Rasch rating scale model (RRSM). Particularly, the maximum likelihood estimation (MLE) approach was used to estimate the item parameters in this study. Markov Chain Monte Carlo (MCMC) simulation technique was carried out using the data generated according to RRSM. The data was simulated under the condition that the normality assumption was satisfied. Different sample sizes and the number of items were manipulated for the comparison purposes. The results showed that as the sample size got smaller, the MLE estimates of the item parameter became less accurate, with larger root mean square error (RMSE) and mean absolute error (MAE). Besides that, smaller sample sizes also produced more biased estimates of the item parameters compared to larger sample sizes because the bias measure (i.e., mean difference of estimate and the true value of the item parameter) was higher in the smaller sample sizes compared to the larger ones.

Keywords: Rasch rating scale model (RRSM), Maximum likelihood estimation (MLE), Root mean square error (RMSE), Mean absolute error (MAE) and Bias.