MULTIVARIATE STATISTICAL INFERENCE UNDER MARGINAL STRUCTURE
Leon Jay Gleser, Ingram Olkin · British Journal of Mathematical and Statistical Psychology · 1973
Suppose that we are utilizing k different psychological tests, each having one subtest in common. Of particular concern is the hypothesis that these tests are parallel with respect to their means and/or covariances. A complete hierarchy of hypotheses for this situation has been developed. For example, H m've is the hypothesis that the tests are parallel only with respect to the means of the common test, but with respect to the covariances of both tests. (The prime indicates equality for the common test only.) This hypothesis might be tested against H vc , the hypothesis of parallelism with respect to the covariances. Other hypotheses considered are H mvc , H m'vc , H m'vc and H vc . Maximum‐likelihood estimators under the various models (and under the assumption of normally distributed test scores) have been obtained, as well as the related likelihood‐ratio statistics. Approximate distributions of the likelihood‐ratio statistics are worked out, so that the tests can be applied, and an example of their use is provided.