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ACBC summed pricing: Is the utility function of price non-linear?

I am wondering wheter it makes sense to use the stepwise or non-linear function to get partworths for price-levels in ACBC.

Has anybody experience or knows literature about this / about a theory that requires this?

Thank you very much!
asked Aug 10, 2015 by steve

1 Answer

0 votes
Best way to check whether linear or non-linear specification of the summed price function in ACBC is better is with the use of holdout choice tasks.  However, unless you were planning ahead for this, it is probably the case that you don't have holdouts.

Without holdouts, you will probably need to use the "eyeball" test.  You cannot rely on internal fit statistics (RLH), because adding more terms to the model will nearly always increase the model fit with HB.  There isn't a handy "adjusted r-squared" statistic for HB like there is for OLS.

So, I would recommend trying the piecewise function for your summed price in ACBC.  First, examine the tab in the counting report that gives you the distribution of the actual prices for concepts shown to respondents.  You'll want to make sure you specify cutpoints where between those cutpoints (across people) you have "enough" observations to support estimation of betas for that line segment within the function.  How many is "enough" I don't know, sorry.  Maybe >30?  Maybe >50?

Recent research ("ACBC Revisited," 2013 Sawtooth Software Conference, Hoogerbrugge et al.) has shown that if you constrain price utilities to be negative (higher prices always preferred to lower prices), ACBC will support stable estimation of a great deal of cutpoints along the price continuum (assuming you've got ample sample size and "enough" observations of product concepts at the prices within each of the price segments).  Some researchers (like Hoogerbrugge et al. but also collabrated by Bob Goodwin and also us at Sawtooth Software) have tried 20 or even 30 cutpoints with good success under this approach.  Using lots of cutpoints gives you the opportunity to with the eyeball plot the resulting utilities and see whether there are points that appear to be elbows and drops along the price continuum representing non-linearity.  Specifying 20 or 30 cutpoints in your first investigation also helps you figure out where the specific points along the curve are that mark the elbows and drops.

(However, if the product concept you are studying might involve a legitimate region of the price curve with a positive price elasticity, where higher prices signal greater quantity demanded, then you might first want to run the model without price constraints.  Examples could include houses, luxury cars, locks, laser eye surgery, etc.  Sometimes, too cheap of a price is rejected by buyers for fear of quality problems.)

After you've had a chance to eyeball the plotted price curve under 20 or 30 cutpoints, you'll be in a better position to probably drop some of those cutpoints in regions of the curve that seem to represent on average a straight line.

Sorry if all this seems a bit qualitative (and long-winded).  Holdout choice tasks (if you had something like 5 holdout tasks or more) would give you the quantitative ammo you need to assess this more quantitatively.
answered Aug 10, 2015 by Bryan Orme Platinum Sawtooth Software, Inc. (134,015 points)
Thank you for these advices.