ASYMPTOTIC ROBUST INFERENCES IN THE ANALYSIS OF MEAN AND COVARIANCE STRUCTURES.

Academic Journal

Sociological Methodology; 1992, Vol. 22 Issue 1, p249-278, 30p, 3 Charts

Structural equation models are widely used in economic, social, and behavioral studies to analyze linear interrelationships among variables, some of which may be unobservable or subject to measurement error. Alternative estimation methods that exploit different distributional assumptions are now available. This paper deals with issues of asymptotic statistical inferences, such as the evaluation of standard errors of estimates and chi-square goodness-of-fit statistics, in the general context of mean and covariance structures. The emphasis is on drawing correct statistical inferences regardless of the distribution of the data and the method of estimation employed. A simple expression for a consistent estimate (given any distribution of the data) of Γ, the matrix of asymptotic variances of the vector of sample second-order moments, is used to compute asymptotic robust standard errors and an asymptotic robust chi-square goodness-of- fit statistic. Simple modifications of the usual estimate of Γ also permit correct asymptotic inferences in multistage complex samples. We also discuss the conditions under which, regardless of the distribution of the data, one can rely on the usual (nonrobust) normal-theory inferential statistics. Finally, we use a multivariate regression model with errors-in-variables to illustrate, by means of simulated data, various theoretical aspects of the paper. [ABSTRACT FROM AUTHOR]