Logistic Regression And Discrete Choice Models

Design of Experiments for Logistic Regression:

a)      Recently, increased attention has been given to the planning of experiments to support logistic regression and discrete choice methoding.

b)      Like usual design of experiments, part of planning is selecting which prototype systems should be constructed for testing. An added complication in discrete choice modeling is how to present the prototype system alternatives to decision-makers. “Choice sets” refer to combinations of prototypes that are presented from which the people in the experiment select their choices.

Example (Product Pricing) Develop and experimental plan with the following properties. Threeprototypes (short, medium, and tall) are required. Two prices ($10, $15) are tested.Three people are involved in choosing (Frank, Neville, and Maria). People neverchoose between more than two alternatives at a time.

Answer: There are many possible plans. One solution is shown in Table. Note that, with the restriction on the choice set size, this becomes a discrete choice problem.

For example, Sandor and Wedel (2001) used the so-called “Db-error criterion” to generate lists of recommended prototypes and arrangements for their presentation to representative samples of consumers.

 The Db-error criterion is analogous to the D-optimality objective (pick the array by maximizing |X′X|) in response surface contexts because it is based on the maximization of the determinant of the fitted model design matrix. Like D-optimal designs,

experimental plans that maximize the Db-error criterion might, in general, be expected to lead to models that have high prediction errors because the fit model form differs from the true model form, i.e., bias. Therefore, an open research topic

is the selection of experimental designs that fosters low prediction errors even if there is bias.