Rasch measurement model: a review of Bayesian estimation for estimating the person and item parameters

Abstract

Abstract This paper focuses on the methods used for estimating the parameters in Rasch Measurement Model (RMM). These include the MLE and Bayesian Estimation (BE) techniques. The accuracy and precision of the parameter estimates based on these two MLE and BE were discussed and compared. A questionnaire is a well-known measurement instrument used by most of the researchers. It is a powerful tool for collecting data in survey research. It should be noted that the quality of a measurement instrument used plays a key role in ensuring the quality of data obtained in the survey. Therefore, it has become essential for the researchers to carefully design their questionnaire so that the quality of the data obtained can be preserved. Then, it is also vital for the researchers to assess the quality of the data obtained before it can be successfully used for further analysis. Review of the literature shows that RMM is a psychometric approach widely used as an assessment tool of many measurement instruments developed in various fields of study. At present, the Maximum Likelihood Estimation (MLE) techniques were used to estimate the parameters in the RMM. In order to obtain more precise and accurate parameter estimates, a certain number of sample size and normality assumption are usually required. However, in a small sample, MLE could produce bias, imprecise and less accurate estimates with bigger standard error. A proper selection of the parameter estimation techniques to deal with small sample and non-normality of data is required to obtain more precise and accurate parameter estimates. From the review, it reveals that BE has successfully dealt with the issues of small sample and non-normality of the data. It produced a more accurate parameter estimate with smallest Mean Squared Error (MSE), particularly in a small sample compared to MLE.