An importance sampling algorithm for exact conditional tests in log-linear models

A simple but quite general simulation method for conducting exact conditional lack-of-fit tests in log-linear models is proposed. Our Monte Carlo approximation utilises an importance sampling method motivated by the crude normal approximation to the Poisson distribution. Examples considered include...

Full description

Saved in:
Bibliographic Details
Published in:Biometrika 1999-06, Vol.86 (2), p.321-332
Main Authors: Booth, JG, Butler, RW
Format: Article
Language:English
Subjects:
Approximation
Contingency tables
Covariance matrices
Degrees of freedom
Delta method
Exact sciences and technology
Inference
Linear inference, regression
Markov analysis
Markov chain
Markov chains
Mathematics
Methods
Monte Carlo error
Normal approximation
P values
Probability and statistics
Ratio estimate
Sampling methods
Sciences and techniques of general use
Simulation
Statistical variance
Statistics
Symmetry
Tanneries
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A simple but quite general simulation method for conducting exact conditional lack-of-fit tests in log-linear models is proposed. Our Monte Carlo approximation utilises an importance sampling method motivated by the crude normal approximation to the Poisson distribution. Examples considered include tests of quasi-symmetry and related models for square tables and tests concerning higher-order interactions in multi-way tables. The method is competitive with direct simulation from the exact conditional distribution when this is feasible and outperforms alternative Monte Carlo procedures when direct simulation is infeasible and outperforms alternative Monte Carlo procedures when direct simulation is infeasible provided the number of degrees of freedom of the test is not too large. Extension of the method to tests against non-saturated alternatives is straightforward and is briefly discussed and illustrated.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/86.2.321