A general Bayesian multilevel multidimensional IRT model for locally dependent data

The Accuracy of Bayesian Model Fit Indices in Selecting Among Multidimensional Item Response Theory Models

Item response theory (IRT) models are often compared with respect to predictive performance to determine the dimensionality of rating scale data. However, such model comparisons could be biased toward nested-dimensionality IRT models (e.g., the bifactor model) when comparing those models with non-nested-dimensionality IRT models (e.g., a unidimensional or a between-item-dimensionality model). The reason is that, compared with non-nested-dimensionality models, nested-dimensionality models could have a greater propensity to fit data that do not represent a specific dimensional structure. However, it is unclear as to what degree model comparison results are biased toward nested-dimensionality IRT models when the data represent specific dimensional structures and when Bayesian estimation and model comparison indices are used. We conducted a simulation study to add clarity to this issue. We examined the accuracy of four Bayesian predictive performance indices at differentiating among non-nested- and nested-dimensionality IRT models. The deviance information criterion (DIC), a commonly used index to compare Bayesian models, was extremely biased toward nested-dimensionality IRT models, favoring them even when non-nested-dimensionality models were the correct models. The Pareto-smoothed importance sampling approximation of the leave-one-out cross-validation was the least biased, with the Watanabe information criterion and the log-predicted marginal likelihood closely following. The findings demonstrate that nested-dimensionality IRT models are not automatically favored when the data represent specific dimensional structures as long as an appropriate predictive performance index is used.

Bayesian Model Assessment for Jointly Modeling Multidimensional Response Data with Application to Computerized Testing

Computerized assessment provides rich multidimensional data including trial-by-trial accuracy and response time (RT) measures. A key question in modeling this type of data is how to incorporate RT data, for example, in aid of ability estimation in item response theory (IRT) models. To address this, we propose a joint model consisting of a two-parameter IRT model for the dichotomous item response data, a log-normal model for the continuous RT data, and a normal model for corresponding paper-and-pencil scores. Then, we reformulate and reparameterize the model to capture the relationship between the model parameters, to facilitate the prior specification, and to make the Bayesian computation more efficient. Further, we propose several new model assessment criteria based on the decomposition of deviance information criterion (DIC) the logarithm of the pseudo-marginal likelihood (LPML). The proposed criteria can quantify the improvement in the fit of one part of the multidimensional data given the other parts. Finally, we have conducted several simulation studies to examine the empirical performance of the proposed model assessment criteria and have illustrated the application of these criteria using a real dataset from a computerized educational assessment program.

Psychometric properties of the cultural mix coping inventory for stressful situations using physical education teachers: a multidimensional item response theory analysis

The incidence of the COVID-19 pandemic heightened the levels of stress of not only students but for teachers, particularly physical education (PE) teachers. The reference to PE teachers is due to their role in engaging students in practical in-person lessons after the resumption of school. Previous literature has revealed that PE teachers exhibit significantly increased levels of anxiety, fear, tension and uncertainty that they could contract the virus during these lessons. Given this scenario, there is a growing need for identifying a suitable coping scale which can accurately measure coping strategies employed these teachers. This research assessed the psychometric properties of the 16-item coping inventory using a multidimensional item response theory approach. The study surveyed 484 PE teachers through the convenience sampling technique, after which the cultural mix coping instrument was administered to them. The findings of this study confirmed the 4-factor structure of the coping measure which is consistent with the original measure. Results further revealed that a modified 14-item compared to the original 16-item coping inventory was optimal in measuring coping strategies among PE teachers. The study concluded that the 14-item cultural mix coping inventory was appropriate, applicable and reproducible to the PE teachers' population.

A General Bayesian Multidimensional Item Response Theory Model for Small and Large Samples

Although item response theory (IRT) models such as the bifactor, two-tier, and between-item-dimensionality IRT models have been devised to confirm complex dimensional structures in educational and psychological data, they can be challenging to use in practice. The reason is that these models are multidimensional IRT (MIRT) models and thus are highly parameterized, making them only suitable for data provided by large samples. Unfortunately, many educational and psychological studies are conducted on a small scale, leaving the researchers without the necessary MIRT models to confirm the hypothesized structures in their data. To address the lack of modeling options for these researchers, we present a general Bayesian MIRT model based on adaptive informative priors. Simulations demonstrated that our MIRT model could be used to confirm a two-tier structure (with two general and six specific dimensions), a bifactor structure (with one general and six specific dimensions), and a between-item six-dimensional structure in rating scale data representing sample sizes as small as 100. Although our goal was to provide a general MIRT model suitable for smaller samples, the simulations further revealed that our model was applicable to larger samples. We also analyzed real data from 121 individuals to illustrate that the findings of our simulations are relevant to real situations.

State of the psychometric methods: patient-reported outcome measure development and refinement using item response theory

BACKGROUND

This paper is part of a series comparing different psychometric approaches to evaluate patient-reported outcome (PRO) measures using the same items and dataset. We provide an overview and example application to demonstrate 1) using item response theory (IRT) to identify poor and well performing items; 2) testing if items perform differently based on demographic characteristics (differential item functioning, DIF); and 3) balancing IRT and content validity considerations to select items for short forms.

METHODS

Model fit, local dependence, and DIF were examined for 51 items initially considered for the Patient-Reported Outcomes Measurement Information System® (PROMIS®) Depression item bank. Samejima's graded response model was used to examine how well each item measured severity levels of depression and how well it distinguished between individuals with high and low levels of depression. Two short forms were constructed based on psychometric properties and consensus discussions with instrument developers, including psychometricians and content experts. Calibrations presented here are for didactic purposes and are not intended to replace official PROMIS parameters or to be used for research.

RESULTS

Of the 51 depression items, 14 exhibited local dependence, 3 exhibited DIF for gender, and 9 exhibited misfit, and these items were removed from consideration for short forms. Short form 1 prioritized content, and thus items were chosen to meet DSM-V criteria rather than being discarded for lower discrimination parameters. Short form 2 prioritized well performing items, and thus fewer DSM-V criteria were satisfied. Short forms 1-2 performed similarly for model fit statistics, but short form 2 provided greater item precision.

CONCLUSIONS

IRT is a family of flexible models providing item- and scale-level information, making it a powerful tool for scale construction and refinement. Strengths of IRT models include placing respondents and items on the same metric, testing DIF across demographic or clinical subgroups, and facilitating creation of targeted short forms. Limitations include large sample sizes to obtain stable item parameters, and necessary familiarity with measurement methods to interpret results. Combining psychometric data with stakeholder input (including people with lived experiences of the health condition and clinicians) is highly recommended for scale development and evaluation.

The Bayesian Multilevel Trifactor Item Response Theory Model

Advancements in item response theory (IRT) have led to models for dual dependence, which control for cluster and method effects during a psychometric analysis. Currently, however, this class of models does not include one that controls for when the method effects stem from two method sources in which one source functions differently across the aspects of another source (i.e., a nested method-source interaction). For this study, then, a Bayesian IRT model is proposed, one that accounts for such interaction among method sources while controlling for the clustering of individuals within the sample. The proposed model accomplishes these tasks by specifying a multilevel trifactor structure for the latent trait space. Details of simulations are also reported. These simulations demonstrate that this model can identify when item response data represent a multilevel trifactor structure, and it does so in data from samples as small as 250 cases nested within 50 clusters. Additionally, the simulations show that misleading estimates for the item discriminations could arise when the trifactor structure reflected in the data is not correctly accounted for. The utility of the model is also illustrated through the analysis of empirical data.