Small-sample robust estimators of noncentrality-based and incremental model fit

Structural Equation Modeling

Volumn 16, Issue 1, 2009, Pages 1-27

  Herzog, Walter ^a,c   Boomsma, Anne ^b  

^a UNIVERSITY OF ST GALLEN   (Switzerland)

^b UNIVERSITY OF GRONINGEN   (Netherlands)

^c Institute of Marketing and Retailing   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

CHI-SQUARE STATISTICS; CONFIDENCE INTERVAL; ESTIMATED PARAMETER; INCREMENTAL MODELING; INDEPENDENCE MODELS; MODEL MISSPECIFICATION; NONCENTRAL CHI-SQUARE DISTRIBUTION; ROOT MEAN SQUARE ERRORS;

MEAN SQUARE ERROR; PROBABILITY DISTRIBUTIONS; SAMPLING;

ESTIMATION;

EID: 61449163071     PISSN: 10705511     EISSN: None     Source Type: Journal    
DOI: 10.1080/10705510802561279     Document Type: Article

References (53)

1. Bartlett, M. S. (1937). Properties of sufficiency and statistical tests. Proceedings of the Royal Society of London, Series A, 160, 268-282.
2. Bartlett, M. S. (1950). Tests of significance in factor analysis. British Journal of Psychology (Statistical Section), 3, 77-85.
3. 2 approximations. Journal of the Royal Statistical Society, Series B, 16, 296-298.
4. Bentler, P. M., & Chou, C.-P. (1987). Practical issues in structural equation modeling. Sociological Methods & Research 16, 78-117.
5. Bentler, P. M., & Yuan, K.-H. (1999). Structural equation modeling with small samples: Test statistics. Multivariate Behavioral Research, 34, 181-197.
6. Boomsma, A. (1983). On the robustness of LISREL (maximum likelihood estimation) against small sample size and non-normality. Unpublished doctoral dissertation, University of Groningen, The Netherlands.
7. Boomsma, A. (1985). Nonconvergence, improper solutions, and starting values in LISRBL maximum likelihood estimation. Psychometrika, 50, 229-242.
8. Boomsma, A., & Herzog, W. (2007). R function swain: Correcting structural equation model fit statistics and indexes under small-sample and/or large-model conditions. Retrieved January 21, 2008, from http: //www. gmw. rug. nl/ ̃boomsma
9. Brown, T. A. (2006). Confirmatory factor analysis for applied research. New York: Guilford.
10. Browne, M. W. (1982). Covariance structures. In D. M. Hawkins (Ed.), Topics in applied multivariate analysis (pp. 72-142). Cambridge, UK: Cambridge University Press.
11. Browne, M. W. (1984). Asymptotically distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37, 62-83.
12. Browne, M. W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 136-162). Newbury Park, CA: Sage.
13. Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling, 14, 464-504.
14. Chen, R, Curran, P. J., Bollen, K. A., Kirby, J., & Paxton, P. (2008), An empirical evaluation of the use of fixed cutoff points in RMSEA test statistic in structural equation models. Sociological Methods & Research, 36, 462-494,
15. Cheung, M. W. L. (2007). Comparison of approaches to constructing confidence intervals for mediating effects using structural equation models. Structural Equation Modeling, 14, 227-246.
16. Cudeck, R" & Henly, S. J. (1991). Model selection in covariance structures analysis and the "problem" of sample size: A clarification. Psychological Bulletin, 109, 512-519.
17. Curran, P. J., Bollen, K. A., Chen, F. Paxton, P., & Kirby, J. (2003). Finite sampling properties of the point estimates and confidence intervals of the RMSEA. Sociological Methods & Research, 32, 208-252.
18. Curran, P. J., Bollen, K. A., Paxton, P., Kirby, J., & 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.
19. Curran, P. J., West, S. G., & Finch, J. F. (1996). The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. Psychological Methods, I, 16-29.
20. Fouladi, R. T. (2000). Performance of modified test statistics in covariance and correlation structure analysis under conditions of multivariate nonnormality. Structural Equation Modeling, 7, 356-410.
21. Gerbing, D. W., & 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.
22. Gerbing, D. W., & Anderson, J. C. (1993). Monte Carlo evaluations of goodness-of-fit indices for structural equation models. In K. A. Bollen & J. S, Long (Eds.), Testing structural equation models (pp. 40-65). Newbury Park, CA: Sage.
23. Herzog, W., Boomsma, A., & Reinecke, S. (2007). The model-size effect on traditional and modified tests of covariance structures. Structural Equation Modeling, 14, 361-390.
24. Homburg, C., & Fürst, A. (2005). How organizational complaint handling drives customer loyalty: An analysis of the mechanistic and the organic approach. Journal of Marketing, 69, 95-114.
25. Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1-55.
26. Hu, L. T., Bentler, P. M., & Kano, Y. (1992). Can test statistics in covariance structure analysis be trusted? Psychological Bulletin, 112, 351-362.
27. Jackson, D. L. (2001). Sample size and number of parameter estimates in maximum likelihood confirmatory factor analysis: A Monte Carlo investigation. Structural Equation Modeling, 8, 205-223.
28. Jackson, D. L. (2003). Revisiting sample size and number of parameter estimates: Some support for the N:q hypothesis. Structural Equation Modeling, 10, 128-141.
29. 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.
30. Kenny, D. A., Kashy, D. A., & Cook, W. L. (2006). Dyadic data analysis. New York: Guilford.
31. Kensuke, O., Takahiro, H., & Kazuo, S. (2005, July). Bartlett correction of likelihood ratio statistics in structural equation modeling. Paper presented at the annual meeting of the Psychometric Society, Tilburg, The Netherlands.
32. Marsh, H. W., Hau, K.-T, Balla, J. R., & Grayson, D. (1998). Is more ever too much? The number of indicators per factor in confirmatory factor analysis. Multivariate Behavioral Research, 33, 181-220.
33. Marsh, H. W., Hau, K.-T, & Wen, Z. L. (2004). In search of golden rules: Comment on hypothesis-testing approaches to setting cutoff values for fit indexes and danger in overgeneralizing Hu and Bentler's 1999 findings. Structural Equation Modeling, 11, 320-341.
34. McDonald, R. P., & Marsh, H. W. (1990). Choosing a multivariate model: Noncentrality and goodness of fit. Psychological Bulletin, 107, 247-255.
35. Morhart, F. M., Herzog, W., & Tomczak, I. (in press). Brand-specific leadership: Turning employees into brand champions. Journal of Marketing.
36. Muthén, L. K, & Muthén, B. O. (2007). Mplus user's guide (4th ed.). Los Angeles: Muthén & Muthén.
37. Neale, M. C., & Miller, M. B. (1997). The use of likelihood-based confidence intervals in genetic models. Behavior Genetics, 27, 113-120.
38. Nevitt, J., & Hancock, G. R. (2001). Performance of bootstrapping approaches to model test statistics and parameter standard error estimation in structural equation modeling. Structural Equation Modeling, 8, 353-377.
39. Nevitt, J., & Hancock, G. R. (2004). Evaluating small sample approaches for model test statistics in structural equation modeling. Multivariate Behavioral Research, 39, 439-478.
40. Obermiller, C, Spangenberg, E, & MacLachlan, D. L. (2005). Ad skepticism: The consequences of disbelief. Journal of Advertising, 34, 7-17.
41. Olsson, U. H., Foss, T., & Breivik, E. (2004). Two equivalent discrepancy functions for maximum likelihood estimation: Do their test statistics follow a non-central chi-square distribution under model misspecification? Sociological Methods & Research, 32, 453-500.
42. Olsson, U. H, Foss, T, Troye, S. V., & Howell, R. D. (2000). The performance of ML, GLS, and WLS estimation in structural equation modeling under conditions of misspecification and nonnormality. Structural Equation Modeling 7, 557-595.
43. Satorra, A., & Bender, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye & C. C. Clogg (Eds.), Latent variable analysis: Applications for developmental research (pp. 399-419). Thousand Oaks, CA: Sage.
44. Savalei, V. (2008). Is the ML chi-square ever robust to nonnormality? A cautionary note with missing data. Structural Equation Modeling, 15, 1-22.
45. Sobel, M. E., & Bohrnstedt, G. W. (1985). Use of null models in evaluating the fit of covariance structure models. In N. B. Tuba (Ed.), Sociological methodology (pp. 152-178). San Francisco: Jossey-Bass.
46. Steiger, I. H., & Lind, I. C. (1980, May). Statistically-based tests for the number of factors. Paper presented at the annual meeting of the Psychometric Society, Iowa City, IA.
47. Steiger, J. H., Shapiro, A., & Browne, M. W. (1985). On the multivariate asymptotic distribution of sequential chisquare statistics. Psychometrika, 50, 253-264.
48. Swain, A. J. (1975). Analysis of parametric structures for variance matrices. Unpublished doctoral dissertation, Department of Statistics, University of Adelaide, Australia.
49. Tomarken, A. J., & Waller, N. G. (2005). Structural equation modeling: Strengths, limitations, and misconceptions. Annual Review of Clinical Psychology, I, 31-65.
50. Venables, W. N., Smith, D. M., & The R Development Core Team. (2006). An introduction to R (Version 2.4.1). Retrieved June 14, 2007, from http://www.r-project .org/
51. Wakaki, H., Eguchi, S., & Fujikoshi, Y. (1990). A class of tests for a general covariance structure. Journal of Multivariate Analysis, 32, 313-325.
52. Wilks, S. S. (1938). The large-sample distribution of the likelihood ratio for testing composite hypotheses. Annals of Mathematical Statistics, 9, 60-62.
53. Yuan, K.-H. (2005). Fit indices versus test statistics. Multivariate Behavioral Research, 40, 115-148.