Paper #16

Title:

Multi-sample analysis of moment-structures: Asymptotic validity of inferences based on second-order moments

Author:

Albert Satorra

Date:

June 1992

Abstract:

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.

Area of Research:

Statistics, Econometrics and Quantitative Methods

Published in:

Statistical Modelling and Latent Variables Elsevier, North Holland. K. Haagen, D. J.Bartholomew and M. Deistler (eds.), pp. 283-298.] Special issue Vernon L. Smith Experimental Methods in Economics. (June 1992)

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