  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.
