The fit between a structural equation model and a data set is operationalized as the value of goodness-of-fit indices. The discrepancy between the estimated value and the value indicating perfect fit has three sources: misspecification, error arising from theoretical parsimony in the description of the model (parsimony error), and sampling error. Misspecification, which represents a disparity between “realworld” relationships and relationships in the model, is the most important source of error for researchers. It cannot be accurately assessed, however, unless parsimony error and sampling error are taken into account. Parsimony error occurs in measurement models when secondary relationships are excluded. Secondary relationships are defined here as secondary factor loadings and error term correlations that have small values, no theoretical bases, and no substantive meaning. A simulation was conducted to examine the effects of parsimony error on perfect measurement models and to establish appropriate criteria for model fit when parsimony error is present.
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References
1.
Anderson, J. C., & 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.
2.
Arbuckle, J. L., & Wothke, W. (1999). Amos 4.0 user’s guide. Chicago: Small Waters.
3.
Bearden, W. O., Sharma, S., & Teel, J. R. (1982). Sample size effects on chi-square and other statistics used in evaluating causal models. Journal of Marketing Research, 19, 425-430.
4.
Bentler, P. M., & Bonett, D. G. (1980). Significance tests and goodness of fit in the analysis of covariance structures. Psychological Bulletin, 88, 588-606.
5.
Bentler, P. M., & Yuan, K. H. (1999). Structural equation modeling with small samples: Test statistics. Multivariate Behavioral Research, 34(2), 181-197.
6.
Bollen, K. A. (1989). A new incremental fit index for general structural equation models. Sociological Methods and Research, 17, 303-316.
7.
Bollen, K. A., & Stine, R. A. (1993). Bootstrapping goodness-of-fit measures in structural equation models. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models, (pp. 111-135). Newbury Park, CA: Sage.
8.
Boomsma, A. (1982). The robustness of LISREL against small sample sizes in factor analysis models. In K. G. Jöreskog & H. Wold (Eds.), Systems under indirect observation: Causality, structure, prediction (Part I) (pp. 149-173). Amsterdam: North-Holland.
9.
Cheung, G. W., & Rensvold, R. B. (1998, August). A bootstrap procedure for testing the statistical significance of goodness-of-fit indices in structural equations models. Paper presented to the Research Methods Division of the Academy of Management, San Diego, CA.
10.
Cudeck, R., & Browne, M. W. (1992). Constructing a covariance matrix that yields a specified minimizer and a specified minimum discrepancy function value. Psychometrika, 3, 357-369.
11.
Cudeck, R., & Henly, S. J. (1991). Model selection in covariance structures analysis and the “problem” of sample size: A clarification. Psychological Bulletin, 109(3), 512-519.
12.
Efron, B. (1982). The jackknife, the bootstrap, and other resampling plans. Philadelphia: Society for Industrial and Applied Mathematics.
13.
Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. New York: Chapman & Hall.
14.
Fedor, D. (1991). Recipient responses to performance feedback: A proposed model and its implications. In G. Ferris & K. Rowland (Eds.), Research in personnel and human resources management (Vol. 9, pp. 73-120). Greenwich, CT: JAI.
15.
Fornall, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18, 39-50.
16.
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. Newbury Park, CA: Sage.
17.
Greller, M. M., & Herold, D. M. (1975). Sources of feedback: A preliminary investigation. Organizational Behavior and Human Performance, 13, 244-256.
18.
Hair, J. F., Jr., Anderson, R. E., Tatham, R. L., & Black, W. C. (1995). Multivariate data analysis with readings (4th ed.). London: Prentice Hall.
19.
Hall, R. J., Snell, A. F., & Foust, M. S. (1999). Item parcelling strategies in SEM: Investigating the subtle effects of unmodeled secondary constructs. Organizational Research Methods, 2(3), 233-256.
20.
Herold, D. M., Parsons, C. K., & Rensvold, R. B. (1996). Individual differences in the generation and processing of performance feedback. Educational and Psychological Measurement, 56, 5-25.
21.
Hu, L. T., & Bentler, P. M. (1998). Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. Psychological Methods, 3(4), 424-453.
22.
Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equations Modeling, 6(1), 1-55.
23.
Ilgen, D. R., Fisher, C. D., & Taylor, S. M. (1979). Consequences of individual feedback on behavior in organizations. Journal of Applied Psychology, 64(4), 349-371.
24.
Jablin, F. M. (1979). Supervisor-subordinate communication: The state of the art. Psychological Bulletin, 86, 1201-1222.
25.
Jöreskog, K., & Sörbom, D. (1993). LISREL 8: User’s reference guide. Chicago: Scientific Software.
26.
La Du, T. J., & Tanaka, J. S. (1989). The influence of sample size, estimation method, and model specification on goodness-of-fit assessment in structural equation models. Journal of Applied Psychology, 74, 625-635.
27.
Marsh, H. W., Balla, J. R., & McDonald, R. P. (1988). Goodness-of-fit indexes in confirmatory factor analysis: The effect of sample size. Psychological Bulletin, 103, 391-410.
28.
Marsh, H. W., Hau, T.-K., 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.
29.
Mooney, C. Z., & Duval, R. D. (1993). Bootstrapping: A nonparametric approach to statistical inference. Newbury Park, CA: Sage.
30.
Mulaik, S. A., James, L. R., Van Alstine, J., Bennet, N., Lind, S., & Stilwell, C. D. (1989). Evaluation of goodness-of-fit indices for structural equations models. Psychological Bulletin, 105, 430-445.
31.
Norusis, M. J. (1988). SPSS-X advanced statistics guide. Chicago: SPSS.
32.
Steenkamp, J.E.M., & Baumgartner, H. (1998). Assessing measurement invariance in crossnational consumer research. Journal of Consumer Research, 25, 78-90.
33.
Taylor, S. E., Fisher, C. D., & Ilgen, D. R. (1984). Individuals’ reactions to performance feedback in organizations: A control theory perspective. In K. M. Rowland & G. R. Ferris (Eds.), Research in personnel and human resources management (Vol. 2). Greenwich, CT: JAI.
