attributes of individuals in discrete choice tasks

#1
Hello stat talkers, :wave:
I'm currently working on a marketing (discrete choice) project concerning brand choice and I stumbled upon some questions I would like to ask here.
in Louviere et al "stated choice methods" page 63 the authors write: "...any variable that is not an attribute of an alternative of the choice set (e.g. not attribute of brand A, B, or C ; such as the individuals gender), cannot be included as a seperate variable in all utility expressions, since it does not vary across the alternatives(brands). ... To enable a non-brand attribute to be included in all utility expressions, it must be interacted with an alternative-specific attribute."

Question A: What is the consequence of these variables not variing across alternatives in terms of estimation of parameters for the model? Does somebody have an idea where to read more on specifically this matter?
Question B: Does this mean that when I am interested in if women are more likely to choose brand A, B, or C, I cannot include gender in all utility-specifications, yet if I include the gender price interaction (to see how much women pay more for a certain brand) than I can include my gender AND the gender*price interaction? (I do have to include the main effects when using interactions in a regression context)
Another interpretation of what the authors say is that I should only include the interaction (instead of the two variables: one brand-specific, one individual-specific) but only do so if the created variable is interpretable (e.g. price / income could be relative cost).

I would be happy if some of you would share your thoughts of this with me.
from Germany
alex
 
#3
Interpretation

Basically, your model will cover what attributes of the product influence choice. You can make the product blue or pink, but you can’t make the subject male or female. When they are talking about interactions is this context, they are really talking about different models for different kinds of people. So, I would look at subgroups of my respondents and see if their utility scores are dramatically different. If they are, I would create separate models for the subgroups. So, if boys like blue sweaters and girls like pink ones, we have two models. If you want to sell to boys make blue sweaters if you want to sell to girls make pink ones. Often I will combine the models by allowing the client to designate a population distribution. Essentially, I would produce separate models for boys and girls then produce a weighted average, based on what my client believes to be the distribution in his target audience.

There is probably a more statistically elegant way to deal with interactions. However, this is simple, useful and more importantly simple to explain to a be used by a non-math savvy salesman.
 
#4
Re: Interpretation

Hello John,
thank you for your suggestions! For a practitioner this would definitely be a way to ship around the problem adressed by the authors. My project is actually my thesis paper and for what I have chosen to do in my research unfortunately I will have to find a "statistically elegant way" rather than the practical approach you suggested ;)
Fortunately the Kenneth Train book explains in great detail and with very comprehensible examples the issues about individual attributes. So I know now how to include them. Yet you are right in suggesting a "two model approach" (or statistically more elegant: a mixed logit) in case I find significant signs of heteroscedasticity.

cheers
alex