A Note on Sample Size and Solution Propriety for Confirmatory Factor Analytic Models

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
• Bandalos , D. L. 2006 . “ The use of Monte Carlo studies in structural equation modeling research. ” . In Structural equation modeling: A second course Edited by: Hancock , G. R. and Mueller , R. O. Greenwich , CT : Information Age. .
   Google Scholar
• 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 , NY : Wiley. .
   Google Scholar
• Boomsma , A. 1982 . “ The robustness of LISREL against small sample sizes in factor analysis models. ” . In Systems under indirect observation: Causality, structure, prediction Edited by: Joreskog , K. G. and Wold , H. 149 – 285 . Amsterdam , , Netherlands : North-Holland. .
   Google Scholar
• Boomsma , A. 1985 . Nonconvergence, improper solutions, and starting values in LISREL maximum likelihood estimation . Psychometrika , 50 : 229 – 242 .
   Web of Science ®Google Scholar
• Breckler , S. J. 1990 . Applications of covariance structure modeling in psychology: Cause for concern? . Psychological Bulletin , 107 : 260 – 273 .
   PubMed Web of Science ®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
• Curran , P. J. , Bollen , K. A. , Paxton , P. , Kirby , J. and Chen , F. 2002 . The noncentral chi-square distribution in misspecified structural equation models: Finite sample results from a Monte Carlo simulation . Multivariate Behavioral Research , 37 : 1 – 36 .
   PubMed Web of Science ®Google Scholar
• Ding , L. , Velicer , W. F. and Harlow , L. L. 1995 . Effects of estimation methods, number of indicators per factor, and improper solutions on structural equation modeling fit indices . Structural Equation Modeling , 2 : 119 – 144 .
   Web of Science ®Google Scholar
• Fan , X. , Thompson , B. and Wang , L. 1999 . Effects of sample size, estimation methods, and model specification on structural equation modeling fit indexes . Structural Equation Modeling , 6 : 56 – 83 .
   Web of Science ®Google Scholar
• Fouladi , R. T. 2000 . Performance of modified test statistics in covariance and correlation structure analysis under conditions of multivariate normality . Structural Equation Modeling , 7 : 356 – 410 .
   Web of Science ®Google Scholar
• Gagné , P. and Hancock , G. R. 2006 . Measurement model quality, sample size, and solution propriety in confirmatory factor analysis . Multivariate Behavioral Research , 41 : 65 – 83 .
   PubMed Web of Science ®Google Scholar
• Gerbing , D. W. and Anderson , J. C. 1985 . The effects of sampling error and model characteristics on parameter estimation for maximum likelihood confirmatory factor analysis . Multivariate Behavioral Research , 20 : 255 – 271 .
   PubMed Web of Science ®Google Scholar
• Gorsuch , R. L. 1983 . Factor analysis, , 2nd ed. Hillsdale , NJ : Erlbaum. .
   Google Scholar
• Hancock , G. R. and Mueller , R. O. 2001 . “ Rethinking construct reliability within latent variable systems. ” . In Structural equation modeling: Present and future. A festschrift in honor of Karl Jöreskog Edited by: Cudeck , R. , du Toit , S. and Sörbom , D. 195 – 216 . Lincolnwood , IL : Scientific Software International. .
   Google Scholar
• Hershberger , S. L. 2003 . The growth of structural equation modeling: 1994–2001 . Structural Equation Modeling , 10 : 35 – 46 .
   Web of Science ®Google Scholar
• Herzog , W. and Boomsma , A. 2009 . Small-sample robust estimators of noncentrality-based and incremental model fit . Structural Equation Modeling , 16 : 1 – 27 .
   Web of Science ®Google Scholar
• Herzog , W. , Boomsma , A. and Reinecke , S. 2007 . The model-size effect on traditional and modified tests of covariance structures . Structural Equation Modeling , 14 : 361 – 390 .
   Web of Science ®Google Scholar
• Jackson , D. L. 2001 . Sample size and the number of parameter estimates in maximum likelihood confirmatory factor analysis: A Monte Carlo investigation . Structural Equation Modeling , 8 : 205 – 223 .
   Web of Science ®Google Scholar
• Jackson , D. L. 2003 . Revisiting sample size and the number of parameter estimates: Some support for the N:q hypothesis . Structural Equation Modeling , 10 : 128 – 141 .
   Web of Science ®Google Scholar
• Jackson , D. L. 2007 . The effect of the number of observations per parameter in misspecified confirmatory factor analytic models . Structural Equation Modeling , 14 : 48 – 76 .
   Web of Science ®Google Scholar
• Kenny , D. A. and McCoach , D. B. 2003 . Effect of the number of variables on measures of fit in structural equation modeling . Structural Equation Modeling , 10 : 333 – 351 .
   Web of Science ®Google Scholar
• Kim , K. H. and Bentler , P. M. 2006 . “ Data modeling: Structural equation modeling. ” . In Handbook of complementary methods in education research Edited by: Green , J. L. , Camilli , G. and Elmore , P. B. 161 – 175 . Mahwah , NJ : Erlbaum. .
   Google Scholar
• Kline , R. B. 2005 . Principles and practice of structural equation modeling, , 2nd ed. New York , NY : Guilford. .
   Google Scholar
• MacCallum , R. C. 2003 . Working with imperfect models . Multivariate Behavioral Research , 38 : 113 – 139 .
   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
• MacCallum , R. C. , Widaman , K. F. , Preacher , K. J. and Hong , S. 2001 . Sample size in factor analysis: The role of model error . Multivariate Behavioral Research , 36 : 611 – 637 .
   PubMed Web of Science ®Google Scholar
• MacCallum , R. C. , Widaman , K. F. , Zhang , S. and Hong , S. 1999 . Sample size in factor analysis . Psychological Methods , 4 : 84 – 99 .
   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. , Hau , K.-T. , Balla , J. R. and Grayson , D. 1998 . Is more ever too much? The number of indicators per factor in confirmatory factor analysis . Multivariate Behavioral Research , 33 : 181 – 220 .
   PubMed Web of Science ®Google Scholar
• Marsh , H. W. , Hau , K.-T. and Grayson , D. 2005 . “ Goodness of fit in structural equation models. ” . In Contemporary psychometrics: A festschrift for Roderick P. McDonald Edited by: Maydeu-Olivares , A. and McArdle , J. J. 275 – 340 . Mahwah , NJ : Erlbaum .
   Google Scholar
• Martens , M. P. 2005 . The use of structural equation modeling in counseling psychology research . The Counseling Psychologist , 33 : 269 – 298 .
   Web of Science ®Google Scholar
• McDonald , R. P. 1985 . Factor analysis and related methods Hillsdale , NJ : Erlbaum. .
   Google Scholar
• Mueller , R. O. 1996 . Basic principles of SEM: An introduction to LISREL and EQS New York , NY : Springer. .
   Google Scholar
• Nevitt , J. and Hancock , G. R. 2004 . Evaluating small sample approaches for model test statistics in structural equation modeling . Multivariate Behavioral Research , 39 : 439 – 478 .
   Web of Science ®Google Scholar
• Rindskopf , D. 1984 . Structural equation models: Empirical identification, Heywood cases, and related problems . Sociological Methods and Research , 13 : 109 – 119 .
   Web of Science ®Google Scholar
• Skrondal , A. 2000 . Design and analysis of Monte Carlo experiments: Attacking the conventional wisdom . Multivariate Behavioral Research , 35 : 137 – 167 .
   PubMed Web of Science ®Google Scholar
• Steiger , J. H. and Lind , J. M. Statistically based tests for the number of common factors . Paper presented at the annual meeting of the Psychometric Society . Iowa City , IA . June .
   Google Scholar
• Swain , A. J. 1975 . Analysis of parametric structures for variance matrices Australia : University of Adelaide. . Unpublished doctoral dissertation
   Google Scholar
• Tanaka , J. S. 1987 . “How big is big enough?”: Sample size and goodness of fit in structural equation models with latent variables . Child Development , 58 : 134 – 146 .
   Web of Science ®Google Scholar
• Tremblay , P. F. and Gardner , R. C. 1996 . On the growth of structural equation modeling in psychological journals . Structural Equation Modeling , 3 : 93 – 104 .
   Web of Science ®Google Scholar
• Ullman , J. B. 1996 . “ Structural equation modeling. ” . In Using multivariate statistics Edited by: Tabachnick , B. G. and Fidell , L. S. 709 – 811 . New York , NY : HarperCollins. .
   Google Scholar
• Wothke , W. 1993 . “ Nonpositive definite matrices in structural modeling. ” . In Testing structural equation models Edited by: Bollen , K. and Long , S. 256 – 293 . Newbury Park , CA : Sage. .
   Google Scholar