Abstract: The main purpose of this paper is to develop some asymptotic properties in analysis of covariance structures with independent but non-identically distributed observations. Consistency and asymptotic normality for the maximum likelihood estimation will be developed. Analogous results for the generalized least squar es estimation will be provided. Applications of the general theory to two specific models are discussed. Finally, results from a simulation study will be presented to illustrate the theory developed.
Key words and phrases: Analysis of covariance structures, asymptotic normality, consistency, information matrix, missing data, multi-level structural equation model.