Multivariate Generalizations of Student's t-Distribution
Robert David Gibbons, Donald Hedeker, R. Darrell Bock · 1990
Abstract : In the process of developing a conditionally dependent item-response theory model, we were confronted with the problem of modeling an underlying multivariate normal (MVN) response process with general correlation among the items. Without the assumption of conditional of conditional independence, for which the underlying MVN cdf takes on comparatively simple forms, and can be numerically evaluated using existing reduction formulae, our task required the development of a computationally fast, tractable and accurate approximation of multivariate normal orthant probabilities for general correlation. The focus of our previous technical reports have provided such a method, based on Clark's approximation of the moments of n correlated random normal variables. The major thrust of this work continues in the area of applying this algorithm to problems in item-response theory (IRT). The focus of this report, however, is on the application of our previous results to another problem in statistics; namely, the generation of simultaneous confidence bounds for multiple correlated comparisons. In this report the authors illustrate how the results we have obtained in the IRT context can be applied to simultaneous statistical inference problems of various kinds.