I am trying to process the warning expressed earlier here on forum about that one should not be using dollars spent as chips allocated (even if we do them volume metric way with proper None allocation), because in principle any price attribute in the design would NOT be truly independent.
It sounded scary at first, but what it actually means? Independent variables are called independent because they are supposed to be low correlation to each other, not necessarily to the dependent variable.
Local dependence between price levels within an attribute does exist, but it will not change, will not inflate/deflate, because of type or format of dependent variable we chose.
Such price part-worths will be non zero correlation to each other anyway, just because of their nature. Some deal with it via linear coding, but lots of analysts still want to see price as part-worths. And we are not saying it would be wrong in principle...
So why it would be wrong to model share of budget as volumetric CBC where each unit is simply 1$?
- What is your budget for lunch?
- Which one of the following would you buy?
Option1: Meal=Burger, Price=$10.00
Option2: Meal=HotDog, Price=$3.00
Option3: Meal=Can of Kimchi, Price=$1.00
- I would buy Option2
- Okay we code your answer as ...
Option2 = 15% (or 3 chips) while None gets 85% (or 17 chips)...
I understand that utilities for such price attribute in dollar allocation exercise would come weird, like highest utility for highest price, because higher price takes away more dollars from the budget or wallet (aka % of chips) therefore would get higher share and higher utility. But utilities would not increase proportionally to nominal price as demand would be declining resulting in lagging share of wallet.
Aside from that formal weirdness with their relative magnitudes, would these price utilities along with other attributes & utilities still come relevant predicting proper shares of wallet in simulations?
I don't see the reason why they would not.
What am I missing?