Simulate sales by sampling from the posterior distribution

Question

After obtaining Partworths from CBC/HB software for each attribute level, I am interested in getting sales.

Instead of calculating share of preference for a specific product by creating a hypothetical scenario, is it possible for me to simulate sales by sampling from the posterior distribution? If yes, I am wondering how that can be done and what the steps I should follow?

Answer 1

Sales to me means estimates of Revenue (Price x share of preference x category volume).  

Predictions of share of preference and resulting volume or market share predictions to me seem like it needs to have the firm's product placed in competition against competing products plus the outside good (the None). Thus, I'm confused by your statement that you want to do something instead of calculating share of preference.

Comments

By using CBC/HB, the software will generate thousands of "utilities"  for each attribute level of each participant. I think that's what so called posterior. And then the software will choose a final "utilities" for me.

However, what the "Choice Simulator" did is that it allows the input of the final "utilities" and then calculate the share of preference for me. From my perspective, it's not a simulation process since there's no random draw.

My question before probably is not correct. What I really want to ask is whether there's a way I can truly "simulate" the share of preference (i.e. sales) by sampling from the thousands of "utilities".

Thank you in advance

---

Ah, indeed we "shortcut" the Bayesian posteriors for the market simulators we create for practitioners (we've found the results aren't much different for simulating on the granular draws versus the averaged draws per respondent).  Most practitioners don't care about the granularity of the draws and prefer the snappier "point estimates" (averages) of the draws for each respondent.  

Our HB software can indeed write out the many draws (after convergence) for each respondent.  With a bit of data formatting, you can "trick" our software into reading the draws into either our desktop market simulator or our online market simulator (using the file import options for reading in utilities).  If you do so, I don't recommend using more than about 100 or so draws per respondent, as the wait time can be considerable for running simulations.  For example, in your HB chain, if you have 10,000 draws after convergence for each respondent, you could select every 100th of those draws to select the 100 draws to use in the market simulator for each respondent.  

And, of course, our market simulators will now think you have 100x as many respondents, so the estimates of standard errors for the simulated shares will be incorrect and too small.

---

Thank you so much for the great response! If I trick the software to do this, then I will get 100 choice shares for a specific product for each participant, then I cannot do the individual level analysis, right?