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The Huff Model is an established theory in spatial analysis. It is based on the principle that the probability of a given consumer visiting and purchasing at a given site is a function of the distance to that site, its attractiveness, and the distance and attractiveness of competing sites.

This specific model, in the area of spatial interaction research, was refined and made operational by Dr. David Huff of the University of Texas. The advent of powerful desktop computers has made it possible to apply the model.

Where:- P
_{ij}= the probability of consumer j shopping at store i. - W
_{i}= a measure of the attractiveness of each store or site i. - D
_{ij}= the distance from consumer j to store or site i. - a = an exponent applied to distance so the probability of distant sites is dampened. It usually ranges between 1.5 and 2.

In practice, census polygons—for example, block groups—are substituted for individual consumers. The calculated probability for each polygon is multiplied by a data element in the polygon database—for example, households and dollars spent on groceries. This measure can be summarized to provide an estimate of the total. Some measure of size, such as gross leasable area (GLA), is often used as a substitute for attractiveness.

A site has many attributes that make it attractive to consumers. Attractiveness can be computed as a function of many attributes. For a retail store, these are its retail floor space, number of parking spaces, and product pricing. Attractiveness of a car dealership may be a function of its display area, frontage, and advertisement. The attractiveness of an office building may be a function of the number of offices currently located within it. Attractiveness is expressed as one number that combines all the factors that make a center attractive. This number is usually referred to as an index. This index can also be derived by counting how many people come to that destination or by conducting a consumer survey.

You can control the distance the Huff Model will extend. Enter a value that will encompass all your competitors. You can use the Measure tool to estimate the distance. The distance units can be either miles or kilometers.

## Huff Model Calibration

The Huff Model Calibration tool calculates the exponent values for attractiveness and distance variables. which allow you to adjust and refine your settings. The result is a file that contains the exponent value for any attractiveness variable—for example, sales and distance variable.

When using the Huff Model tool without calibration, the default exponent values are arbitrarily set at 1 and 1.5 and may not apply to the trade area for which you are modeling. Calibration requires an existing store or facility layer, a customer layer, and a layer defining potential sales. Employing user-defined exponent values allows you to fine-tune the exponent values of a Huff model, thus providing a more accurate, predictive model.

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The exponential function is typically used for computing interactions over a small distance, such as within a city.

## Distance-decay function

The perception of how far away a destination is may not be a linear function of distance. People are more likely to shop at a place close to home than one far away. Distance is viewed as a nonlinear deterrent to movement. This phenomenon can be modeled using a distance-decay function. The use of a power distance-decay function is borrowed from Newton's law of gravitation, from which the term gravity model is derived. A distance-decay parameter, symbolized by the Greek letter beta, can be used to exaggerate the distance to destinations. Some activities, such as grocery shopping, have a large exponent, indicating that people will travel only a short distance for such things. Other activities, such as furniture shopping, have a small exponent, because people are willing to travel farther to shop for furniture.

All Huff Model inputs, exponents, trade area size, and results require detailed analysis by someone who is experienced in the operation of such a model. Some calibration is always required to account for other factors such as leakage; that is, when people don't buy all their groceries at food stores, some of that spending leaks to other trade areas such as convenience stores, farmer's markets, and online grocery delivery options.