Linear models of coregionalization for multivariate lattice data: a general framework for coregionalized multivariate...

Area of Science:

• Spatial statistics
• Bayesian inference
• Geostatistics

Background:

• Traditional univariate Gaussian conditional autoregressive (CAR) models are limited for multivariate lattice data.
• Existing methods often struggle to capture complex, spatially structured cross-variable interactions.
• Multivariate disease mapping requires flexible models for analyzing simultaneous spatial patterns.

Purpose of the Study:

• To present a general coregionalization framework for developing coregionalized multivariate Gaussian conditional autoregressive (cMCAR) models.
• To extend univariate CAR models to a multivariate setting for lattice data analysis.
• To enable flexible modeling of spatial and cross-variable interactions in multivariate data.

Main Methods:

• Developed a general coregionalization framework for cMCAR models.
• Formulated precision structures for classes of cMCARs.
• Established conditional properties of the resulting multivariate spatial models.
• Applied the methods to a Minnesota county-level cancer dataset.

Main Results:

• The framework allows flexible modeling of symmetric or asymmetric spatial interactions and covariance structures.
• New insights into cMCARs with structured covariances and cross-covariances of varying spatial ranges.
• Demonstrated the estimation and mapping of covariances and cross-covariances for disease risks.
• Identified spatial risk associations between areas and diseases.

Conclusions:

• The proposed cMCAR framework offers a flexible approach for multivariate spatial data analysis, particularly in disease mapping.
• Mapping covariances and cross-covariances provides novel spatial characterizations and risk association insights.
• This work advances Bayesian disease mapping by incorporating detailed spatial dependency structures.