Estimating the Multidimensional Generalized Graded Unfolding Model with Covariates Using a Bayesian Approach

Abstract

Noncognitive constructs are commonly assessed in educational and organizational research. They are often measured by summing scores across items, which implicitly assumes a dominance item response process. However, research has shown that the unfolding response process may better characterize how people respond to noncognitive items. The Generalized Graded Unfolding Model (GGUM) representing the unfolding response process has therefore become increasingly popular. However, the current implementation of the GGUM is limited to unidimensional cases, while most noncognitive constructs are multidimensional. Fitting a unidimensional GGUM separately for each dimension and ignoring the multidimensional nature of noncognitive data may result in suboptimal parameter estimation. Recently, an R package bmggum was developed that enables the estimation of the Multidimensional Generalized Graded Unfolding Model (MGGUM) with covariates using a Bayesian algorithm. However, no simulation evidence is available to support the accuracy of the Bayesian algorithm implemented in bmggum. In this research, two simulation studies were conducted to examine the performance of bmggum. Results showed that bmggum can estimate MGGUM parameters accurately, and that multidimensional estimation and incorporating relevant covariates into the estimation process improved estimation accuracy. The effectiveness of two Bayesian model selection indices, WAIC and LOO, were also investigated and found to be satisfactory for model selection. Empirical data were used to demonstrate the use of bmggum and its performance was compared with three other GGUM software programs: GGUM2004, GGUM, and mirt.

Keywords

• multidimensional generalized graded unfolding model (MGGUM)
• item response theory (IRT)
• Bayesian estimation
• covariates