Multivariate Generalizations of Student's t-Distribution. ONR Technical Report. [Biometric Lab Report No. 90-3.]
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| Title: | Multivariate Generalizations of Student's t-Distribution. ONR Technical Report. [Biometric Lab Report No. 90-3.] |
|---|---|
| Language: | English |
| Authors: | Gibbons, Robert D., Illinois State Psychiatric Inst., Chicago. |
| Peer Reviewed: | N |
| Page Count: | 19 |
| Publication Date: | 1990 |
| Sponsoring Agency: | Office of Naval Research, Arlington, VA. Cognitive and Neural Sciences Div. |
| Document Type: | Reports - Research |
| Descriptors: | Equations (Mathematics), Estimation (Mathematics), Generalizability Theory, Item Response Theory, Mathematical Models, Multivariate Analysis, Statistical Inference |
| Abstract: | In the process of developing a conditionally-dependent item response theory (IRT) model, the problem arose of modeling an underlying multivariate normal (MVN) response process with general correlation among the items. Without the assumption of conditional independence, for which the underlying MVN cdf takes on comparatively simple forms and can be numerically evaluated using existing reduction formulae, the task required the development of a computationally fast, tractable, and accurate approximation of MVN orthant probabilities for general correlation--"rho(sub ij)". Previous technical reports by the present authors have provided such a method, based on C. E. Clark's (1961) approximation of the moments of "n" correlated random normal variables. Research continues in the area of applying this algorithm to problems in IRT. This report focuses on the application of previous research results to another problem in statistics--the generation of simultaneous confidence bounds for multiple correlated comparisons. C. W. Dunnett's test for multiple treatments compared to a single control is generalized to various unbalanced cases. There is a large amount of statistical literature on this topic. However, as in IRT, the solutions have been based on reduction formulae that are limited to special cases, which arise in the comparison of multiple treatment groups each of size "n(sub i) = m" to a single control group of size "n(sub 0)". More general problems, such as obtaining simultaneous confidence bounds for regression coefficients cannot be solved using these existing methods. This report illustrates how the results obtained in the IRT context can be applied to simultaneous statistical inference problems of various kinds. (Author/RLC) |
| Entry Date: | 1991 |
| Accession Number: | ED326573 |
| Database: | ERIC |
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