In moment structure analysis with nonnormal data, asymptotic valid
inferences require the computation of a consistent (under general
distributional assumptions) estimate of the matrix $\Gamma$ of asymptotic
variances of sample second--order moments. Such a consistent estimate
involves the fourth--order sample moments of the data. In practice, the
use of fourth--order moments leads to computational burden and lack of
robustness against small samples. In this paper we show that, under
certain ...
In moment structure analysis with nonnormal data, asymptotic valid
inferences require the computation of a consistent (under general
distributional assumptions) estimate of the matrix $\Gamma$ of asymptotic
variances of sample second--order moments. Such a consistent estimate
involves the fourth--order sample moments of the data. In practice, the
use of fourth--order moments leads to computational burden and lack of
robustness against small samples. In this paper we show that, under
certain assumptions, correct asymptotic inferences can be attained when
$\Gamma$ is replaced by a matrix $\Omega$ that involves only the second--
order moments of the data. The present paper extends to the context
of multi--sample analysis of second--order moment structures, results
derived in the context of (simple--sample) covariance structure
analysis (Satorra and Bentler, 1990). The results apply to a variety of
estimation methods and general type of statistics. An example involving
a test of equality of means under covariance restrictions illustrates
theoretical aspects of the paper.
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