Sensitivity of Fit Indices to Misspecification in Growth Curve Models

REFERENCES

• Bentler , P. M. 1990 . Comparative fit indexes in structural models. . Psychological Bulletin , 107 : 238 – 246 .
   PubMed Web of Science ®Google Scholar
• Bollen , K. A. 1989 . Structural equations with latent variables New York : Wiley. .
   Google Scholar
• Bollen , K. A. and Curran , P. J. 2006 . Latent curve models: A structural equation perspective New York : Wiley. .
   Google Scholar
• Box , G. E. P. 1979 . “ Robustness in the strategy of scientific model building. ” . In Robustness in statistics Edited by: Launer , R. L. and Wilkinson , G. N. 201 – 236 . New York : Academic. .
   Google Scholar
• Browne , M. W. and Cudeck , R. 1993 . “ Alternative ways of assessing model fit. ” . In Testing structural equation models Edited by: Bollen , K. A. and Long , J. S. 136 – 162 . Newbury Park, CA : Sage .
   Google Scholar
• Chun , S. Y. and Shapiro , A. 2010 . Construction of covariance matrices with a specified discrepancy function minimizer, with application to factor analysis. . SIAM Journal on Matrix Analysis and Applications , 31 : 1570 – 1583 .
   Web of Science ®Google Scholar
• Cohen , J. 1988 . Statistical power analysis for the behavioral sciences, , 2nd ed. Hillsdale, NJ : Erlbaum .
   Google Scholar
• Cudeck , R. and Browne , M. W. 1992 . Constructing a covariance matrix that yields a specified minimizer and a specified minimum discrepancy value. . Psychometrika , 57 : 357 – 369 .
   Web of Science ®Google Scholar
• Enders , C. and Finney , S. April 2003 . SEM fit index criteria re-examined: An investigation of ML and robust fit indices in complex models April , Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL
   Google Scholar
• Fan , X. and Sivo , S. A. 2005 . Sensitivity of fit indices to misspecified structural or measurement model components: Rationale of two-index strategy revisited. . Structural Equation Modeling , 12 : 343 – 367 .
   Web of Science ®Google Scholar
• Fan , X. and Sivo , S. A. 2007 . Sensitivity of fit indices to model misspecification and model types. . Multivariate Behavioral Research , 42 : 509 – 529 .
   Web of Science ®Google Scholar
• Fitzmaurice , G. , Laird , N. and Ware , J. 2004 . Applied longitudinal data analysis Hoboken, NJ : Wiley .
   Google Scholar
• Gerbing , D. W. and Anderson , J. C. 1993 . “ Monte Carlo evaluations of goodness-of-fit indices for structural equation models. ” . In Testing structural equation models Edited by: Bollen , K. A. and Long , J. S. 40 – 65 . Newbury Park, CA : Sage .
   Google Scholar
• Grimm , K. J. 2007 . Multivariate longitudinal methods for studying developmental relationships between depression and academic achievement. . International Journal of Behavioral Development , 34 : 328 – 339 .
   Web of Science ®Google Scholar
• Hedeker , D. and Gibbons , R. D. 2006 . Longitudinal data analysis Hoboken, NJ : Wiley .
   Google Scholar
• Hu , L.-T. and Bentler , P. M. 1998 . Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. . Psychological Methods , 3 : 424 – 453 .
   Web of Science ®Google Scholar
• Hu , L.-T. and Bentler , P. M. 1999 . Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. . Structural Equation Modeling , 6 : 1 – 55 .
   Web of Science ®Google Scholar
• Jackson , D. L. , Gillaspy , J. A. and Purc-Stephenson , R. 2009 . Reporting practices in confirmatory factor analysis: An overview and some recommendations. . Psychological Methods , 14 : 6 – 23 .
   PubMed Web of Science ®Google Scholar
• Jöreskog , K. G. and Sörbom , D. 1981 . LISREL VI: Analysis of linear structural relationship by maximum likelihood and least squares methods Chicago : National Educational Resources .
   Google Scholar
• Kreft , I. and de Leeuw , J. 1998 . Introducing multilevel modeling Thousand Oaks, CA : Sage .
   Google Scholar
• Kwok , O. , West , S. G. and Green , S. B. 2007 . The impact of misspecifying the within-subject covariance structure in multiwave longitudinal multilevel models: A Monte Carlo study. . Multivariate Behavioral Research , 42 : 557 – 592 .
   Web of Science ®Google Scholar
• Leite , W. L. and Stapleton , L. M. 2006 . Sensitivity of fit indices to detect misspecifications of growth shape in latent growth modeling Paper presented at the annual meeting of the American Educational Research Association, San Francisco, CA
   Google Scholar
• MacCallum , R. C. , Browne , M. W. and Cai , L. 2006 . Testing differences between nested covariance structure models: Power analysis and null hypotheses. . Psychological Methods , 11 : 19 – 35 .
   PubMed Web of Science ®Google Scholar
• MacCallum , R. C. , Browne , M. W. and Sugawara , H. M. 1996 . Power analysis and determination of sample size for covariance structure modeling. . Psychological Methods , 1 : 130 – 149 .
   Web of Science ®Google Scholar
• Marsh , H. W. , Balla , J. R. and McDonald , R. P. 1988 . Goodness-of-fit indexes in confirmatory factor analysis: The effect of sample size. . Psychological Bulletin , 103 : 391 – 410 .
   Web of Science ®Google Scholar
• Marsh , H. W. and Hau , K.-T. 1996 . Assessing goodness of fit: Is parsimony always desirable? . Journal of Experimental Education , 64 : 364 – 390 .
   Web of Science ®Google Scholar
• Meredith , W. and Tisak , J. 1990 . Latent curve analysis. . Psychometrika , 55 : 107 – 122 .
   Web of Science ®Google Scholar
• Muthén , B. O. and Curran , P. J. 1997 . General longitudinal modeling of individual differences in experimental designs: A latent variable framework for analysis and power estimation. . Psychological Methods , 2 : 371 – 402 .
   Web of Science ®Google Scholar
• Muthén , L. K. and Muthén , B. O. 1998–2006 . Mplus user's guide Los Angeles : Author. .
   Google Scholar
• Olsson , U. , Troye , S. V. and Howell , R. D. 1999 . Theoretic fit and empirical fit: The performance of maximum likelihood versus generalized least squares estimation in structural equation models. . Multivariate Behavioral Research , 34 : 31 – 58 .
   PubMed Web of Science ®Google Scholar
• Saris , W. E. and Satorra , A. 1993 . “ Power evaluations in structural equation models. ” . In Testing structural equation models Edited by: Bollen , K. A. and Long , J. S. 181 – 204 . Newbury Park, CA : Sage .
   Google Scholar
• SAS Institute, Inc. 1999 . SAS procedures guide, version 8 Cary, NC : Author .
   Google Scholar
• Satorra , A. and Saris , W. E. 1985 . Power of the likelihood ratio test in covariance structure analysis. . Psychometrika , 50 : 83 – 90 .
   Web of Science ®Google Scholar
• Singer , J. D. and Willett , J. B. 2003 . Applied longitudinal data analysis: Modeling change and event occurrence New York : Oxford University Press .
   Google Scholar
• Sivo , S. A. , Fan , X. and Witta , E. L. 2005 . The biasing effects of unmodeled ARMA time series processes on latent growth curve model estimates. . Structural Equation Modeling , 12 : 215 – 231 .
   Web of Science ®Google Scholar
• Steiger , J. H. and Lind , J. C. May 1980 . Statistically based tests for the number of common factors May , Paper presented at the annual meeting of the Psychometric Society, Iowa City, IA
   Google Scholar
• Sun , J. 2005 . Assessing goodness of fit in confirmatory factor analysis. . Measurement and Evaluation in Counseling and Development , 37 : 240 – 256 .
   Web of Science ®Google Scholar
• Taylor , A. B. 2008 . Two new methods of studying the performance of SEM fit indexes Unpublished doctoral dissertation, Arizona State University, Tempe, AZ
   Google Scholar
• Tomarken , A. J. and Waller , N. G. 2003 . Potential problems with well fitting models. . Journal of Abnormal Psychology , 112 : 578 – 98 .
   PubMed Web of Science ®Google Scholar
• Tomarken , A. J. and Waller , N. G. 2005 . Structural equation modeling: Strength, limitations, and misconceptions. . Annual Review of Clinical Psychology , 1 : 31 – 65 .
   PubMed Web of Science ®Google Scholar
• Tucker , L. R. and Lewis , C. 1973 . A reliability coefficient for maximum likelihood factor analysis. . Psychometrika , 38 : 1 – 10 .
   Web of Science ®Google Scholar
• West , S. G. , Taylor , A. B. and Wu , W. “ Model fit and model selection in structural equation modeling ” . In Handbook of structural equation modeling Edited by: Hoyle , R. H. New York : Guilford . (in press)
   Google Scholar
• Widaman , K. F. and Thompson , J. S. 2003 . On specifying the null model for incremental fit indices in structural equation modeling. . Psychological Methods , 8 : 16 – 37 .
   PubMed Web of Science ®Google Scholar
• Wu , W. , West , S. G. and Hughes , J. N. 2008 . Effect of retention in first grade on children's achievement trajectories over four years: A piecewise growth analysis using propensity score matching. . Journal of Educational Psychology , 100 : 727 – 740 .
   PubMed Web of Science ®Google Scholar
• Wu , W. , West , S. G. and Taylor , A. B. 2009 . Evaluating model fit for growth curve models: Integration of fit indices from SEM and MLM frameworks. . Psychological Methods , 14 : 183 – 201 .
   PubMed Web of Science ®Google Scholar
• Yu , C. Y. 2002 . Evaluating cutoff criteria of model fit indices for latent variable models with binary and continuous outcomes Unpublished doctoral dissertation, University of California, Los Angeles
   Google Scholar
• Yuan , K.-H. 2005 . Fit indices versus test statistics. . Multivariate Behavioral Research , 40 : 115 – 148 .
   PubMed Web of Science ®Google Scholar
• Yuan , K.-H. , Bentler , P. M. and Zhang , W. 2005 . The effect of skewness and kurtosis on mean and covariance structure analysis. . Sociological Methods & Research , 34 : 240 – 258 .
   Web of Science ®Google Scholar