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...enerate a data matrix X, say of order n*p, where n represents independent row-vectors and p correlated col vectors. Let the row representation be X = (X’_1, . . ., X’_n)’. I generate the differences of these vectors as D_{ab} = X_a – X_b, with different indices a and b, and similarly D_{cd} = X_c – X_d, and make a quadratic form D’_{ab}D_{cd} = A_{abcd}, say. Please note that, here a is unequal b, c is unequal d, a is unequal c, b is unequal d. By slightly shuffling the same set of vectors, I generate two other similar quadratic forms, say A_{acbd} and A_{adcb}, where the indices are again as u...

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...parameters (age, sex, income etc..) I call x_cust. Finally, the customer is confronted with two products (e.g. A and D; combinations may vary, I call each combination of two products a scenario) and asked which one he would like to buy. Bottom line: your data are in the format 1 x_A x_cust 0 x_D x_cust meaning that a certain customer chose product A against product D; similarly 1 x_C x_cust 0 x_B x_cust would mean that the customer choosing between C and B finally selected C. Every customer needs to choose a product in a variety of different scenarios. How would you analyze this kin...