Multivariate data with spatial dependencies arise in many areas of applicat
ion, including geology, precision agriculture, and ecology. For analysis of
such data, a methodology based on a generalized shifted-factor model is de
veloped. The model incorporates potential lagged dependencies between facto
rs and observed variables, representing asymmetric spatial dependencies obs
erved in practice. Identification and estimation issues are discussed. A pr
ediction procedure that exploits both the multivariate and spatial dependen
ce in the data is proposed and illustrated.