Behavior of Asymptotically Distribution Free Test Statistics in Covariance Versus Correlation Structure Analysis |
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| Authors: | Yafei Huang Peter M Bentler |
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| Institution: | 1. University of California, Los Angelesyafeihuang@ucla.edu;3. University of California, Los Angeles |
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| Abstract: | The asymptotically distribution free (ADF) method is often used to estimate parameters or test models without a normal distribution assumption on variables, both in covariance structure analysis and in correlation structure analysis. However, little has been done to study the differences in behaviors of the ADF method in covariance versus correlation structure analysis. The behaviors of 3 test statistics frequently used to evaluate structural equation models with nonnormally distributed variables, χ2 test TAGLS and its small-sample variants TYB and TF(AGLS) were compared. Results showed that the ADF method in correlation structure analysis with test statistic TAGLS performs much better at small sample sizes than the corresponding test for covariance structures. In contrast, test statistics TYB and TF(AGLS) under the same conditions generally perform better with covariance structures than with correlation structures. It is proposed that excessively large and variable condition numbers of weight matrices are a cause of poor behavior of ADF test statistics in small samples, and results showed that these condition numbers are systematically increased with substantial increase in variance as sample size decreases. Implications for research and practice are discussed. |
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| Keywords: | asymptotically distribution free correlation structure analysis covariance structure analysis |
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