Can test statistics in covariance structure analysis be trusted?
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.
Hu
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LT
Department of Psychology, University of California, Los Angeles 90024-1563.
Bentler
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PM
Kano
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Y
D005260:Female; D006801:Humans; D008297:Male; D015233:Models, Statistical; D008962:Models, Theoretical