A bivariate logistic regression model based on latent variables

TL;DR

This paper introduces a new bivariate logistic regression model using latent variables, extending existing models to better analyze binary and ordinal data with a focus on marginal distributions and their association.

Contribution

It proposes a novel bivariate logistic distribution based on the Ali-Mikhail-Haq model, extending the Gumbel type 2 distribution, and studies its properties with practical data applications.

Findings

Model effectively captures marginal distributions and associations.

Applied to real datasets on hiking habits and visual recognition.

Demonstrates the model's usefulness in practical bivariate data analysis.

Abstract

Bivariate observations of binary and ordinal data arise frequently and require a bivariate modelling approach in cases where one is interested in aspects of the marginal distributions as separate outcomes along with the association between the two. We consider methods for constructing such bivariate models with logistic marginals and propose a model based on the Ali-Mikhail-Haq bivariate logistic distribution. We motivate the model as an extension of that based on the Gumbel type 2 distribution as considered by other authors and as a bivariate extension of the logistic distribution which preserves certain natural characteristics. Basic properties of the obtained model are studied and the proposed methods are illustrated through analysis of two data sets, one describing the trekking habits of Norwegian hikers, the other stemming from a cognitive experiment of visual recognition and awareness.