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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 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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