Bayesian estimation of latent traits parameters in a polytomous rasch rating scale model for subjective well-being responses survey

Generally, large sample sizes and normality assumption play vital roles in estimating model parameters. Unfortunately, small sample sizes and non-normally distributed data are common issues encountered in the real-world quantitative survey research, including studies on the subjective well-being. The frequentist approach, like the classical maximum likelihood (CML) estimation technique, has often been found impractical under these two circumstances, as demonstrated by previous scholars. While several studies have been carried out to address the issues of poor estimation accuracy resulting from CML under small sample sizes and non-normally distributed datasets, to date, very few studies have been conducted on the Rasch measurement model with polytomous responses survey datasets (i.e., Likert scale), and none have specifically attempted on the rating scale model. Therefore, the present study highlights the challenges related to accuracy in the estimation of the latent traits parameters in the polytomous Rasch rating scale model (pR-RSM). Specifically, this study proposes a more powerful technique known as the Bayesian estimation (BE) to address the negative impact of the small sample sizes with skewed data distributions on the estimation accuracy of latent traits in the pR-RSM obtained through the CML. The BE approach has been successfully tested in the dichotomous Rasch model, and the polytomous Rasch model (i.e., graded response model and the generalized partial credit model) in dealing with unfavourable datasets including small sample sizes and non-normally distributed data. Due to these convincing results, the present study proposed to extend the use of BE approach in the pR-RSM. The analyses in this study were performed using both simulated and actual survey datasets. The simulated survey data were generated according to the pR-RSM, incorporating a combination of shape of distributions (i.e., the standard normal distribution and the standard skew-normal distribution with various skewness values), along with different sample sizes and numbers of items. For the simulated survey data, the performance of the BE approach was evaluated and compared with the CML according to the accuracy and bias measures. The root mean square error (RMSE) and mean absolute error (MAE) were used to examine the accuracy of the parameter estimates. Meanwhile, bias in estimation was assessed through the mean difference of the estimates and true values of the latent traits parameters. To comprehensively evaluate the estimation performance for the simulated survey datasets, Markov Chain Monte Carlo (MCMC) simulation was carried out using 1000 iterations. Furthermore, the performance of BE and CML on the actual survey datasets was assessed and compared using two goodness of fit measures, namely Akaike information criterion (AIC) and Bayesian information criterion (BIC). Overall, the results of this study successfully revealed that small sample sizes and skewed data distributions were negatively impact the performance of the CML in estimating the latent traits parameters of the pR-RSM. The findings show that BE consistently outperformed CML, producing more accurate and less biased estimates, particularly in cases of small sample sizes with skewed data distributions. Consequently, this study suggests that BE emerges as the preferable and most powerful technique in treating the issues highlighted. Ultimately, this study provides a useful guideline for future researchers in selecting the most suitable parameter estimation technique in the context of the pR-RSM, based on the sample sizes and the skewness values.