Logistic Approximations of Marginal Trace Lines for Bifactor Item Response Theory Models

Stucky, Brian Dale

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March 22, 2019

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Stucky, Brian Dale
- Affiliation: College of Arts and Sciences, Department of Psychology and Neuroscience

Abstract

Bifactor item response theory models are useful when item responses are best represented by a general, or primary, dimension and one or more secondary dimensions that account for relationships among subsets of items. Understanding slope parameter estimates in multidimensional item response theory models is often challenging because interpretation of a given slope parameter must be made conditional on the item's other parameters. The present work provides a method of computing marginal trace lines for an item loading on more than one dimension. The marginal trace line provides the relationship between the item response and the primary dimension, after accounting for all other dimensions. Findings suggest that a logistic function, common in many applications of item response theory, closely approximates the marginal trace line in a variety of model related conditions. Additionally, a method of IRT-based scoring is proposed that uses the logistic approximation marginal trace lines in a unidimensional fashion to compute scaled scores and standard deviation estimates for the primary dimension. The utility of the logistic approximation for marginal trace lines is considered across a wide range of varying bifactor parameter estimates, and under each condition the marginal is closely approximated by a logistic function. In addition, it is shown that use of the logistic approximations to conduct item response theory-based scoring should be restricted to selecting a single item from each secondary dimension in order to control for local dependence. Under this restriction, scaled scores and posterior standard deviations are nearly equivalent to other MIRT-based scoring procedures. Finally, a real-data application is provided which illustrates the utility of logistic approximations of marginal trace lines in item selection and scale development scenarios.

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