Analysis of multivariate spatial data using latent variables

Modeling and analysis of multivariate geo-referenced data are of great interest in disciplines such as ecology, agriculture, and the Environmental Sciences; However, the development of statistical methods for such data has been rather limited. This dissertation consisting of three papers discusses latent variable analysis of multivariate spatial data;The first paper introduces the generalized shifted-factor model and its use in modeling a wide variety of spatial dependence characteristics. The model incorporates potential lagged dependencies between factors and observed variables, representing asymmetric spatial, cross-variable dependencies observed in practice. Identification of such lagged dependencies or shifted factors is discussed, and tools for practical implementation of the approach are given. Methods for parameter estimation, inference, and latent variable prediction are described for researchers in applied sciences;The second paper develops distribution-free statistical procedures for analysis using the generalized shifted-factor model. The augmented observation model-fitting approach is proposed. The large-sample properties of the parameter estimators are derived. An extensive simulation study investigates the various statistical and practical issues associated with the approach. An example from precision farming is presented;The third paper proposes a systematic approach to model-building and spatial prediction in factor analysis of multivariate spatial data. A very unrestrictive and practical condition is derived under which a simple inference procedure based on a pseudo-independent likelihood is valid for any spatial processes with unspecified covariance functions and distributions. Procedures for assessing such a condition, for checking the model fit, and for selecting a model are developed. For multivariate prediction, a procedure combining the latent variable modeling and a measurement-error-free kriging technique is introduced, and is compared to other methods. A simulation study and an illustrative example are also discussed