Evaluating Equivalence Testing Methods for Measurement Invariance

References

• Anderson, S., & Hauck, W. W. (1983). A new procedure for testing equivalence in comparative bioavailability and other clinical trials. Statistics and Communications – Theory and Methods, 12(23), 2663–2692. doi: 10.1080/03610928308828634
   Web of Science ®Google Scholar
• Bentler, P. M. (1990). Comparative fit indices in structural models. Psychological Bulletin, 107(2), 238. doi: 10.1037/0033-2909.107.2.238
   PubMed Web of Science ®Google Scholar
• Bradley, J. V. (1978). Robustness? British Journal of Mathematical and Statistical Psychology, 31(2), 144–152. doi: 10.1111/j.2044-8317.1978.tb00581.x
   Web of Science ®Google Scholar
• Brotherton, R., French, C. C., & Pickering, A. D. (2013). Measuring belief in conspiracy theories: The Generic Conspiracist Beliefs Scale. Frontiers in Psychology, 4, 1–15. doi: 10.3389/fpsyg.2013.00279
   PubMed Web of Science ®Google Scholar
• Browne, M. W. (1984). Asymptotically distribution free methods in the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37, 127–141. doi: 10.1111/j.2044-8317.1984.tb00789.x
   Web of Science ®Google Scholar
• Browne, M. W., & Cudeck, R. (1992). Alternative ways of assessing model fit. Sociological Methods & Research, 21, 230–258. doi: 10.1177/0049124192021002005
   Web of Science ®Google Scholar
• Byrne, B. M. (2008). Testing for multigroup equivalence of a measuring instrument: A walkthrough the process. Psicothema, 20, 872–882.
   PubMed Web of Science ®Google Scholar
• Byrne, B. M., Shavelson, R. J., & Muthén, B. (1989). Testing for the equivalence of factor covariance and mean structures: The issue of partial measurement invariance. Psychological Bulletin, 105(3), 456–466. doi: 10.1037/0033-2909.105.3.456
   Web of Science ®Google Scholar
• Chen, F. F. (2007). Sensitivity of goodness of fit indices to lack of measurement invariance. Structural Equation Modeling, 14(3), 464–504. doi: 10.1080/10705510701301834
   Web of Science ®Google Scholar
• Cheung, G. W., & Rensvold, R. B. (2002). Evaluating goodness-of-fit indices for testing measurement invariance. Structural Equation Modeling, 9(2), 233–255. doi: 10.1207/S15328007SEM0902_5
   Web of Science ®Google Scholar
• Counsell, A., & Cribbie, R. A. (2015). Equivalence tests for comparing correlation and regression coefficients. British Journal of Mathematical and Statistical Psychology, 68(2), 292–309. doi: 10.1111/bmsp.12045
   PubMed Web of Science ®Google Scholar
• Cribbie, R. A., Gruman, J. A., & Arpin-Cribbie, C. A. (2004). Recommendations for applying tests of equivalence. Journal of Clinical Psychology, 60, 1–10. doi: 10.1037/a0033357
   PubMed Web of Science ®Google Scholar
• Cudeck, R., & Henly, S. J. (1991). Model selection in covariance structures analysis and the "problem" of sample size: A clarification. Psychological Bulletin, 109(3), 512–519. doi: 10.1037/0033-2909.109.3.512
   PubMed Web of Science ®Google Scholar
• Goertzen, J. R., & Cribbie, R. A. (2010). Detecting a lack of association: An equivalence testing approach. British Journal of Mathematical and Statistical Psychology, 63(3), 527–537. doi: 10.1348/000711009X475853
   PubMed Web of Science ®Google Scholar
• Horn, J. L., & McArdle, J. J. (1992). A practical and theoretical guide to measurement invariance in aging research. Experimental Aging Research, 18(3), 117–144. doi: 10.1080/03610739208253916
   PubMed Web of Science ®Google Scholar
• Hu, L.-T., & Bentler, P. M. (1999). Cutoff criteria in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1–55. doi: 10.1080/10705519909540118
   Web of Science ®Google Scholar
• Jackson, D. L., Gillaspy, J. A., Jr., & Purc-Stephenson, R. (2009). Reporting practices in confirmatory factor analysis: An overview and some recommendations. Psychological Methods, 14(1), 6–23. doi: 10.1037/a0014694
   PubMed Web of Science ®Google Scholar
• Jiang, G., Mai, Y., & Yuan, K. H. (2017). equaltestMI: Examine measurement invariance via equivalence testing and projection method. R package version 0.1.0. https://CRAN.R-project.org/package=equaltestMI
   Google Scholar
• Kang, Y., McNeish, D. M., & Hancock, G. R. (2016). The role of measurement quality on practical guidelines for assessing measurement and structural invariance. Educational and Psychological Measurement, 76(4), 533–561. doi: 10.1177/0013164415603764
   PubMed Web of Science ®Google Scholar
• Koh, A., & Cribbie, R. (2013). Robust tests of equivalence for k independent groups. British Journal of Mathematical and Statistical Psychology, 66, 426–434. doi: 10.1111/j.2044-317.2012.02056.x
   PubMed Web of Science ®Google Scholar
• MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996). Power analysis and determination of sample size for covariance structure modeling. Psychological Methods, 1(2), 130–149. doi: 10.1037//1082-989X.1.2.130
   Web of Science ®Google Scholar
• Mara, C. A., & Cribbie, R. A. (2012). Paired-samples tests of equivalence. Communications in Statistics-Simulation and Computation, 41(10), 1928–1943. doi: 10.1080/03610918.2011.626545
   Web of Science ®Google Scholar
• Marsh, H. W., Hau, K. T., & Wen, Z. (2004). In search of golden rules: Comment on hypothesis- testing approaches to setting cutoff values for fit indices and dangers in overgeneralizing Hu and Bentler's findings. Structural Equation Modeling, 11(3), 320–341. doi: 10.1207/s15328007sem1103_2
   Web of Science ®Google Scholar
• McDonald, R. P. (1989). An index of goodness-of-fit based on noncentrality. Journal of Classification, 6(1), 97–103. doi: 10.1007/BF01908590
   Web of Science ®Google Scholar
• Meade, A. W., Johnson, E. C., & Braddy, P. W. (2008). Power and sensitivity of alternative fit indices in tests of measurement invariance. Journal of Applied Psychology, 93(3), 568–592. doi: 10.1037/0021-9010.93.3.568
   PubMed Web of Science ®Google Scholar
• Meredith, W. (1993). Measurement invariance, factor analysis and factorial invariance. Psychometrika, 58(4), 525–543. doi: 10.1007/BF02294825
   Web of Science ®Google Scholar
• Millsap, R. E. (2011). Statistical approaches to measurement invariance. New York, NY. Routledge.
   Google Scholar
• Morey, R. D., & Rouder, J. N. (2011). Bayes factor approaches for testing interval null hypotheses. Psychological Methods, 16(4), 406–419. doi: 10.1037/a0024377
   PubMed Web of Science ®Google Scholar
• Muthén, B. (1984). A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika, 49(1), 115–132. doi: 10.1007/BF02294210
   Web of Science ®Google Scholar
• Muthén, B., Du Toit, S. H. C., & Spisic, D. (1997). Robust inference using weighted least squares and quadratic estimating equations in latent variable modeling with categorical and continuous outcomes (Unpublished manuscript).
   Google Scholar
• Muthén, B. O., & Satorra, A. (1995). Technical aspects of Muthén’s LISCOMP approach to estimation of latent variable relations with a comprehensive measurement model. Psychometrika, 60(4), 489–503. doi: 10.1007/BF02294325
   Web of Science ®Google Scholar
• R Core Team (2016). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved from https://www.R-project.org/.
   Google Scholar
• Reise, S. P., Widaman, K. F., & Pugh, R. H. (1993). Confirmatory factor analysis and item response theory: Two approaches for exploring measurement invariance. Psychological Bulletin, 114(3), 552–566. doi: 10.1037/0033-2909.114.3.552
   PubMed Web of Science ®Google Scholar
• Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3), 354–373. doi: 10.1037/a0029315
   PubMed Web of Science ®Google Scholar
• Rogers, J. L., Howard, K. I., & Vessey, J. T. (1993). Using significance tests to evaluate equivalence between two experimental groups. Psychological Bulletin, 113(3), 553–565. doi: 10.1037/0033-2909.113.3.553
   PubMed Web of Science ®Google Scholar
• Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48 (2), 1–36. Retrieved from http://www.jstatsoft.org/v48/i02
   Web of Science ®Google Scholar
• Saris, W. E., Satorra, A., & van der Veld, W. M. (2009). Testing structural equation models or detection of misspecifications?. Structural Equation Modeling, 16(4), 561–582. doi: 10.1080/10705510903203433
   Web of Science ®Google Scholar
• Satorra, A. (1992). Asymptotic robust inferences in the analysis of mean and covariance structures. Sociological Methodology, 22, 249–278. doi: 10.2307/270998
   Google Scholar
• Satorra, A., & Bentler, P. M. (2001). A scaled difference chi-square test statistic for moment structure analysis. Psychometrika, 66(4), 507–514. doi: 10.1007/BF02296192
   Web of Science ®Google Scholar
• Schuirmann, D. J. (1987). A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability. Journal of Pharmacokinetics and Biopharmaceutics, 15(6), 657–680. doi: 10.1007/BF01068419
   PubMedGoogle Scholar
• Steenkamp, J. B. E., & Baumgartner, H. (1998). Assessing measurement invariance in cross-national consumer research. Journal of Consumer Research, 25, 78–90. doi: 10.1086/209528
   Web of Science ®Google Scholar
• Steiger, J. H. (1989). EzPATH: Causal modeling. Evanston, IL: SYSTAT.
   Google Scholar
• Steiger, J. H. (1998). A note on multiple sample extensions of RMSEA fit index. Structural Equation Modeling, 5(4), 411–419. doi: 10.1080/10705519809540115
   Web of Science ®Google Scholar
• Steiger, J. H. (2007). Understanding the limitations of global fit assessment in structural equation modeling. Personality and Individual Differences, 42(5), 893–898. doi: 10.1016/j.paid.2006.09.017
   Web of Science ®Google Scholar
• Wellek, S. (2010). Testing statistical hypotheses of equivalence and noninferiority (2nd ed.). Boca Raton, FL: Chapman & Hall/CRC.
   Google Scholar
• Westlake, W. J. (1972). Use of confidence intervals in analysis of comparative bioavailability trials. Journal of Pharmaceutical Sciences, 61 (8), 1340–1341. doi: 10.1002/jps.2600610845
   PubMed Web of Science ®Google Scholar
• Widaman, K. F., & Reise, S. P. (1997). Exploring the measurement invariance ofpsychological instruments: Applications in the substance abuse domain. In K. J. Bryant (Eds.), Alcohol and substance use research (pp. 281–324). Washington, DC. APA.
   Google Scholar
• Yuan, K. H. (2005). Fit indices versus test statistics. Multivariate Behavioral Research, 40(1), 115–148. doi: 10.1207/s15327906mbr4001_5
   PubMed Web of Science ®Google Scholar
• Yuan, K. H., & Bentler, P. M. (1997). Mean and covariance structure analysis: Theoretical and practical improvements. Journal of the American Statistical Association, 92(438), 767–774. doi: 10.1080/01621459.1997.10474029
   Web of Science ®Google Scholar
• Yuan, K. H., & Bentler, P. M. (1999). F tests for mean and covariance structure analysis. Journal of Educational and Behavioral Statistics, 24(3), 225–243. doi: 10.3102/10769986024003225
   Web of Science ®Google Scholar
• Yuan, K. H., & Chan, W. (2016). Measurement invariance via multigroup SEM: Issues and solutions with chi-square-difference tests. Psychological Methods, 21(3), 405–426. doi: 10.1037/met0000080
   PubMed Web of Science ®Google Scholar
• Yuan, K. H., Chan, W., Marcoulides, G. A., & Bentler, P. M. (2016). Assessing structural equation models by equivalence testing with adjusted fit indices. Structural Equation Modeling: A Multidisciplinary Journal, 23(3), 319–330. doi: 10.1080/10705511.2015.1065414
   Web of Science ®Google Scholar