Generalized graded unfolding model with structural equation for subject parameters

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

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.

The Explanatory Generalized Graded Unfolding Model: Incorporating Collateral Information to Improve the Latent Trait Estimation Accuracy

Collateral information has been used to address subpopulation heterogeneity and increase estimation accuracy in some large-scale cognitive assessments. The methodology that takes collateral information into account has not been developed and explored in published research with models designed specifically for noncognitive measurement. Because the accurate noncognitive measurement is becoming increasingly important, we sought to examine the benefits of using collateral information in latent trait estimation with an item response theory model that has proven valuable for noncognitive testing, namely, the generalized graded unfolding model (GGUM). Our presentation introduces an extension of the GGUM that incorporates collateral information, henceforth called Explanatory GGUM. We then present a simulation study that examined Explanatory GGUM latent trait estimation as a function of sample size, test length, number of background covariates, and correlation between the covariates and the latent trait. Results indicated the Explanatory GGUM approach provides scoring accuracy and precision superior to traditional expected a posteriori (EAP) and full Bayesian (FB) methods. Implications and recommendations are discussed.

Fitting item response unfolding models to Likert-scale data using mirt in R

While a large family of unfolding models for Likert-scale response data have been developed for decades, very few applications of these models have been witnessed in practice. There may be several reasons why these have not appeared more widely in published research, however one obvious limitation appears to be the absence of suitable software for model estimation. In this article, the authors demonstrate how the mirt package can be adopted to estimate parameters from various unidimensional and multidimensional unfolding models. To concretely demonstrate the concepts and recommendations, a tutorial and examples of R syntax are provided for practical guidelines. Finally, the performance of mirt is evaluated via parameter-recovery simulation studies to demonstrate its potential effectiveness. The authors argue that, armed with the mirt package, applying unfolding models to Likert-scale data is now not only possible but can be estimated to real-datasets with little difficulty.

Using SAS PROC MCMC for Item Response Theory Models

Interest in using Bayesian methods for estimating item response theory models has grown at a remarkable rate in recent years. This attentiveness to Bayesian estimation has also inspired a growth in available software such as WinBUGS, R packages, BMIRT, MPLUS, and SAS PROC MCMC. This article intends to provide an accessible overview of Bayesian methods in the context of item response theory to serve as a useful guide for practitioners in estimating and interpreting item response theory (IRT) models. Included is a description of the estimation procedure used by SAS PROC MCMC. Syntax is provided for estimation of both dichotomous and polytomous IRT models, as well as a discussion on how to extend the syntax to accommodate more complex IRT models.

[Unfolding item response model using best-worst scaling]

In attitude measurement and sensory tests, the unfolding model is typically used. In this model, response probability is formulated by the distance between the person and the stimulus. In this study, we proposed an unfolding item response model using best-worst scaling (BWU model), in which a person chooses the best and worst stimulus among repeatedly presented subsets of stimuli. We also formulated an unfolding model using best scaling (BU model), and compared the accuracy of estimates between the BU and BWU models. A simulation experiment showed that the BWU modell performed much better than the BU model in terms of bias and root mean square errors of estimates. With reference to Usami (2011), the proposed models were apllied to actual data to measure attitudes toward tardiness. Results indicated high similarity between stimuli estimates generated with the proposed models and those of Usami (2011).