A Hybrid Sampling Method For Three Way Contingency Tables

Abstract

We develop an algorithm blending Sequential Importance Sampling (SIS) and Markov Chain Monte Carlo (MCMC) to conduct goodness of fit testing on three-way contingency tables under the no-three-way interaction model. Unlike previous studies, we conduct SIS utilizing the hypergeometric distribution. Further, our hybrid method capitalizes on the positive aspects of SIS and MCMC while reducing their inefficiencies. We demonstrate the algorithms performance on equal marginal data sets to highlight computational speed and accuracy. We then demonstrate the algorithm in accurately constructing the null distribution for dense tables that satisfy the asymptotic distribution assumptions. With this result in mind, we estimate the null distribution for sparse tables that violate these assumptions. Our hybrid scheme is shown, via simulation, to be more accurate than simply using the asymptotic distribution for sparse tables.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 2018
Accession Number
AD1060075

Entities

People

  • Aaron Stone

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Cell Count
  • Computations
  • Data Science
  • Data Sets
  • Estimators
  • Goodness Of Fit Tests
  • Information Science
  • Monte Carlo Method
  • Probability
  • Random Variables
  • Sampling
  • Simulations
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Inference
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Regression Analysis.
  • Statistical inference.