Multivariate normal integrals and contingency tables with ordered categories

Yuchung J. Wang

doi:10.1007/BF02295280

Multivariate normal integrals and contingency tables with ordered categories

Yuchung J. Wang

Rutgers Camden, Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

A k-dimensional multivariate normal distribution is made discrete by partitioning the k-dimensional Euclidean space with rectangular grids. The collection of probability integrals over the partitioned cubes is a k-dimensional contingency table with ordered categories. It is shown that loglinear model with main effects plus two-way interactions provides an accurate approximation for the k-dimensional table. The complete multivariate normal integral table is computed via the iterative proportional fitting algorithm from bivariate normal integral tables. This approach imposes no restriction on the correlation matrix. Comparisons with other numerical integration algorithms are reported. The approximation suggests association models for discretized multivariate normal distributions and contingency tables with ordered categories.

Original language	English (US)
Pages (from-to)	267-284
Number of pages	18
Journal	Psychometrika
Volume	62
Issue number	2
DOIs	https://doi.org/10.1007/BF02295280
State	Published - Jun 1997

All Science Journal Classification (ASJC) codes

General Psychology
Applied Mathematics

Keywords

Association model
Iterative proportional fitting algorithm
Local odds ratios
Loglinear model
Multivariate dependence functions

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10.1007/BF02295280

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title = "Multivariate normal integrals and contingency tables with ordered categories",

abstract = "A k-dimensional multivariate normal distribution is made discrete by partitioning the k-dimensional Euclidean space with rectangular grids. The collection of probability integrals over the partitioned cubes is a k-dimensional contingency table with ordered categories. It is shown that loglinear model with main effects plus two-way interactions provides an accurate approximation for the k-dimensional table. The complete multivariate normal integral table is computed via the iterative proportional fitting algorithm from bivariate normal integral tables. This approach imposes no restriction on the correlation matrix. Comparisons with other numerical integration algorithms are reported. The approximation suggests association models for discretized multivariate normal distributions and contingency tables with ordered categories.",

keywords = "Association model, Iterative proportional fitting algorithm, Local odds ratios, Loglinear model, Multivariate dependence functions",

author = "Wang, {Yuchung J.}",

note = "Funding Information: This research was sponsored by the National Science Council, Republic of China. Requests for reprints should be sent to Yuchung J. Wang, Department of Mathematical Sciences, Rutgers University, Camden, New Jersey 08102.",

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AU - Wang, Yuchung J.

N1 - Funding Information: This research was sponsored by the National Science Council, Republic of China. Requests for reprints should be sent to Yuchung J. Wang, Department of Mathematical Sciences, Rutgers University, Camden, New Jersey 08102.

PY - 1997/6

Y1 - 1997/6

N2 - A k-dimensional multivariate normal distribution is made discrete by partitioning the k-dimensional Euclidean space with rectangular grids. The collection of probability integrals over the partitioned cubes is a k-dimensional contingency table with ordered categories. It is shown that loglinear model with main effects plus two-way interactions provides an accurate approximation for the k-dimensional table. The complete multivariate normal integral table is computed via the iterative proportional fitting algorithm from bivariate normal integral tables. This approach imposes no restriction on the correlation matrix. Comparisons with other numerical integration algorithms are reported. The approximation suggests association models for discretized multivariate normal distributions and contingency tables with ordered categories.

AB - A k-dimensional multivariate normal distribution is made discrete by partitioning the k-dimensional Euclidean space with rectangular grids. The collection of probability integrals over the partitioned cubes is a k-dimensional contingency table with ordered categories. It is shown that loglinear model with main effects plus two-way interactions provides an accurate approximation for the k-dimensional table. The complete multivariate normal integral table is computed via the iterative proportional fitting algorithm from bivariate normal integral tables. This approach imposes no restriction on the correlation matrix. Comparisons with other numerical integration algorithms are reported. The approximation suggests association models for discretized multivariate normal distributions and contingency tables with ordered categories.

KW - Association model

KW - Iterative proportional fitting algorithm

KW - Local odds ratios

KW - Loglinear model

KW - Multivariate dependence functions

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JO - Psychometrika

JF - Psychometrika

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Multivariate normal integrals and contingency tables with ordered categories

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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