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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.