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Linear Coding and Interaction Effect. Thanks in advance!

Question1: In CBC/HB, when to define the level values
 1. what is suggested range? As in the Help file, it says ""Part worth coded attributes have values of 1, 0 or -1 in the design matrix. For best results, we also recommend that you scale your values for linear attributes such that when zero-centered, their range is about +1 to -1.  
 2. Any suggestion on how to define the exact level values for each level?

Question2: when there are 2 attributes tested, SKU and Price. And coding method for SKU is Part Worth; for Price is Linear. Also, there is interaction between these 2 attributes. In this case, how to use the raw Utility to estimate the Utility for combination of SKU1 and exact Price Point?
asked May 5, 2016 by weiwei
retagged May 5, 2016 by Walter Williams

1 Answer

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Best answer
I've done some simulation work regarding this question and while indeed a range of 1 unit for "linear variable specification" works just great in HB estimation (to obtain unbiased estimates and quick convergence), a range a bit smaller than that or a bit larger is still fine.  For example, a total range of 0.5 also is fine and a total range of 5 is fine too.  Just don't specify level values that have something extreme, such as a range of only 0.1 or less or a range of 10 or more.  (The priors settings in the software for linear coefficients are less appropriate for such extreme scaling of your X values in the design matrix.)

So, for example, if you are modeling price that was shown to respondents as 10000, 20000, and 30000 it would be fine to specify the price values for those three prices as 1, 2, 3 which would be convenient since in the market simulator specifying a 1 would correspond to a price of 10000 and specifying 3 would correspond to a price of 30000.

As for question 2, if you have part-worth brand and linear price plus the interaction effect, our software will report the utilities for the brands, the slope coefficient (linear term) for the main effect of price and a slope coefficient for each brand for the interaction term.  To compute the total utility for a specific brand at a specific price, take Ubrand + Price*MainEffectPrice + Price*InteractionEffectPrice

...where Ubrand is the utility for the specific brand, Price is the level coded price associated with the price such as 1 corresponding to 10000 in my example above, MainEffectPrice is the utility coefficient for the main effect of price, and InteractionEffectPrice is the utility coefficient for the interaction effect of price for the specific brand in question.
answered May 5, 2016 by Bryan Orme Platinum Sawtooth Software, Inc. (148,140 points)