Abstract
The purpose of the present investigation is to examine the influence of sample size (N) and model parsimony on a set of 22 goodness-of-fit indices including those typically used in confirmatory factor analysis and some recently developed indices. For sample data simulated from two known population data structures, values for 6 of 22 fit indices were reasonably independent ofN and were not significantly affected by estimating parameters known to have zero values in the population: two indices based on noncentrality described by McDonald (1989; McDonald and Marsh, 1990), a relative (incremental) index based on noncentrality (Bentler, 1990; McDonald & Marsh, 1990), unbiased estimates of LISREL's GFI and AGFI (Joreskog & Sorbom, 1981) presented by Steiger (1989, 1990) that are based on noncentrality, and the widely known relative index developed by Tucker and Lewis (1973). Penalties for model complexity designed to control for sampling fluctuations and to address the inevitable compromise between goodness of fit and model parsimony were evaluated.
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References
Akaike, H. (1974). A new look at the statistical model identification,IEEE Transactions on Automatic Control 19: 716–723.
Bentler, P. M. (1990). Comparative fit indices in structural models,Psychological Bulletin 107: 238–246.
Bentler, P. M. & Bonett, D. G. (1980). Significance tests and goodness of fit in the analysis of covariance structures,Psychological Bulletin 88: 588–606.
Bollen, K. A. (1986). Sample size and Bentler and Bonett's nonnormed fit index,Psychometrika 51: 375–377.
Bollen, K. A. (1990). Overall fit in covariance structure models: Two types of sample size effects,Psychological Bulletin 107: 256–259.
Bozdogan, H. (1987). Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions,Psychometrika 52: 345–370.
Browne, M. W. (1974). Generalized least squares estimators in the analysis of covariance structures.South African Statistical Journal 8: 1–24.
Browne, M. W. & Cudeck, R. (1989). Single sample cross-validation indices for covariance structures.Multivariate Behavioral Research 24: 445–455.
Cudeck, R. & Browne, M. W. (1983). Cross-validation of covariance structures,Multivariate Behavioral Research 18: 147–167.
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.
Hoelter, J. W. (1983). The analysis of covariance structures: Goodness-of-fit indices,Sociological Methods & Research 11: 325–344.
Hull, C. H. & Nie, N. H. (1981).SPSS update 7–9, New York: McGraw-Hill.
James, L. R., Mulaik, S. A., & Brett, J. M. (1982). Causal Analysis, Assumptions, Models, and Data, Beverly Hills, CA: Sage.
Joreskog, K. G. & Sorbom, D. (1981).LISREL V: Analysis of Linear Structural Relations by the Method of Maximum Likelihood, Chicago: International Educational Services.
Marsh, H. W. (1987). The factorial invariance of responses by males and females to a multidimensional self-concept instrument: Substantive and methodological issues,Multivariate Behavioral Research 22: 457–480.
Marsh, H. W., Balla, J. R., & McDonald, R. P. (1988). Goodness-of-fit indices in confirmatory factor analysis: The effect of sample size,Psychological Bulletin 102: 391–410.
McDonald, R. P., & Marsh, H. W. (1990). Choosing a multivariate model: Noncentrality and goodness-of-fit,Psychological Bulletin 107: 247–255.
McDonald, R. P. (1989). An index of Goodness-of-fit based on noncentrality,Journal of Classification 6: 97–103.
Mulaik, S. A. (October, 1991).Clarifying Misconceptions about Parsimony Adjustments of Goodness of Fit Indices, Paper presented at the 1991 Annual Meeting of the Society of Multivariate Experimental Psychology.
Mulaik, S. A., James, L. R., Van Alstine, J., Bennett, N., Lind, S., & Stilwell, C. D. (1989). Evaluation of goodness-of-flt indices for structural equation models,Psychological Bulletin 105: 430–445.
Schwartz, G. (1978). Estimating the dimension of a model,Annals of Statistics 6: 461–464.
Steiger, J. H. (1989).EzPATH: A Supplementary Module for SYSTAT and SYSGRAPH, Evanston, IL: SYSTAT, Inc.
Steiger, J. (1990). Structure model evaluation and modification: An interval estimation approach,Multivariate Behavioral Research 25: 1731180.
Steiger, J. H. & Lind, J. M. (May, 1980).Statistically-Based Tests for the Number of Common Factors, Paper presented at the Psychometrika Society Meeting, Iowa City.
Tanaka, J. S. & Huba, G. J. (1985). A fit index for covariance structure models under arbitrary GLS estimation,British Journal of Mathematical and Statistical Psychology 38: 197–201.
Tucker, L. R. & Lewis, C. (1973). The reliability coefficient for maximum likelihood factor analysis.Psychometrika 38: 1–10.
Wald, A. (1943). Tests of statistical hypotheses concening several parameters when the number of observations is large. Transactions of the American Mathematical Society 54: 426–482.
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Marsh, H.W., Balla, J. Goodness of fit in confirmatory factor analysis: The effects of sample size and model parsimony. Qual Quant 28, 185–217 (1994). https://doi.org/10.1007/BF01102761
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DOI: https://doi.org/10.1007/BF01102761