Modeling and Multivariate Methods - SAS

Chapter 16 Performing Choice Modeling 403
Introduction to Choice Modeling
Introduction to Choice Modeling
Choice modeling, pioneered by McFadden (1974), is a powerful analytic method used to estimate the
probability of individuals making a particular choice from presented alternatives. Choice modeling is also
called conjoint modeling, discrete choice analysis, and conditional logistic regression.
The Choice Modeling platform uses a form of conditional logistic regression. Unlike simple logistic
regression, choice modeling uses a linear model to model choices based on response attributes and not solely
upon subject characteristics. For example, in logistic regression, the response might be whether you buy
brand A or brand B as a function of ten factors or characteristics that describe you such as your age, gender,
income, education, etc. However, in choice modeling, you might be choosing between two cars that are a
compound of ten attributes such as price, passenger load, number of cup holders, color, GPS device, gas
mileage, anti-theft system, removable-seats, number of safety features, and insurance cost.
Choice Statistical Model
Parameter estimates from the choice model identify consumer utility, or marginal utilities in the case of a
linear utility function. Utility is the level of satisfaction consumers receive from products with specific
attributes and is determined from the parameter estimates in the model.
The choice statistical model is expressed as follows.
Let X[k] represent a subject attribute design row, with intercept
Let Z[j] represent a choice attribute design row, without intercept
Then, the probability of a given choice for the k'th subject to the j'th choice of m choices is
P i
[ jk]
where
exp( β' ( Xk [ ] ⊗ Zj []))
= ---------------------------------------------------------------
m
exp( β' ( Xk [ ] ⊗ Zl []))
l = 1
⊗ is the Kronecker row-wise product
the numerator calculates for the j'th alternative actually chosen, and
the denominator sums over the m choices presented to the subject for that trial.
Product Design Engineering
When engineers design a product, they routinely make hundreds or thousands of small design decisions.
Most of these decisions are not tested by prospective customers. Consequently, these products are not
optimally designed. However, if customer testing is not too costly and test subjects (prospective customers)
are readily available, it is worthwhile to test more of these decisions via consumer choice experiments.