Bayesian Estimation of a Ramsay-Curve Graded Response Model Using Metropolis–Hastings Sampling Method

In most psychological tests using Likert-type scales, graded response model (GRM) is frequently used to describe the latent traits of subjects. However, many psychological constructs, such as dysthymia disorder, are typically non-normally distributed in a general population. Thus, GRM incorporated with Ramsay curves – graded response model (RC-GRM) allowing for flexible latent trait distributions is proposed in this article. In addition, an estimation procedure using metropolis–hastings (MH) sampling method for the RC-GRM model is given to estimate the item parameters in GRM and the shape parameter in the RC simultaneously. The algorithm is easy to apply and not restricted to the close form of parameter estimate. Four simulation studies reveal that the recovery results of this MH algorithm are accurate and the proposed algorithm is not sensitive to the chosen prior density distributions and specifications of knots and degree of B-spline functions. Moreover, RC-GRM has an obvious advantage to the traditional GRM when the true latent trait is non-normal according to estimation accuracy. The application to a real data set from the Programme for International Student Assessment (PISA) 2015 tests demonstrates that the proposed model and algorithm are effective in some real circumstances.