Can test statistics in covariance structure analysis be trusted?

L T Hu; P M Bentler; Y Kano

doi:10.1037/0033-2909.112.2.351

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Can test statistics in covariance structure analysis be trusted?

L T Hu·P M Bentler·Y Kano

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Abstract

Covariance structure analysis uses chi 2 goodness-of-fit test statistics whose adequacy is not known. Scientific conclusions based on models may be distorted when researchers violate sample size, variate independence, and distributional assumptions. The behavior of 6 test statistics is evaluated with a Monte Carlo confirmatory factor analysis study. The tests performed dramatically differently under 7 distributional conditions at 6 sample sizes. Two normal-theory tests worked well under some conditions but completely broke down under other conditions. A test that permits homogeneous nonzero kurtoses performed variably. A test that permits heterogeneous marginal kurtoses performed better. A distribution-free test performed spectacularly badly in all conditions at all but the largest sample sizes. The Satorra-Bentler scaled test statistic performed best overall.

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Female Humans Male Models, Statistical Models, Theoretical Journal Article Research Support, U.S. Gov't, P.H.S.

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L T Hu, P M Bentler, Y Kano. 1992. Can test statistics in covariance structure analysis be trusted?. https://doi.org/10.1037/0033-2909.112.2.351

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