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Class: CompactClassificationTree
Mean predictive measure of association for surrogate splits in decision tree
ma = meanSurrVarAssoc(tree)
ma = meanSurrVarAssoc(tree,N)
ma = meanSurrVarAssoc(tree) returns a matrix of predictive measures of association for the predictors in tree.
ma = meanSurrVarAssoc(tree,N) returns a matrix of predictive measures of association averaged over the nodes in vector N.
tree 
A classification tree constructed with fitctree, or a compact regression tree constructed with compact. 
N 
Vector of node numbers in tree. 
ma 

The predictive measure of association between the optimal split on variable i and a surrogate split on variable j is:
Here
P_{L} and P_{R} are the node probabilities for the optimal split of node i into Left and Right nodes respectively.
is the probability that both (optimal) node i and (surrogate) node j send an observation to the Left.
is the probability that both (optimal) node i and (surrogate) node j send an observation to the Right.
Clearly, λ_{i,j} lies from –∞ to 1. Variable j is a worthwhile surrogate split for variable i if λ_{i,j}>0.
Element ma(i,j) is the predictive measure of association averaged over surrogate splits on predictor j for which predictor i is the optimal split predictor. This average is computed by summing positive values of the predictive measure of association over optimal splits on predictor i and surrogate splits on predictor j and dividing by the total number of optimal splits on predictor i, including splits for which the predictive measure of association between predictors i and j is negative.
Find the mean predictive measure of association between the variables in the Fisher iris data:
load fisheriris obj = fitctree(meas,species,'surrogate','on'); msva = meanSurrVarAssoc(obj) msva = 1.0000 0 0 0 0 1.0000 0 0 0.4633 0.2500 1.0000 0.5000 0.2065 0.1413 0.4022 1.0000
Find the mean predictive measure of association averaged over the oddnumbered nodes in obj:
N = 1:2:obj.NumNodes; msva = meanSurrVarAssoc(obj,N) msva = 1.0000 0 0 0 0 1.0000 0 0 0.7600 0.5000 1.0000 1.0000 0.4130 0.2826 0.8043 1.0000