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annotate toolboxes/FullBNT-1.0.7/KPMstats/partial_corr_coef.m @ 0:e9a9cd732c1e tip

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first hg version after svn
author wolffd
date Tue, 10 Feb 2015 15:05:51 +0000
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wolffd@0 1 function [r, c] = partial_corr_coef(S, i, j, Y)
wolffd@0 2 % PARTIAL_CORR_COEF Compute a partial correlation coefficient
wolffd@0 3 % [r, c] = partial_corr_coef(S, i, j, Y)
wolffd@0 4 %
wolffd@0 5 % S is the covariance (or correlation) matrix for X, Y, Z
wolffd@0 6 % where X=[i j], Y is conditioned on, and Z is marginalized out.
wolffd@0 7 % Let S2 = Cov[X | Y] be the partial covariance matrix.
wolffd@0 8 % Then c = S2(i,j) and r = c / sqrt( S2(i,i) * S2(j,j) )
wolffd@0 9 %
wolffd@0 10
wolffd@0 11 % Example: Anderson (1984) p129
wolffd@0 12 % S = [1.0 0.8 -0.4;
wolffd@0 13 % 0.8 1.0 -0.56;
wolffd@0 14 % -0.4 -0.56 1.0];
wolffd@0 15 % r(1,3 | 2) = 0.0966
wolffd@0 16 %
wolffd@0 17 % Example: Van de Geer (1971) p111
wolffd@0 18 %S = [1 0.453 0.322;
wolffd@0 19 % 0.453 1.0 0.596;
wolffd@0 20 % 0.322 0.596 1];
wolffd@0 21 % r(2,3 | 1) = 0.533
wolffd@0 22
wolffd@0 23 X = [i j];
wolffd@0 24 i2 = 1; % find_equiv_posns(i, X);
wolffd@0 25 j2 = 2; % find_equiv_posns(j, X);
wolffd@0 26 S2 = S(X,X) - S(X,Y)*inv(S(Y,Y))*S(Y,X);
wolffd@0 27 c = S2(i2,j2);
wolffd@0 28 r = c / sqrt(S2(i2,i2) * S2(j2,j2));