Evaluating bifactor models: Calculating and interpreting statistical indices.

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

[1]  Richard Scheines,et al.  When Are Multidimensional Data Unidimensional Enough for Structural Equation Modeling? An Evaluation of the DETECT Multidimensionality Index , 2015 .

[2]  M. Edelen,et al.  Using Hierarchical IRT Models to Create Unidimensional Measures From Multidimensional Data , 2014 .

[3]  Thomas J. Dunn,et al.  From alpha to omega: a practical solution to the pervasive problem of internal consistency estimation. , 2014, British journal of psychology.

[4]  Gilles E. Gignac,et al.  Bifactor Modeling and the Estimation of Model-Based Reliability in the WAIS-IV , 2013, Multivariate behavioral research.

[5]  Todd D Little,et al.  Why the items versus parcels controversy needn't be one. , 2013, Psychological methods.

[6]  S. Reise,et al.  Scoring and Modeling Psychological Measures in the Presence of Multidimensionality , 2013, Journal of personality assessment.

[7]  Richard Scheines,et al.  Multidimensionality and Structural Coefficient Bias in Structural Equation Modeling , 2013 .

[8]  T. Raykov,et al.  Essential Unidimensionality Examination for Multicomponent Scales , 2013 .

[9]  D. Thissen,et al.  Using Logistic Approximations of Marginal Trace Lines to Develop Short Assessments , 2013 .

[10]  S. Reise.  The Rediscovery of Bifactor Measurement Models , 2012 .

[11]  M. Donnellan,et al.  An Item Response Theory Analysis of the Narcissistic Personality Inventory , 2012, Journal of personality assessment.

[12]  J. Laurenceau,et al.  Modeling general and specific variance in multifaceted constructs: a comparison of the bifactor model to other approaches. , 2012, Journal of personality.

[13]  A. Beauducel.  Indeterminacy of Factor Score Estimates In Slightly Misspecified Confirmatory Factor Models , 2011 .

[14]  Sonya K. Sterba,et al.  Implications of Parcel-Allocation Variability for Comparing Fit of Item-Solutions and Parcel-Solutions , 2011 .

[15]  S. Haberman,et al.  An NCME Instructional Module on Subscores , 2011 .

[16]  S. Green,et al.  Coefficient Alpha: A Reliability Coefficient for the 21st Century? , 2011 .

[17]  Jan-Willem Romeijn,et al.  Mind the Gap: A Psychometric Approach to the Reduction Problem , 2011 .

[18]  S. Reise,et al.  Bifactor Models and Rotations: Exploring the Extent to Which Multidimensional Data Yield Univocal Scale Scores , 2010, Journal of personality assessment.

[19]  Sonya K. Sterba,et al.  Variability in Parameter Estimates and Model Fit Across Repeated Allocations of Items to Parcels , 2010, Multivariate behavioral research.

[20]  A. Osman,et al.  Further Evidence of the Reliability and Validity of the Multidimensional Anxiety , 2009 .

[21]  Peter M. Bentler,et al.  Alpha, Dimension-Free, and Model-Based Internal Consistency Reliability , 2009, Psychometrika.

[22]  W. Revelle,et al.  Coefficients Alpha, Beta, Omega, and the glb: Comments on Sijtsma , 2009 .

[23]  Richard N. Jones,et al.  Measurement Differences in Depression: Chronic Health-Related and Sociodemographic Effects in Older Americans , 2008, Psychosomatic medicine.

[24]  David Watson,et al.  Parsing the general and specific components of depression and anxiety with bifactor modeling , 2008, Depression and anxiety.

[25]  J. Immekus,et al.  Dimensionality Assessment Using the Full-Information Item Bifactor Analysis for Graded Response Data , 2008 .

[26]  Gautam Puhan,et al.  Subscores Based on Classical Test Theory: To Report or Not to Report , 2007 .

[27]  Gilles E. Gignac,et al.  A Confirmatory Factor Analytic Investigation of the TAS–20: Corroboration of a Five-Factor Model and Suggestions for Improvement , 2007, Journal of personality assessment.

[28]  Steven P. Reise,et al.  The role of the bifactor model in resolving dimensionality issues in health outcomes measures , 2007, Quality of Life Research.

[29]  J. Graham.  Congeneric and (Essentially) Tau-Equivalent Estimates of Score Reliability , 2006 .

[30]  S. West,et al.  A Comparison of Bifactor and Second-Order Models of Quality of Life , 2006, Multivariate behavioral research.

[31]  William Revelle,et al.  Estimating Generalizability to a Latent Variable Common to All of a Scale's Indicators: A Comparison of Estimators for ωh , 2006 .

[32]  T. Ivarsson.  Normative data for the Multidimensional Anxiety Scale for Children (MASC) in Swedish adolescents , 2006, Nordic journal of psychiatry.

[33]  S. Reise,et al.  Item Response Theory and the Measurement of Clinical Change , 2005, Journal of personality assessment.

[34]  William Revelle,et al.  Cronbach’s α, Revelle’s β, and Mcdonald’s ωH: their relations with each other and two alternative conceptualizations of reliability , 2005 .

[35]  Robert C MacCallum,et al.  Using Parcels to Convert Path Analysis Models Into Latent Variable Models , 2005, Multivariate behavioral research.

[36]  Jos M. F. ten Berge,et al.  The greatest lower bound to the reliability of a test and the hypothesis of unidimensionality , 2004 .

[37]  D. Olason,et al.  Psychometric properties of the Multidimensional Anxiety Scale for Children (MASC) among Icelandic schoolchildren. , 2004, Scandinavian journal of psychology.

[38]  T. Little,et al.  To Parcel or Not to Parcel: Exploring the Question, Weighing the Merits , 2002 .

[39]  D. Bandalos.  The Effects of Item Parceling on Goodness-of-Fit and Parameter Estimate Bias in Structural Equation Modeling , 2002 .

[40]  J. Grice.  Computing and evaluating factor scores , 2001 .

[41]  G. Hancock.  Effect size, power, and sample size determination for structured means modeling and mimic approaches to between-groups hypothesis testing of means on a single latent construct , 2001 .

[42]  William Stout,et al.  The theoretical detect index of dimensionality and its application to approximate simple structure , 1999 .

[43]  T Raykov,et al.  Scale Reliability, Cronbach's Coefficient Alpha, and Violations of Essential Tau-Equivalence with Fixed Congeneric Components. , 1997, Multivariate behavioral research.

[44]  T. Brown,et al.  Hierarchical structure and general factor saturation of the Anxiety Sensitivity Index : Evidence and implications , 1997 .

[45]  T. Raykov.  Estimation of Composite Reliability for Congeneric Measures , 1997 .

[46]  N. Schmitt.  Uses and abuses of coefficient alpha. , 1996 .

[47]  J. M. Cortina,et al.  What Is Coefficient Alpha? An Examination of Theory and Applications , 1993 .

[48]  Bengt Muthén,et al.  On structural equation modeling with data that are not missing completely at random , 1987 .

[49]  Stanley A. Mulaik,et al.  Comments on “the measurement of factorial indeterminacy” , 1976 .

[50]  K. G. Jöreskog,et al.  Statistical analysis of sets of congeneric tests , 1971 .

[51]  Louis Guttman,et al.  THE DETERMINACY OF FACTOR SCORE MATRICES WITH IMPLICATIONS FOR FIVE OTHER BASIC PROBLEMS OF COMMON‐FACTOR THEORY1 , 1955 .

[52]  L. Cronbach.  Coefficient alpha and the internal structure of tests , 1951 .

[53]  Harry H. Harman,et al.  Comparison of two factorial analyses , 1938 .

[54]  K. Holzinger,et al.  The Bi-factor method , 1937 .

[55]  Gary L. Canivez,et al.  Bifactor modeling in construct validation of multifactored tests: Implications for understanding multidimensional constructs and test interpretation. , 2016 .

[56]  Janet F. Carlson,et al.  APA handbook of testing and assessment in psychology, Vol. 1: Test theory and testing and assessment in industrial and organizational psychology. , 2013 .

[57]  S. Reise,et al.  Applying unidimensional item response theory models to psychological data. , 2013 .

[58]  O. John,et al.  The importance of being valid: Reliability and the process of construct validation. , 2007 .

[59]  S. Finney,et al.  Item parceling issues in structural equation modeling , 2001 .

[60]  Michael Miller.  Coefficient alpha: A basic introduction from the perspectives of classical test theory and structural equation modeling , 1995 .