This paper presents a personal view of structural models for covariance matrices arising from continuous variates. The lack of robustness of statistical tests involving the assumption of multivariate normality will receive some attention and alternative approaches will be examined. Modern developments will be considered but no attempt will be made to provide an exhaustive review. Readers who require additional information are refereed to the review article by Bentler (1980) and to the bibliographies in Harman (1976) and Mulaik (1972). The paper is divided into two main parts. Part I is concerned with general technical background common to all structural models for covariance matrices. Part II is concerned with some specific covariance structures.
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