Multivariate Analysis and Spatial/Temporal Scales: Real and Complex Models

Comparing different scales in space or time the correlation between regionalized quantities can change substantially. Coregionalization models incorporate a description of the variation and covariation of a set of variables at different characteristic scales either in space or in time. Such models can be used as a device to explore the structure of multivariate spatial or temporal data in the framework of a regionalized multivariate data analysis. We review the work done using the classical Linear Model of Coregionalization (LMC) which is adequate to model sets of variograms and cross variograms as well as sets of covariance functions with even cross covariance functions. We also present a new generalization of the LMC due to Grzebyk (1993), the Bilinear Model of Coregionalization (BMC), which is suitable for modeling a coregionalization in space or along the time axis using cross covariance functions which are not even.