Methods and apparatus to model consumer choice sourcing

Abstract

Methods and apparatus are disclosed to model consumer choices. An example method includes adding, with a processor, a set of products having respondent choice data to a base multinomial logit (MNL) model, the base MNL model including an item utility parameter and a price utility parameter associated with corresponding ones of products in the set of products, generating, with the processor, a number of copies of the base MNL model to form an aggregate model based on a number of the corresponding ones of products in the set of products, each one of the number of copies of the base MNL model exhibiting an effect of an independence of irrelevant alternatives (IIA) property, proportionally affecting interrelationships, with the processor, between dissimilar ones of the number of products in the set by inserting sourcing effect values in the aggregate model to be subtracted from respective ones of the item utility parameters, estimating, with the processor, the item utility parameters of the aggregate model based on the number of copies of the base MNL model and the respondent choice data, and calculating, with the processor, the choice probability for the corresponding ones of the products in the set of products based on the estimated item utility parameters and the price utility parameters.

What is claimed is: 
     
         1 . A computer implemented method to calculate a choice probability, comprising:
 adding, with a processor, a set of products having respondent choice data to a base multinomial logit (MNL) model, the base MNL model including an item utility parameter and a price utility parameter associated with corresponding ones of products in the set of products;   generating, with the processor, a number of copies of the base MNL model to form an aggregate model based on a number of the corresponding ones of products in the set of products, each one of the number of copies of the base MNL model exhibiting an effect of an independence of irrelevant alternatives (IIA) property;   proportionally affecting interrelationships, with the processor, between dissimilar ones of the number of products in the set by inserting sourcing effect values in the aggregate model to be subtracted from respective ones of the item utility parameters;   estimating, with the processor, the item utility parameters of the aggregate model based on the number of copies of the base MNL model and the respondent choice data; and   calculating, with the processor, the choice probability for the corresponding ones of the products in the set of products based on the estimated item utility parameters and the price utility parameters.   
     
     
         2 . A method as defined in  claim 1 , wherein inserting the sourcing effect values reduces the effect of the IIA property of the aggregate model. 
     
     
         3 . A method as defined in  claim 1 , further comprising converging the sourcing effect values from initially random values via the estimating. 
     
     
         4 . A method as defined in  claim 3 , further comprising building a closed-form choice probability solution based on the converged sourcing effect values. 
     
     
         5 . A method as defined in  claim 1 , wherein estimating the item utility values comprises at least one of performing a maximum likelihood estimation, performing a Bayes estimation, or performing a minimum squared error estimation. 
     
     
         6 . A method as defined in  claim 1 , wherein the aggregate model comprises a number of rows equal to the number of the corresponding ones of products in the set of products. 
     
     
         7 . A method as defined in  claim 1 , wherein inserting the sourcing effect values in the aggregate model to be subtracted from respective ones of the item utility parameters generates a product offset value for respective ones of products in the set of products. 
     
     
         8 . A method as defined in  claim 7 , wherein corresponding columns of the number of rows comprises a product quantity based on a mathematical product of (a) the product offset value and (b) a corresponding price utility parameter. 
     
     
         9 . A method as defined in  claim 8 , wherein the corresponding columns intersect corresponding ones of the number of rows of the aggregate model to reflect a relationship between (a) a product of the corresponding column and (b) a product of the corresponding row. 
     
     
         10 . An apparatus to calculate a choice probability, comprising:
 a multinomial logit (MNL) engine to add a set of products having respondent choice data to a base MNL model, the MNL engine to include an item utility parameter and a price utility parameter associated with corresponding ones of products in the set of products;   an aggregate building engine to generate a number of copies of the base MNL model to form an aggregate model based on a number of the corresponding ones of products in the set of products, each one of the number of copies of the base MNL model exhibiting an effect of an independence or irrelevant alternatives (IIA) property;   a sourcing modifier to proportionally affect interrelationships between dissimilar ones of the number of products in the set by inserting sourcing effect values in the aggregate model to be subtracted from respective ones of the item utility parameters;   an estimator to estimate the item utility parameters of the aggregate model based on the number of copies of the base MNL model and the respondent choice data; and   a simulation engine to calculate the choice probability for the corresponding ones of the products in the set of products based on the estimated item utility parameters and the price utility parameters.   
     
     
         11 . An apparatus as defined in  claim 10 , wherein the sourcing modifier is to reduce the effect of the IIA property of the aggregate model. 
     
     
         12 . An apparatus as defined in  claim 10 , wherein the estimator is to converge the sourcing effect values from initially random values. 
     
     
         13 . An apparatus as defined in  claim 12 , further comprising a measure of fit engine to determine a fit value between the respondent choice data and the converged sourcing effect values. 
     
     
         14 . An apparatus as defined in  claim 13 , wherein the measure of fit engine is to stop the estimator when a threshold measure of fit value is identified. 
     
     
         15 . An apparatus as defined in  claim 12 , wherein the estimator is to build a closed-form choice probability solution based on the converged sourcing effect values. 
     
     
         16 . An apparatus as defined in  claim 10 , wherein the estimator is to use at least one of a maximum likelihood estimation, a Bayes estimation, or a minimum squared error estimation. 
     
     
         17 . An apparatus as defined in  claim 10 , further comprising a matrix engine to generate a number of rows equal to the number of the corresponding ones of products in the set of products. 
     
     
         18 . A tangible machine-readable storage medium comprising instructions that, when executed, cause a sourcing engine to, at least:
 add a set of products having respondent choice data to a base multinomial logit (MNL) model, the base MNL model including an item utility parameter and a price utility parameter associated with corresponding ones of products in the set of products;   generate a number of copies of the base MNL model to form an aggregate model based on a number of the corresponding ones of products in the set of products, each one of the number of copies of the base MNL model exhibiting an effect of an independence of irrelevant alternatives (IIA) property;   proportionally affect interrelationships between dissimilar ones of the number of products in the set by inserting sourcing effect values in the aggregate model to be subtracted from respective ones of the item utility parameters;   estimate the item utility parameters of the aggregate model based on the number of copies of the base MNL model and the respondent choice data; and   calculate the choice probability for the corresponding ones of the products in the set of products based on the estimated item utility parameters and the price utility parameters.   
     
     
         19 . A machine-readable storage medium as defined in  claim 18 , further comprising instructions that, when executed, cause the sourcing engine to reduce the effect of the IIA property of the aggregate model in response to inserting the sourcing effect values. 
     
     
         20 . A machine-readable storage medium as defined in  claim 18 , further comprising instructions that, when executed, cause the sourcing engine to converge the sourcing effect values from initially random values during the estimation. 
     
     
         21 . A machine-readable storage medium as defined in  claim 20 , further comprising instructions that, when executed, cause the sourcing engine to build a closed-form choice probability solution based on the converged sourcing effect values. 
     
     
         22 . A machine-readable storage medium as defined in  claim 18 , further comprising instructions that, when executed, cause the sourcing engine to estimate via at least one of a maximum likelihood estimation, a Bayes estimation, or a minimum squared error estimation. 
     
     
         23 . A machine-readable storage medium as defined in  claim 18 , further comprising instructions that, when executed, cause the sourcing engine to subtract the sourcing effect values from respective ones of the item utility parameters to generate a product offset value for respective ones of products in the set of products. 
     
     
         24 . A machine-readable storage medium as defined in  claim 23 , further comprising instructions that, when executed, cause the sourcing engine to calculate a mathematical product of (a) the product offset value and (b) a corresponding price utility parameter.