Simulating an interaction between a categorical and linear variable

Question

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

Answer 1

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.

Comments

Thanks Kenneth, you have helped me remember what I did a few years ago!  Many thanks for your detailed answer.

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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