Article2004

A Note on Extending Steiger's (1998) Multiple Sample RMSEA Adjustment to Other Noncentrality Parameter-Based Statistics

41 citations0/0 files storedStructural Equation Modeling A Multidisciplinary Journal

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Psychometric Methodologies and Testing Statistical Distribution Estimation and Applications Statistical Methods and Bayesian Inference

Abstract

This article considers the implications for other noncentrality parameter-based statistics from Steiger's (1998) multiple sample adjustment to the root mean square error of approximation (RMSEA) measure. When a structural equation model is fitted simultaneously in more than 1 sample, it is shown that the calculation of the noncentrality parameter used in tests of approximate fit and in point and interval estimators of other noncentral fit statistics (except the expected cross-validation index) also requires a likeminded adjustment. Furthermore, it is shown that an adjustment is needed in multiple sample models for correctly calculating MacCallum, Browne, and Sugawara's (1996) approach to power analysis. The accuracy of these proposals is investigated and demonstrated in a small Monte Carlo study in which particular attention is paid to using appropriately constructed covariance matrices that give specified nonzero population discrepancy values under maximum likelihood estimation.

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References

1992Alternative Ways of Assessing Model Fit 1996Power analysis and determination of sample size for covariance structure modeling.1990Structural Model Evaluation and Modification: An Interval Estimation Approach 1984Asymptotically distribution‐free methods for the analysis of covariance structures 1989Single Sample Cross-Validation Indices for Covariance Structures 1985On the Multivariate Asymptotic Distribution of Sequential Chi-Square Statistics 1998A note on multiple sample extensions of the RMSEA fit index 1992Constructing a Covariance Matrix that Yields a Specified Minimizer and a Specified Minimum Discrepancy Function Value

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