  There are many data sources available that report related variables of
interest that are also referenced over geographic regions and time; however,
there are relatively few general statistical methods that one can readily use
that incorporate these multivariate-spatio-temporal dependencies. As such, we
introduce the multivariate-spatio-temporal mixed effects model (MSTM) to
analyze areal data with multivariate-spatio-temporal dependencies. The proposed
MSTM extends the notion of Moran's I basis functions to the
multivariate-spatio-temporal setting. This extension leads to several
methodological contributions including extremely effective dimension reduction,
a dynamic linear model for multivariate-spatio-temporal areal processes, and
the reduction of a high-dimensional parameter space using a novel parameter
model. Several examples are used to demonstrate that the MSTM provides an
extremely viable solution to many important problems found in different and
distinct corners of the spatio-temporal statistics literature including:
modeling nonseparable and nonstationary covariances, combing data from multiple
repeated surveys, and analyzing massive multivariate-spatio-temporal datasets.
