Multilevel latent Gaussian process model for mixed discrete and continuous multivariate response data

TL;DR

This paper introduces a Bayesian multilevel Gaussian process model for analyzing mixed discrete and continuous multivariate data, enabling latent variable estimation and spatial prediction, with applications in ecological wetland assessment.

Contribution

The paper presents a novel Bayesian latent Gaussian process model for mixed data types, allowing spatial prediction and variable ranking in ecological studies.

Findings

Successfully applied to wetland condition assessment in Colorado.

Enabled prediction of latent variables at new locations.

Provided rankings of response variables by correlation with the latent field.

Abstract

We propose a Bayesian model for mixed ordinal and continuous multivariate data to evaluate a latent spatial Gaussian process. Our proposed model can be used in many contexts where mixed continuous and discrete multivariate responses are observed in an effort to quantify an unobservable continuous measurement. In our example, the latent, or unobservable measurement is wetland condition. While predicted values of the latent wetland condition variable produced by the model at each location do not hold any intrinsic value, the relative magnitudes of the wetland condition values are of interest. In addition, by including point-referenced covariates in the model, we are able to make predictions at new locations for both the latent random variable and the multivariate response. Lastly, the model produces ranks of the multivariate responses in relation to the unobserved latent random field. This is an important result as it allows us to determine which response variables are most closely correlated with the latent variable. Our approach offers an alternative to traditional indices based on best professional judgment that are frequently used in ecology. We apply our model to assess wetland condition in the North Platte and Rio Grande River Basins in Colorado. The model facilitates a comparison of wetland condition at multiple locations and ranks the importance of in-field measurements.