How can I incoporate choice set information in the multinomial logistic regression?

For example, I want to estimate the probability that the customer will buy the product. The total choice set consists of 5 products. However, for each customer, there may be only 2 or 3 probducts available. Suppose we know each customer's choice set. One way is to set different likelihood function for each customer and estimate the coefficients.

I find that 'mnrfir' doesn't have the input for choice set information. Is there any way to do this?

Answer 1

[Thiago Henrique Gomes Lobato]

What you expect to gain giving the set information? If you do it individually per costumer you lose almost all of your generalization capability. If you restringe yourself to a product set you have to first cluster all costumers that have had the same product set and then perform one logistic regression per cluster.

If you simply do a logistic regression with everything you may indeed assign probabilities for products that the customer can't even see, but you can either just ignore them (and make the analysis only for the products the person has) or, if the probability is extremely high, maybe even considering someway to offer the extra product to this specific customer.

If you really want to have the set information and use all the data you can add them as additionaly prediction variables, as example a 1x5 vector that you could concatenate to your prediction variables with 0 and 1 corresponding to a product belonging or not to the set of this specific costumer.