Generalized full-information item bifactor analysis.

Abstract

Full-information item bifactor analysis is an important statistical method in psychological and educational measurement. Current methods are limited to single group analysis and inflexible in the types of item response models supported. We propose a flexible multiple-group item bifactor analysis framework that supports a variety of multidimensional item response theory models for an arbitrary mixing of dichotomous, ordinal, and nominal items. The extended item bifactor model also enables the estimation of latent variable means and variances when data from more than one group are present. Generalized user-defined parameter restrictions are permitted within or across groups. We derive an efficient full-information maximum marginal likelihood estimator. Our estimation method achieves substantial computational savings by extending Gibbons and Hedeker's (1992) bifactor dimension reduction method so that the optimization of the marginal log-likelihood only requires two-dimensional integration regardless of the dimensionality of the latent variables. We use simulation studies to demonstrate the flexibility and accuracy of the proposed methods. We apply the model to study cross-country differences, including differential item functioning, using data from a large international education survey on mathematics literacy. Keywordshierarchical factor model; item response theory; multidimensional IRT; item factor analysis; differential item functioning Full-information item bifactor analysis (Gibbons & Hedeker, 1992;Gibbons et al., 2007) has been increasingly recognized as an important statistical method in psychological and educational measurement. Item bifactor analysis, as a special case of confirmatory multidimensional item response theory (IRT) modeling, provides information about the dimensionality of the measurement instrument, strategies for scaling individual differences, and new approaches to computerized adaptive testing. For instance, Reise, Morizot, and Hays (2007) applied item bifactor analysis to patient reported health outcomes data and concluded that the item bifactor model provides a valuable tool for exploring dimensionality. In psychopathology research, Simms, Grös, Watson, and O'Hara (2008) found that a bifactor structure is needed for describing mood and anxiety symptoms. In the area of psychiatric services research, Gibbons et al. (2008) applied the bifactor model to the construction of item banks and computerized adaptive tests and demonstrated dramatic reductions in patient and clinician burden. In educational measurement, DeMars (2006) applied the item bifactor model to data from testlet-based assessments and found the bifactor model a practical alternative to more specialized testlet response models (e.g. Wainer, Bradlow, & Wang, 2007).Address correspondence to: Li Cai, UCLA, Los Angeles, CA, USA 90095-1521. lcai@ucla.edu. Phone: 310.206.0583. Fax: 310.206.5830. NIH Public Access Author ManuscriptPsychol Methods. Author manuscript; available in PMC 2012 September 1. NIH-PA Author Manuscript...

Summed Score Likelihood–Based Indices for Testing Latent Variable Distribution Fit in Item Response Theory

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“…Our first analysis is designed to mirror the conceptual factors of the PAI-BOR as described in Crick et al (2005) using the methods of full-information bifactor analysis. Item bifactor analysis refers to a type of confirmatory multidimensional IRT model in which one general factor and one or more specific factors are specified (Cai, Yang, & Hansen, 2011). Table 1 presents the IRT slope parameters and standard errors for the full-information item bifactor model.…”

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