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Bayesian Approach to Multivariate Component-Based Logistic Regression: Analyzing Correlated Multivariate Ordinal

Ju-Hyun Park¹, Ji Yeh Choi², Jungup Lee³

¹Department of Statistics, Dongguk University.

Multivariate Behavioral Research

|February 1, 2021

Summary

This summary is machine-generated.

This study introduces a Bayesian approach for analyzing correlated ordinal data, addressing limitations in existing component-based models. The new method improves statistical inference for multivariate outcomes in social science research.

Keywords:

Bayesian inference Correlation and covariance matrices component-based models ordinal logistic regression

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Area of Science:

Statistics
Social Sciences
Behavioral Sciences

Background:

Component-based models are used for dimension reduction in regression.
Existing models often assume independence for multivariate ordinal outcomes, leading to biased results.
There is a need for models that account for residual covariances in multivariate ordinal data.

Purpose of the Study:

To propose a Bayesian methodology for component-based models that handles unstructured residual covariances.
To address the limitations of independence assumptions in existing multivariate ordinal models.
To provide a more accurate statistical inference for correlated ordinal outcome data.

Main Methods:

A Bayesian multivariate ordinal logistic model is proposed.
Ordinal outcomes are re-expressed using latent continuous variables based on an approximate multivariate t-distribution.
An efficient Gibbs sampler (a Markov Chain Monte Carlo algorithm) is developed.

Main Results:

The proposed model accounts for unstructured residual covariances.
Regression coefficients are interpretable as log-transformed odds ratios.
The method facilitates accurate statistical inference for multivariate ordinal outcomes.

Conclusions:

The developed Bayesian methodology offers an improvement over existing component-based models for multivariate ordinal data.
The approach provides a robust framework for analyzing complex correlated outcomes in the social and behavioral sciences.
The method was empirically validated using data on bullying perpetration and victimization.