SPFAC - A FORTRAN-77 PROGRAM FOR SPATIAL FACTOR-ANALYSIS OF MULTIVARIATE DATA

An algorithm and FORTRAN-77 computer program is presented for analyzing multivariate data tha can be combined with measures of spatial relationships. The method requires the derivation of spatial associations through the computation of auto-/crosscorrelation coefficients of a multivariate dataset to form an auto-/crosscorrelation matrix, R. Two matrices are constructed, R(o), and R(d), representing auto- and crosscorrelation coefficients at lag O and lag d, where d < D . D is the maximum spatial range (neighborhood) of the analysis. Spectral decomposition of the product of these two matrices (transition matrix) extracts factors in which the loadings of the variables express the relationships of the variables for the given lag d. When the procedure is applied to the transition matrix at short lags, variables that are correlated for short lags have greater factor loadings than variables that are more significantly correlated at larger lag intervals. Similarly, when the transition matrix is composed of auto-/crosscorrelations for larger lags, the method shows that variables which are correlated over large lags have greater factor loadings than those variables that are more significantly correlated over short lags. Two examples are provided which show how to implement the procedure and interpret the results.