A Third Moment Adjusted Test Statistic for Small Sample Factor Analysis

REFERENCES

• Amemiya , Y. and Anderson , T. 1990 . Asymptotic chi-square tests for a large class of factor analysis models . The Annals of Statistics , 18 : 1453 – 1463 .
   Web of Science ®Google Scholar
• Bentler , P. M. 1994 . “ A testing method for covariance structure analysis. ” . In Multivariate analysis and its applications Edited by: Anderson , T. W. , Fang , K. T. and Olkin , I. Vol. 24 , 123 – 135 . Hayward , CA : Institute of Mathematical Statistics. .
   Google Scholar
• Bentler , P. M. 2006 . EQS 6 structural equations program manual. Encino , CA : Multivariate Software. .
   Google Scholar
• Bollen , K. A. 1989 . Structural equations with latent variables. New York , NY : Wiley. .
   Google Scholar
• Box , G. 1954 . Some theorems on quadratic forms applied in the study of analysis of variance problems: I. Effect of inequality of variance in the one-way classification . The Annals of Mathematical Statistics , 25 : 290 – 302 .
   Google Scholar
• Browne , M. 1974 . Generalized least squares estimators in the analysis of covariance structures . South African Statistical Journal , 8 : 1 – 24 .
   Web of Science ®Google Scholar
• Browne , M. 1984 . Asymptotically 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
• Byrnes , J. E. 2010 . The sem.additions package for R. Retrieved from http://r-forge.r-project.org/projects/sem-additions
   Google Scholar
• Cai , L. and Lee , T. 2009 . Covariance structure model fit testing under missing data: An application of the Supplemented EM Algorithm . Multivariate Behavioral Research , 44 : 24
   Web of Science ®Google Scholar
• Curran , P. , West , S. and Finch , J. 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
• Duchesne , P. and Lafaye De Micheaux , P. 2010 . Computing the distribution of quadratic forms: Further comparisons between the Liu-Tang-Zhang approximation and exact methods . Computational Statistics & Data Analysis , 54 : 858 – 862 .
   Web of Science ®Google Scholar
• Efron , B. and Tibshirani , R. 1993 . An introduction to the bootstrap Vol. 57 , Boca Raton , FL : Chapman & Hall/CRC. .
   Google Scholar
• Fox , J. 2006 . Teacher's corner: Structural Equation Modeling With the sem Package in R . Structural Equation Modeling , 13 : 465 – 486 .
   Web of Science ®Google Scholar
• Hu , L. , Bentler , P. M. and Kano , Y. 1992 . Can test statistics in covariance structure analysis be trusted? . Psychological Bulletin , 112 : 351 – 362 .
   PubMed Web of Science ®Google Scholar
• Imhof , J. 1961 . Computing the distribution of quadratic forms in normal variables . Biometrika , 48 : 419 – 426 .
   Web of Science ®Google Scholar
• Jöreskog , K. 1967 . Some contributions to maximum likelihood factor analysis . Psychometrika , 32 : 443 – 482 .
   Web of Science ®Google Scholar
• J⊘reskog , K. 1970 . A general method for analysis of covariance structures . Biometrika , 57 : 239
   Web of Science ®Google Scholar
• J⊘reskog , K. , Sorbom , D. , du Toit , S. and du Toit , M. 2000 . LISREL 8: New statistical features. Lincolnwood , IL : Scientific Software International. .
   Google Scholar
• Ledoit , O. and Wolf , M. 2004 . A well-conditioned estimator for large-dimensional covariance matrices . Journal of Multivariate Analysis , 88 : 365 – 411 .
   Web of Science ®Google Scholar
• Lei , P. 2009 . Evaluating estimation methods for ordinal data in structural equation modeling . Quality and Quantity , 43 : 495 – 507 .
   Web of Science ®Google Scholar
• Liu , Tang Y. and Zhang , H. 2009 . A new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables . Computational Statistics and Data Analysis , 53 : 853 – 856 .
   Web of Science ®Google Scholar
• Lo , Y. , Mendell , N. and Rubin , D. 2001 . Testing the number of components in a normal mixture . Biometrika , 88 : 767
   Web of Science ®Google Scholar
• Magnus , J. and Neudecker , H. 1986 . Symmetry, 0–1 matrices and Jacobians: A review . Econometric Theory , 2 : 157 – 190 .
   Google Scholar
• Mardia , K. , Kent , J. and Bibby , J. 1980 . Multivariate analysis. London , , UK : Academic Press. .
   Google Scholar
• Muthen , L. and Muthen , B. 2006 . Mplus users guide, , 4th ed. Los Angeles , CA : Author. .
   Google Scholar
• Pearson , E. 1959 . Note on an approximation to the distribution of non-central χ2 . Biometrika , 46 : 364 – 364 .
   Web of Science ®Google Scholar
• R Development Core Team. 2011 . R: A language and environment for statistical computing [Computer software manual] Vienna , , Austria Retrieved from http://www.R-project.org (ISBN 3-900051-07-0)
   Google Scholar
• Satorra , A. and Bentler , P. M. 1988 . Scaling corrections for chi-square statistics in covariance structure analysis . 1988 Proceedings of Business and Economics Sections , 36 : 308 – 313 .
   Google Scholar
• Satorra , A. and Bentler , P. M. 1994 . “ Corrections to test statistics and standard errors in covariance structure analysis. ” . In Latent variables analysis: Applications for developmental research Edited by: von Eye , A. and Clogg , C. C. 399 – 419 . Thousand Oaks , CA : Sage. .
   Google Scholar
• Satterthwaite , F. 1941 . Synthesis of variance . Psychometrika , 6 : 309 – 316 .
   Web of Science ®Google Scholar
• Tibshirani , R. and Leisch , F. 2009 . Functions for the book: An introduction to the bootstrap. Retrieved from http://cran.r-project.org/web/packages/bootstrap/index.html
   Google Scholar
• Yuan , K. H. and Bentler , P. M. 2000 . Three likelihood-based methods for mean and covariance structure analysis with nonnormal missing data . Sociological Methodology , 30 : 165 – 200 .
   Web of Science ®Google Scholar
• Yuan , K. H. and Bentler , P. M. 2010 . Two simple approximations to the distributions of quadratic forms . British Journal of Mathematical and Statistical Psychology , 63 : 273 – 291 .
   PubMed Web of Science ®Google Scholar