System and method for modeling affinity and cannibalization in customer buying decisions

A computer readable medium, comprising instructions that when executed by a processor causes the computer to perform the steps method of providing a computer model of customer response, comprising:

• providing in an affinity and cannibalization model a linear relationship between a first basket share function bi(t) describing transaction frequency for a first product Pi purchased and a second basket share function bj(t) describing transaction frequency for a second product Pj purchased as determined from data observable from customer responses, wherein the linear relationship includes a constant of proportionality between the first and second functions estimated as a difference between a probability of a customer purchasing Pi given that Pj is already selected for purchase, and a probability of a customer purchasing Pi given that Pj is not selected for purchase , given by the following equation:
• {acute over (α)}ij=Γ(Pi|Pj)ΓΓ(Pi|−Pj), where Γ( ) is the conditional probability on the first and second products Pi and Pj, and {acute over (α)}ij is the constant of proportionality;
• and
• solving for the constant of proportionality using data observable from customer responses—the constant of proportionality representing an affinity or cannibalization relationship between the first and second products.

A computer readable medium, comprising instructions that when executed by a processor causes the computer to perform the steps, comprising:

• providing in an affinity and cannibalization model a linear relationship between a first basket share function bi(t) describing transaction frequency for a first product Pi purchased and a second basket share function bj(t) describing transaction frequency for a second product Pj purchased as determined by data observable from customer responses, wherein the model includes a constant of proportionality between the first and second functions estimated as the difference between a probability of the customer purchasing Pi given that Pj is already selected for purchase, and a probability of a customer purchasing Pi given that Pj is not selected for purchase, given by the following equation:
• {acute over (α)}ij=Γ(Pi|Pj)−Γ(Pi|−Pj), where Γ( ) is the conditional probability on the first and second products Pi and Pj, and {acute over (α)}ij is the constant of proportionality;
• and
• solving for the constant of proportionality using the data observable from customer responses, the constant of proportionality representing an affinity or cannibalization relationship between the first and second products purchased.

A computer readable medium, comprising instructions that when executed by a processor causes the computer to perform the steps, comprising:

• relating a first basket share function bi(t) describing transaction frequency for a first product Pi purchased and a second basket share function bj(t) describing transaction frequency for a second product Pj purchased, by a constant of proportionality;
• estimating the constant of proportionality as a difference between a probability of the customer purchasing Pi given that Pj is already selected for purchase, and a probability of a customer purchasing Pi given that Pj is not selected for purchase, given by the following equation:
• {acute over (α)}ij=Γ(Pi|Pj)−Γ(Pi|−Pj), where Γ( ) is the conditional probability on the first and second products Pi and Pj, and {acute over (α)}ij is the constant of proportionality;
• and solving for the constant of proportionality using data observable from customer responses, wherein the constant of proportionality represents affinity or cannibalization relationship between the first and second products purchased.