A Comparison of Four Estimators of a Population Measure of Model Fit in Covariance Structure Analysis

REFERENCES

• Anderson , J. C. and Gerbing , D. W. 1984 . The effect of sampling error on convergence, improper solutions, and goodness of fit indices for maximum likelihood confirmatory factor analysis . Psychometrika. , 49 : 155 – 173 .
   Web of Science ®Google Scholar
• Bentler , P. M. and Yuan , K.-H. 1999 . Structural equation modeling with small samples: Test statistics . Multivariate Behavioral Research , 34 : 181 – 197 .
   PubMed Web of Science ®Google Scholar
• Beran , R. and Srivastava , M. S. 1985 . Bootstrap tests and confidence regions for functions of a covariance matrix . Annals of Statistics. , 13 : 95 – 115 .
   Web of Science ®Google Scholar
• Bollen , K. A. and Stine , R. A. 1993 . “ Bootstrapping goodness-of-fit measures in structural equation modeling ” . In Testing structural equation models , Edited by: Bollen , K. A. and Long , J. S. 111 – 135 . Newbury Park , CA : Sage .
   Google Scholar
• Boomsma , A. 2000 . Reporting on structural equation analyses . Structural Equation Modeling: A Multidisciplinary Journal , 7 : 461 – 483 .
   Web of Science ®Google Scholar
• Browne , M. W. 1984 . Asymptotic distribution-free methods for the analysis of covariance structures . British Journal of Mathematical and Statistical Psychology , 37 : 62 – 83 .
   PubMed Web of Science ®Google Scholar
• Cudeck , R. and Henly , S. J. 1991 . Model selection in covariance structures analysis and the problem of sample size: A clarification . Psychological Bulletin , 109 : 512 – 519 .
   PubMed Web of Science ®Google Scholar
• Curran , P. J. , West , S. G. and Finch , J. F. 1996 . The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis . Psychological Methods , 1 : 16 – 29 .
   Web of Science ®Google Scholar
• Davison , A. C. and Hinkley , D. V. 1997 . Bootstrap methods and their application , Cambridge , UK : Cambridge University Press .
   Google Scholar
• Efron , B. and Tibshirani , R. 1993 . An introduction to the bootstrap , New York : Chapman & Hall .
   Google Scholar
• Kaplan , D. 1988 . The impact of specification error on the estimation, testing, and improvement of structural equation models . Multivariate Behavioral Research , 23 : 69 – 86 .
   PubMed Web of Science ®Google Scholar
• MacCallum , R. C. and Austin , J. T. 2000 . Applications of structural equation modeling in psychological research . Annual Review of Psychology. , 51 : 201 – 226 .
   PubMed Web of Science ®Google Scholar
• McDonald , R. P. and Marsh , H. W. 1990 . Choosing a multivariate model: Noncentrality and goodness of fit . Psychological Bulletin. , 107 : 247 – 255 .
   Web of Science ®Google Scholar
• Muthen , B. O. , Kaplan , D. and Hollis , M. 1987 . On structural equation modeling with data that are not missing completely at random . Psychometrika. , 52 : 431 – 462 .
   Web of Science ®Google Scholar
• Raykov , T. 2000 . On the large-sample bias, variance, and mean squared error of the conventional noncentrality parameter estimator of covariance structure models . Structural Equation Modeling. , 7 : 431 – 441 .
   Web of Science ®Google Scholar
• Raykov , T. 2005 . Bias-corrected estimation of noncentrality parameters of covariance structure models . Structural Equation Modeling. , 12 : 120 – 129 .
   Web of Science ®Google Scholar
• Satorra , A. and Bentler , P. M. Scaling corrections for chi-square statistics in covariance structure analysis . Proceedings of the American Statistical Association . pp. 308 – 313 .
   Google Scholar
• Satorra , A. , Saris , W. and de Pijper , W. M. 1991 . A comparison of several approximations to the power of the likelihood ratio test in covariance structure analysis . Statistica Neerlandica. , 45 : 173 – 185 .
   Google Scholar
• Steiger , J. H. , Shapiro , A. and Browne , M. W. 1985 . On the multivariate asymptotic distribution of sequential chi-square statistics . Psychometrika. , 50 : 253 – 264 .
   Web of Science ®Google Scholar
• Yuan , K.-H. 2005 . Fit indices versus test statistics . Multivariate Behavior Research. , 40 : 115 – 149 .
   PubMed Web of Science ®Google Scholar
• Yuan , K.-H. and Bentler , P. M. 1997 . “ Generating multivariate distributions with specified marginal skewness and kurtosis ” . In SoftStat'97—Advances in statistical software 6 , Edited by: Bandilla , W. and Faulbaum , F. 385 – 391 . Stuggtart , , Germany : Lucius & Lucius .
   Google Scholar
• Yuan , K.-H. , Bentler , P. M. and Zhang , W. 2005 . The effect of skewness and kurtosis on mean and covariance structure analysis: The univariate case and its multivariate implication . Sociological Methods & Research , 34 : 249 – 258 .
   Web of Science ®Google Scholar
• Yuan , K.-H. and Hayashi , K. 2003 . Bootstrap approach to inference and power analysis based on three statistics for covariance structure models . British Journal of Mathematical and Statistical Psychology , 56 : 93 – 110 .
   PubMed Web of Science ®Google Scholar
• Yuan , K.-H. and Marshall , L. L. 2004 . A new measure of misfit for covariance structure models . Behaviormetrika , 31 : 1 – 24 .
   Google Scholar