Conditional Dependence

Abstract

The probability of m correlated random variables drawn from a multivariate normal distribution being non-negative is given. Exact results for this probability integral are unavailable for m > 3. Approximations for higher dimensional problems have generally yielded poor results 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.

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Document Details

Document Type
Technical Report
Publication Date
Mar 15, 1989
Accession Number
ADA207881

Entities

People

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

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Cognition
  • Covariance
  • Data Science
  • Educational Psychology
  • Factor Analysis
  • Information Science
  • Integrals
  • Military Research
  • Monte Carlo Method
  • Normal Distribution
  • Psychology
  • Random Variables
  • Simulations
  • Standards
  • Statistical Algorithms
  • Statistics
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Regression Analysis.