Bias in person parameter estimates: the maximum likelihood approach to Rasch rating scale model against skewed distributions / Nurul Hafizah Azizan, Zamalia Mahmud and Adzhar Rambli

The conventional approach of parameter estimation technique, such as maximum likelihood estimation (MLE), can be negatively affected by the skewed distributions of the data. Consequently, estimates of the parameters in the model produced by the MLE in this condition are more likely to be biased. This article explores the biases in the Rasch rating scale person estimates while using the MLE approach against skewed distributions. The Markov Chain Monte Carlo (MCMC) simulation analysis was carried out with 1000 iterations based on 126 simulation conditions. These simulation conditions were formed using three criteria, which are the number of sample sizes, the number of items, and the type of distributions (i.e., standard normal distribution and skew-normal distribution). The bias in estimation was calculated based on the mean squared difference between the estimated values and actual values of the person parameter. Overall, the findings obtained from the simulation analysis proved that, in skewed distributions, the MLE approach is prone to produce biased person estimates, and the results are getting worse in small sample sizes. Thus, the MLE approach is strongly not recommended when estimating person parameters in Rasch rating scale model (RRSM) under skewed distributions, especially if the sample size is too small.