Approximating Multivariate Normal Orthant Probabilities Using the Clark Algorithm.

Abstract

The probability of m correlated random variables is drawn from a multivariate normal distribution being non-negative. Exact results for this probability integral are unavailable for m > 3. Approximations for higher dimensional problems have generally yielded poor results except for special cases, such as compound symmetry, which is of limited value in practice. The purpose of this paper is to present a general approximation of this probability integral. The algorithm developed here is computationally tractable for m = 50 and accurate for very general correlational structures. The performance of this algorithm is compared to results based on Clark's (1961) original approximation, Gaussian quadrature formulae, and Monte Carlo simulation methods. Application of this approximation to problems of conditional dependence in IRT estimation problems is discussed.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jul 15, 1987
Accession Number
ADA184855

Entities

People

  • Donald Hedeker
  • R. D. Bock
  • Robert D. Gibbons

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Algorithms
  • Classification
  • Computational Science
  • Data Science
  • Education
  • Educational Psychology
  • Illinois
  • Information Science
  • Knowledge Management
  • Military Research
  • New England
  • Normal Distribution
  • Personnel Management
  • Psychology
  • Security
  • South Carolina
  • United States

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Operations Research
  • Regression Analysis.