Customer Taste With Mixed Logit

28 Pages 6903 Words

I. Introduction
In situations where customers choose among products, a customer’s taste parameters
reflect the value that the customer places on each attribute of the products. Knowing the
tastes of individual customers, as well as the distribution of tastes in the population,
allows firms to design products that attract specific customers, recognize opportunities for
targeted marketing, and identify groups of customers with similar tastes. Prediction of
choices in new situations, which is important for assessing the market feasibility of new
products, is also improved with information on individual customers’ tastes.
Previously in this journal (Revelt and Train, 1998), we described discrete-choice
procedures to estimate the distribution of tastes in the population. In the present paper,
we extend these procedures, showing how the models can be used to make inferences
about the tastes of each sampled customer. The general procedure is similar to the
approaches of other studies, described in the next paragraph, that have inferred
observation-specific information from estimates of the overall distribution of this
information and the observation-specific dependent variable. Stated succinctly: The
probability of outcome yn for observation n, labeled ) | ( n n y P β , depends on information
n β that the researcher cannot observe. The unobserved information has density
) | ( θ βn g , characteristized by parameters θ. The marginal probability of outcome yn is
therefore = n n n n n d g y P y P β θ β β θ ) | ( ) | ( ) | ( , and the log-likelihood function for θ=
is
LL= n n y P ) | ( ln θ , which is maximized to provide an estimator of θ.= Inference about
each observation’s n β utilizes yn in relation to ) (⋅ g . In particular, the conditional density
3
of n β is
) | (
) | ( ) | ( ) , | (
θ
θ β β θ β
n
...