In terms of Principal Components Analysis or Multiple Discriminant Analysis, I have used dummy variables to represent a group of like-features that are located in the same geographic region. For example, in the analysis of two metropolitan cities, the census tracts that make up city one are classified as 0 and city two as 1. This binary classification groups the census tracts into two regions.

I am wondering how I could store geographic coordinates (centroid?) of these census tracts so that I could introduce a spatial component to the multivariate analysis. This is dissimilar to the approach mentioned above since I am not grouping any features; but rather, I am interested in determining whether or not spatiality is a statistically significant independent variable (in terms of regression), or if spatiality is a significant part of a component/factor (in terms of PCA/FA).

This would be simple enough if the variable was a single measured value; but alas, we have x and y coordinates to think about.

closed as not a real question by Michael Markieta, Get Spatial, Ian Turton, R.K., Chad Cooper Nov 23 '12 at 21:39

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    This doesn't seem to be a GIS question. If you're going to do PCA with spatial locations, then you have to include x and y as separate variables: there's really no other option. You can also include other spatial variables such as distances to specified features, mean slopes from a DEM, or whatever. – whuber Nov 19 '12 at 16:21