# Simulating an interaction between a categorical and linear variable

Hello

I am building an Excel simulator for a simple conjoint study.  I have specified an interaction between brand (3 levels) and price (linear).

My question is also very simple: How do I include the interaction between brand and price when summing up the utility scores?

If the variables were both part worth estimates, I would add the part-worth utilities for brand + price + brand-price interaction + everything else.

With the linear price, I get a single brand-price interaction term for each of the 3 brand levels.  Do I multiply this term by the (zero-centred) price before summing up with the utility partworths for the other attributes?

Many thanks
Tim
asked Apr 22, 2014

+1 vote

Tim,

Yes, your intuition is correct.

Your model is something like this:

(utility) = X1 * (Price estimate) + X2 * (Brand A estimate) + X1*X2*(Brand A x Price Interaction estimate) + ...

So in this case, X2 should be 0 or 1 (Is it Brand A or not?), and X1 should be price (zero-centered it sounds like).  That equation should continue on for each Brand and Brand/Price interaction. So for each interaction, there should be a 0 or 1 (is it this Brand or isn't it), a price level, and the estimate of the interaction effect, all multiplied together.
answered Apr 22, 2014 by Bronze (3,820 points)
selected Apr 23, 2014 by TJ
Thanks Kenneth, you have helped me remember what I did a few years ago!  Many thanks for your detailed answer.
So we  effectively create a separate linear term for each brand.  That makes sense for a brand-price interaction!
Thanks again for helping me structure the equation code