A Markov random field model with cumulative logistic functions for spatially dependent ordinal data

Area of Science:

• Statistics
• Spatial Analysis
• Ordinal Regression

Background:

• Analyzing spatially dependent ordinal data presents challenges, particularly with irregularly spaced sites.
• Existing models often assume regular spacing or an underlying continuous variable, limiting their applicability.

Purpose of the Study:

• To develop a flexible class of regression models for analyzing spatially dependent ordinal data.
• To provide a model that does not require regularly spaced sites or an underlying continuous variable.
• To enable interpretation of model parameters using odds ratios.

Main Methods:

• Development of a class of regression models using cumulative logistic functions, extending Markov random field models.
• Application of parameterization, neighborhood selection, and standard error calculation techniques.
• Utilizing pseudo-likelihood methods for model fitting in simulation studies.

Main Results:

• The proposed models accommodate both regularly and irregularly spaced sites effectively.
• Incorporating spatial effects significantly improved model performance compared to non-spatial counterparts.
• Analysis of UK daily air quality index data revealed significant spatial effects.

Conclusions:

• The developed regression models offer a robust and flexible approach for analyzing spatially dependent ordinal data.
• The inclusion of spatial effects enhances predictive accuracy and model fit.
• Practical implementation aspects, including model fitting and interpretation, are addressed.