Methods for descriptive factor analysis of multivariate geostatistical data: a case-study comparison

We consider the framework in which vectors of variables are observed at different points in a region. Such data are typically characterized by point-wise correlations among the variables, as well as spatial autocorrelation and cross-correlation. To help understand and model this dependence structure, one may define factors which operate at different spatial scales. We consider four such factor-analytic techniques: the linear model of coregionalization (LMC) and three recently proposed alternatives. We apply them to the same set of data, concentrations of major ions in water samples taken from springs in a carbonate mountain aquifer. The methods give quite different results for the spring chemistry, with those of the LMC being much more interpretable. We suggest some possible explanations for this, which may be relevant in other applications as well.