A class of tests for a general covariance structure

Wakaki, Hirofumi

doi:10.1016/0047-259x(90)90089-z

Cited by 32 publications

(15 citation statements)

References 9 publications

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“…Yuan, Marshall and Bentler (2002) applied it to the rescaled statistic in exploratory factor analysis. The Bartlett correction for general covariance structures also exists for T ML when data are normally distributed (see Wakaki, Eguchi, & Fujikoshi, 1990). However, the correction is quite complicated even for rather simple models.…”

Section: Matching Fit Indices With Statisticsmentioning

confidence: 99%

Fit Indices Versus Test Statistics

Yuan¹

2005

Multivariate Behavioral Research

353

224

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Model evaluation is one of the most important aspects of structural equation modeling (SEM). Many model fit indices have been developed. It is not an exaggeration to say that nearly every publication using the SEM methodology has reported at least one fit index. Most fit indices are defined through test statistics. Studies and interpretation of fit indices commonly assume that the test statistics follow either a central chi-square distribution or a noncentral chi-square distribution. Because few statistics in practice follow a chi-square distribution, we study properties of the commonly used fit indices when dropping the chi-square distribution assumptions. The study identifies two sensible statistics for evaluating fit indices involving degrees of freedom. We also propose linearly approximating the distribution of a fit index/statistic by a known distribution or the distribution of the same fit index/statistic under a set of different conditions. The conditions include the sample size, the distribution of the data as well as the base-statistic. Results indicate that, for commonly used fit indices evaluated at sensible statistics, both the slope and the intercept in the linear relationship change substantially when conditions change. A fit index that changes the least might be due to an artificial factor. Thus, the value of a fit index is not just a measure of model fit but also of other uncontrollable factors. A discussion with conclusions is given on how to properly use fit indices.In social and behavioral sciences, interesting attributes such as stress, social support, socio-economic status cannot be observed directly. They are measured by multiple indicators that are subject to measurement errors. By segregating measurement errors from the true scores of attributes, structural equation modeling (SEM), especially its special case of covariance structure analysis, provides a methodology for modeling the latent variables directly. Although there are many MULTIVARIATE BEHAVIORAL RESEARCH, 40(1),

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Section: Matching Fit Indices With Statisticsmentioning

confidence: 99%

Fit Indices Versus Test Statistics

Yuan¹

2005

Multivariate Behavioral Research

353

224

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“…One direction of further investigation could be to revisit those studies, and to check whether reported findings generalize to larger models. Wakaki, Eguchi, and Fujikoshi (1990) derived a (relatively complex) Bartlett adjustment factor for the test of general covariance structures. In a first simulation study, this correction significantly improved the performance of T ML (Kensuke, Takahiro, & Kazuo, 2005).…”

Section: Limitations and Future Workmentioning

confidence: 99%

The Model-Size Effect on Traditional and Modified Tests of Covariance Structures

Herzog

Boomsma

Reinecke

2007

Structural Equation Modeling: A Multidisciplinary Journal

108

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“…For the test of general covariance structures, Wakaki, Eguchi, and Fujikoshi (1990) developed a Bartlett-like correction that seems to improve the performance of T ML for arbitrary covariance structure models (Kensuke, Takahiro, & Kazuo, 2005). Unfortunately, this correction procedure is quite complicated, even for small models; therefore, Yuan (2005) recommended the "ad hoc correction"…”

Section: Yuan-corrected Statisticsmentioning

confidence: 99%