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Compatibility of conditionally specified models.

¹Division of epidemiology & Biostatistics, School of Public Health, University of Illinois at Chicago, 1603 West Taylor Street, Chicago, IL 60612.

Statistics & Probability Letters

|May 4, 2010

Summary

This summary is machine-generated.

Conditionally specified joint models are useful but can be incompatible. This study introduces a simple odds ratio method to ensure compatibility, construct joint densities, and modify models for reliable statistical applications.

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Area of Science:

Statistics
Computational Statistics
Statistical Modeling

Background:

Conditionally specified joint models offer convenience in spatial data modeling, Gibbs sampling, and missing data imputation.
A key challenge is the potential incompatibility of these conditional models, leading to application issues.

Purpose of the Study:

To develop a method for assessing and ensuring the compatibility of conditionally specified models.
To construct compatible joint densities and provide a framework for modifying incompatible models.

Main Methods:

Utilizing an odds ratio representation of joint density to analyze model compatibility.
Deriving and verifying conditions for the compatibility of conditionally specified distributions.
Explicitly constructing joint densities based on conditional specifications.

Main Results:

The proposed conditions for compatibility are simpler than existing methods.
Joint densities are constructed that are fully compatible when conditional models are compatible and partially compatible otherwise.
The method facilitates checking and modifying conditionally specified models.

Conclusions:

The odds ratio approach provides a straightforward and effective way to manage compatibility issues in conditionally specified joint models.
This work enhances the reliability and applicability of these models in statistical analysis.