Tau-Proportionate Form of Congeneric Covariance Structure

Abstract

From the view point of constructing a composite possessing the largest possible common covariability with all of its constituent tests, the concept of the best equi-covariable composite (BEC) has been introduced. When the covariance matrix of the constituent tests are so structured that its row (column) totals are all equal, the corresponding BEC is shown to be reducible to simple aggregated (or averaged) test. Under the purview of congeneric tests, it is shown that there exists a special form termed tau-proportionate congeneric form in which case the simple aggregated (or averaged) test is not only the BEC but also the most reliable composite. Statistical techniques of the estimation of parameters, testing and goodness-of-fit of the such structure are considered with the aid of an illustrative example.