Period Notes No. of Units FY 1999 FY 2000 FY 2001 FY 2002 FY 2003 FY 2004 FY 2005 FY 2006 7/1/06-12/31/06 FY 2007 FY 2008 FY 2009 FY 2010 FY 2011 FY 2012 FY 2013 FY 2014 Total Units Sold est. est. est. est. est. est. Actual Actual Actual Actual Actual Actual Actual Actual Actual Actual Actual 1,768 3,797 3,755 5,592 3,310 3,218 3,803 3,888 2,144 3,077 3,358 2,590 3,043 2,132 1,649 1,732 855 49,710

The standards for educational and psychological testing.

Bifactor latent structures were introduced over 70 years ago, but only recently has bifactor modeling been rediscovered as an effective approach to modeling construct-relevant multidimensionality in a set of ordered categorical item responses. I begin by describing the Schmid-Leiman bifactor procedure (Schmid & Leiman, 1957), and highlight its relations with correlated-factors and second-order exploratory factor models. After describing limitations of the Schmid-Leiman, two newer methods of exploratory bifactor modeling are considered, namely, analytic bifactor (Jennrich & Bentler, 2011) and target bifactor rotations (Reise, Moore, & Maydeu-Olivares, 2011). In section two, I discuss limited and full-information estimation approaches to confirmatory bifactor models that have emerged from the item response theory and factor analysis traditions, respectively. Comparison of the confirmatory bifactor model to alternative nested confirmatory models and establishing parameter invariance for the general factor also are discussed. In the final section, important applications of bifactor models are reviewed. These applications demonstrate that bifactor modeling potentially provides a solid foundation for conceptualizing psychological constructs, constructing measures, and evaluating a measure's psychometric properties. However, some applications of the bifactor model may be limited due to its restrictive assumptions.

/pdf/the-rediscovery-of-bifactor-measurement-models-1bluokfjre.pdf

The Rediscovery of Bifactor Measurement Models

Bifactor measurement models are increasingly being applied to personality and psychopathology measures (Reise, 2012). In this work, authors generally have emphasized model fit, and their typical conclusion is that a bifactor model provides a superior fit relative to alternative subordinate models. Often unexplored, however, are important statistical indices that can substantially improve the psychometric analysis of a measure. We provide a review of the particularly valuable statistical indices one can derive from bifactor models. They include omega reliability coefficients, factor determinacy, construct reliability, explained common variance, and percentage of uncontaminated correlations. We describe how these indices can be calculated and used to inform: (a) the quality of unit-weighted total and subscale score composites, as well as factor score estimates, and (b) the specification and quality of a measurement model in structural equation modeling. (PsycINFO Database Record

https://psycnet.apa.org/journals/met/21/2/137.pdf

Evaluating bifactor models: Calculating and interpreting statistical indices.

In this study, the authors consider several indices to indicate whether multidimensional data are “unidimensional enough” to fit with a unidimensional measurement model, especially when the goal is to avoid excessive bias in structural parameter estimates. They examine two factor strength indices (the explained common variance and omega hierarchical) and several model fit indices (root mean square error of approximation, comparative fit index, and standardized root mean square residual). These statistics are compared in population correlation matrices determined by known bifactor structures that vary on the (a) relative strength of general and group factor loadings, (b) number of group factors, and (c) number of items or indicators. When fit with a unidimensional measurement model, the degree of structural coefficient bias depends strongly and inversely on explained common variance, but its effects are moderated by the percentage of correlations uncontaminated by multidimensionality, a statistic that rise...

/pdf/multidimensionality-and-structural-coefficient-bias-in-32qlat7ta8.pdf

Multidimensionality and Structural Coefficient Bias in Structural Equation Modeling: A Bifactor Perspective

This study evaluates a model for considering domain-general and domain-specific associations between teacher-child interactions and children's development, using a bifactor analytic strategy. Among a sample of 325 early childhood classrooms there was evidence for both general elements of teacher-child interaction (responsive teaching) and domain-specific elements related to positive management and routines and cognitive facilitation. Among a diverse population of 4-year-old children (n = 1,407) responsive teaching was modestly associated with development across social and cognitive domains, whereas positive management and routines was modestly associated with increases in inhibitory control and cognitive facilitation was associated with gains in early language and literacy skills. The conceptual and methodological contributions and challenges of this approach are discussed.

Evidence for General and Domain‐Specific Elements of Teacher–Child Interactions: Associations With Preschool Children's Development

This article recommends an alternative method for testing multifaceted constructs. Researchers often have to choose between two problematic approaches for analyzing multifaceted constructs: the total score approach and the individual score approach. Both approaches can result in conceptual ambiguity. The proposed bifactor model assesses simultaneously the general construct shared by the facets and the specific facets, over and above the general construct. We illustrate the bifactor model by examining the construct of Extraversion as measured by the Revised NEO Personality Inventory (NEO-PI-R; Costa & McCrae, 1992), with two college samples (N = 383 and 378). The analysis reveals that the facets of the NEO-PI-R Extraversion correlate with criteria in opposite directions after partialling out the general construct. The direction of gender differences also varies by facets. Bifactor models combine the advantages but avoid the drawbacks of the 2 existing methods and can lead to greater conceptual clarity.

Zugui Zhang

Papers

Modeling general and specific variance in multifaceted constructs: a comparison of the bifactor model to other approaches.