Latent variable analysis of multivariate spatial data

Multivariate spatial or geo-referenced data arise naturally in such disciplines as ecology, agriculture, geology, and atmospheric sciences. In practice, interest often lies in modeling underlying structure and representing interrelationships in terms of a smaller number of variables. For such situations, statistical analysis using a latent variable model is proposed. We present a general model that incorporates spatial correlation and potential lagged or shifted dependencies and that can represent subject matter theory or serve as a practical exploratory model. Procedures for model fitting, parameter estimation, inferences, and latent variable prediction are developed without restrictive assumptions on distribution and covariance function forms. The properties and usefulness of the proposed approaches are assessed by asymptotic theory and an extensive simulation study. An example from precision agriculture is also presented.