Q: Earlier when Rob asked why you included price in the model you said there were two types of people--those that respond to price more and the other, more independent kind, who don't care and will pay whatever price. But your model is linear. Wouldn't a mixture model be more appropriate and capture more of what you care about?

A: Right, this is at the aggregate store level, so the difference here is that you're thinking about it at this individual level and once you start aggregating these people you don't have these well-defined extremes in the population. If you did that you would have this bimodal distribution, but now you've got all these extremes -- for some people it's important some of the time and when you start looking at it you still get some normal effects. When you look at it at the aggregate level, a lot of these individual behaviors that explain how prices behave aren't applied at the aggregate level. So there's this difference of aggregate and individual level.

Q: If you look at customers in the store, whether the distribution was bimodal or unimodal to reflect that individual customers have different cutoffs -- it does not seem to be quite captured in your model.

A: I think it goes back to the other point, maybe my model is inadequate, it's different to say yes, there are a lot of possibilities for the model, but the point is that the own price is the most important variable model and that drives most of the action that you see in movement. A lot of these other effects are also important and I think it's just more thinking about them as extensions, but the point is, I think I've captured the essence to the problem; if you want to start going beyond that, I think you're right. There are a lot of reasons you might be interested in some of these other effects, but to get at those, you really would need a different type of data set. That's whole point of the way I phrased the problem -- let's think about the information set that's available to the retailer. All this is internal data, something they've got easy access to and I think that's really what's important, that they're making the decisions.

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