The Correlation Pairs to Matrix node is designed to take a list of Input Correlation Pairs and convert it into an equivalent Correlation Matrix.
The Correlation Matrix represents the degree of Horizontal Differentiation between Features, Benefits, Attributes, Levels, and Products. The Correlation Matrix may be used by a downstream node (such as the Matrix Distributions node or the Feature Generation node) to generate a set of Customer Distributions comprising the Willingness To Pay (WTP) of individual Virtual Customers.
For example, the list of Input Correlation Pairs would individually list the correlations between the 'A', 'B', and 'C' Customer Distributions as A:B, A:C, and B:C pairs. The Output Correlation Matrix would then be a 3x3 matrix of the same correlation values (doubles between -1.0 and +1.0) with row names and column names of A, B, and C. The matrix describes all the correlations between Customer Distribution A, Customer Distribution B, and Customer Distribution C.
The Input Correlation Pairs will first be converted into a clean and symmetrical Correlation Matrix. That means: (a) the diagonal A:A, B:B, C:C correlations will be set to 1.0; (b) correlation values will be limit-ranged to between -1.0 and +1.0; (c) missing correlations will be set to 0.0; and (d) the correlation for A:B will be set the same as the correlation for B:A. The correlation values a the bottom of the Input Correlation Pairs table will supersede correlation values at the top of the input table.
The purpose of this node is to provide the user with flexibility when setting and managing the Horizontal Differentiation (correlations) between Customer Distributions. A downstream Feature Generation node or a downstream Matrix Distribution node both requires an Input Correlation Matrix to generate a set of Customer Distributions. With this node, the user could edit the Correlation Pairs list, scale the Correlation Pairs list so that each Customer Distribution was more-or-less correlated with other Customer Distributions, or concatenate the Correlation Pairs list with another set of correlations developed elsewhere. Working with a list can be easier than working with a matrix.
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