Testing log-linear models with inequality constraints: a comparison of asymptotic, bootstrap, and posterior predictive p-values

An important aspect of applied research is the assessment of the goodness‐of‐fit of an estimated statistical model. In the analysis of contingency tables, this usually involves determining the discrepancy between observed and estimated frequencies using the likelihood‐ratio statistic. In models with...

Full description

Saved in:
Bibliographic Details
Published in:Statistica Neerlandica 2005-02, Vol.59 (1), p.82-94
Main Authors: Galindo-Garre, Francisca, Vermunt, Jeroen K.
Format: Article
Language:English
Subjects:
Assessments
Asymptotic properties
Comparative analysis
Inequalities
Inequality
inequality constraints
Linear programming
Mathematical models
order-restricted inference
parametric bootstrap
Posterior predictive p-values
Samples
Statistical analysis
Statistics
Studies
Tables
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:An important aspect of applied research is the assessment of the goodness‐of‐fit of an estimated statistical model. In the analysis of contingency tables, this usually involves determining the discrepancy between observed and estimated frequencies using the likelihood‐ratio statistic. In models with inequality constraints, however, the asymptotic distribution of this statistic depends on the unknown model parameters and, as a result, there no longer exists an unique p‐value. Bootstrap p‐values obtained by replacing the unknown parameters by their maximum likelihood estimates may also be inaccurate, especially if many of the imposed inequality constraints are violated in the available sample. We describe the various problems associated with the use of asymptotic and bootstrap p‐values and propose the use of Bayesian posterior predictive checks as a better alternative for assessing the fit of log‐linear models with inequality constraints.
ISSN:0039-0402
1467-9574
DOI:10.1111/j.1467-9574.2005.00281.x