On the Dependability of a Popular Procedure for Studying Measurement Invariance: A Cause for Concern?

A theoretically and empirically important multiple-population setting is discussed where a highly popular procedure for studying measurement invariance (MI) can fail. A numerical counter-example is presented where this widely used, traditional method misses a sizeable violation of MI. It is argued that the reason for the failure is in part inherent in the parameterization approach underlying that popular approach to examining MI. Implications for empirical behavioral, social, educational, business, and marketing research are discussed in light of these findings.

[1]  Ariel Linden.  Review of Tenko Raykov and George Marcoulides's a Course in Item Response Theory and Modeling with Stata , 2018, The Stata Journal: Promoting communications on statistics and Stata.

[2]  G. A. Marcoulides,et al.  Examining Population Heterogeneity in Finite Mixture Settings Using Latent Variable Modeling , 2016 .

[3]  R. Millsap,et al.  Factorial Invariance in Multiple Populations , 2013 .

[4]  T. Raykov,et al.  Measurement Invariance for Latent Constructs in Multiple Populations , 2012 .

[5]  Emily C. Johnson,et al.  The Role of Referent Indicators in Tests of Measurement Invariance , 2009 .

[6]  B. French,et al.  Multigroup Confirmatory Factor Analysis: Locating the Invariant Referent Sets , 2008 .

[7]  G. A. Marcoulides,et al.  An Introduction to Applied Multivariate Analysis , 2008 .

[8]  Roger E. Millsap,et al.  Detecting Violations of Factorial Invariance Using Data-Based Specification Searches: A Monte Carlo Study , 2007 .

[9]  W. Meredith,et al.  Factorial Invariance: Historical Perspectives and New Problems , 2007 .

[10]  W. Holmes Finch,et al.  Confirmatory Factor Analytic Procedures for the Determination of Measurement Invariance , 2006 .

[11]  T Raykov,et al.  A first course in structural equation modeling, 2nd ed. , 2006 .

[12]  R. Millsap.  Four Unresolved Problems in Studies of Factorial Invariance. , 2005 .

[13]  B. Muthén,et al.  How to Use a Monte Carlo Study to Decide on Sample Size and Determine Power , 2002 .

[14]  Gordon W. Cheung,et al.  Evaluating Goodness-of-Fit Indexes for Testing Measurement Invariance , 2002 .

[15]  B. Muthén.  BEYOND SEM: GENERAL LATENT VARIABLE MODELING , 2002 .

[16]  G. A. Marcoulides,et al.  A First Course in Structural Equation Modeling , 2000 .

[17]  R. Vandenberg,et al.  A Review and Synthesis of the Measurement Invariance Literature: Suggestions, Practices, and Recommendations for Organizational Research , 2000 .

[18]  Gordon W. Cheung,et al.  Testing Factorial Invariance across Groups: A Reconceptualization and Proposed New Method , 1999 .

[19]  P. Bentler,et al.  Cutoff criteria for fit indexes in covariance structure analysis : Conventional criteria versus new alternatives , 1999 .

[20]  Gordon W. Cheung,et al.  Testing Measurement Models for Factorial Invariance: A Systematic Approach , 1998 .

[21]  R. MacCallum,et al.  Power analysis and determination of sample size for covariance structure modeling. , 1996 .

[22]  M. Browne,et al.  Alternative Ways of Assessing Model Fit , 1992 .