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st: Huff Model in Stata


From   "Dimitriy V. Masterov" <dvmaster@gmail.com>
To   Statalist <statalist@hsphsun2.harvard.edu>
Subject   st: Huff Model in Stata
Date   Wed, 30 Nov 2011 16:50:39 -0500

The Huff Model is a spatial interaction model that calculates
gravity-based probabilities of consumers at each origin location
patronizing each store in the store dataset. The outcome variable
p_{ij} is the probability that consumers located at site i will choose
to shop at store j is given by the following formula:

p_{ij}=\frac{a_{j}^{\alpha }d_{ij}^{-\beta }\varepsilon _{ij}}{%
\sum_{i=1}^{n}a_{j}^{\alpha }d_{ij}^{-\beta }\varepsilon _{ij}}

where
a_{j} is a measure of attractiveness of store j, such as square footage
d_{ij} is the driving distance from customers in area i to store j
\varepsilon_{ij} is the error term.
\alpha is an attractiveness parameter to be estimated
\beta is the distance decay parameter to be estimated
n is the total number of stores near customers in area i, which varies by i

If the TeX notation is confusing, the model is described here (without
the error term):

http://www.directionsmag.com/articles/retail-trade-area-analysis-using-the-huff-model/123411

I have two related questions.

First, I only observe revenue and the number of orders, so that I
can't estimate p_{ij} with the proportion of consumers who purchased
the product in area i. I could make the outcome variable binary
(purchased or not), but I think that may not be quite correct.

Second, once I can redefine the outcome in a suitable way, is there a
way to estimate this model in Stata? There's at least a couple ways to
estimate \alpha and \beta using OLS by taking logs and normalizing by
the geometric means (described in this gated paper
http://www.jstor.org/pss/183931 or this ungated one,
http://www.esri.com/library/whitepapers/pdfs/calibrating-huff-model.pdf),
but I am not sure how to do that with a binary outcome variable.

Any advice would be greatly appreciated.

DVM
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