A Bayesian Approach

From the Bayesian perspective what's going to be good is to say, look, each of these stores does have some unique characteristics, but all these stores have something in common. They're all coming from the same chain, they're all in the same general area, they're all dealing with consumers that are exposed to the same types of advertisements over time, so it makes a lot of sense to say that what's going on here is probably some kind of random coefficient model. And what I'm going to do is I'm going to incorporate this demographic information at this stage of the model, so I'm going to say that look, I'm going to go out and take micro-efficient so let's go out, I've got all the parameters from this model that I just gave, I've got this 192 parameters let's just go out and think about one element from this cross-price elasticity matrix. So let's pull out, like cross-pricing or the cross price elasticity of Minute Maid orange juice. So in this case, what I'm going to say is that this co-efficient is 's for an individual store and it's going to equal to some cost-effect across the stores, plus some kind of demographic effect, plus some type of random effect. Click here to see the mathematical form. So, in this case, you know, this random effect is really, you know, I'm going to go back to these individual store models, or something similar to it. If the demographic effect is strong and there's not a lot of random error here, it's going to look something like a fixed effects model. Or if the demographic effects are nil, and there's not a lot of random error variage across these parameters, then I'm going to back to this xx model case. The point is I'm trying to be inclusive of this, because I don't know exactly how strong these relationships are, for all the reasons I've just stated.

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