huff.shares: Huff model market share/market area simulations

Description

Calculating market areas/local market shares using the probabilistic market area model by Huff

Usage

huff.shares(huffdataset, origins, locations, attrac, dist, gamma = 1, lambda = -2, 
atype = "pow", dtype = "pow", gamma2 = NULL, lambda2 = NULL, check_df = TRUE)

Arguments

huffdataset

an interaction matrix which is a data.frame containing the origins, locations and the explanatory variables (attractivity, transport costs)

origins

the column in the interaction matrix huffdataset containing the origins (e.g. ZIP codes)

locations

the column in the interaction matrix huffdataset containing the locations (e.g. store codes)

attrac

the column in the interaction matrix huffdataset containing the attractivity variable (e.g. sales area)

dist

the column in the interaction matrix huffdataset containing the transport costs (e.g. travelling time or street distance)

gamma

a single numeric value of $\gamma$ for the exponential weighting of the attractivity variable (default: 1)

lambda

a single numeric value of $\lambda$ for the (exponential) weighting of distance (transport costs, default: -2)

atype

Type of attractivity weighting function: atype = "pow" (power function), atype = "exp" (exponential function) or atype = "logistic" (default: atype = "pow")

dtype

Type of distance weighting function: dtype = "pow" (power function), dtype = "exp" (exponential function) or dtype = "logistic" (default: dtype = "pow")

gamma2

if atype = "logistic" a second $\gamma$ parameter is needed

lambda2

if dtype = "logistic" a second $\lambda$ parameter is needed

check_df

logical argument that indicates if the given dataset is checked for correct input, only for internal use, should not be deselected (default: TRUE)

Value

Returns the input interaction matrix including the calculated shares (p_ij) as data.frame.

Details

The Huff model (Huff 1962, 1963, 1964) is the most popular spatial interaction model for retailing and services and belongs to the family of probabilistic market area models. The basic idea of the model, derived from the Luce choice axiom, is that consumer decisions are not deterministic but probabilistic, so the decision of customers for a shopping location in a competitive environment cannot be predicted exactly. The results of the model are probabilities for these decisions, which can be interpreted as market shares of the regarded locations ($j$) in the customer origins ($i$), $p_{ij}$. The model results can be regarded as an equilibrium solution (consumer equilibrium) with logically consistent market shares (0 < $p_{ij}$ < 1, $\sum_{j=1}^n{p_{ij} = 1}$). From a theoretical perspective, the model is based on an utility function with two explanatory variables ("attractivity" of the locations, transport costs between origins and locations), which are weighted by an exponent: $U_{ij}=A_{j}^\gamma d_{ij}^{-\lambda}$. But the weighting functions can also be exponential or logistic. This function computes the market shares from a given interaction matrix and given weighting parameters. The result matrix can be processed by the function shares.total() to calculate the total values (e.g. annual sales) and shares.

References

Huff, D. L. (1962): “Determination of Intra-Urban Retail Trade Areas”. Los Angeles : University of California.

Huff, D. L. (1963): “A Probabilistic Analysis of Shopping Center Trade Areas”. In: Land Economics, 39, 1, p. 81-90.

Huff, D. L. (1964): “Defining and Estimating a Trading Area”. In: Journal of Marketing, 28, 4, p. 34-38.

Loeffler, G. (1998): “Market areas - a methodological reflection on their boundaries”. In: GeoJournal, 45, 4, p. 265-272.

Wieland, T. (2015): “Nahversorgung im Kontext raumoekonomischer Entwicklungen im Lebensmitteleinzelhandel - Konzeption und Durchfuehrung einer GIS-gestuetzten Analyse der Strukturen des Lebensmitteleinzelhandels und der Nahversorgung in Freiburg im Breisgau”. Projektbericht. Goettingen : GOEDOC, Dokumenten- und Publikationsserver der Georg-August-Universitaet Goettingen. http://webdoc.sub.gwdg.de/pub/mon/2015/5-wieland.pdf

Examples

Run this code

data(Freiburg1)
data(Freiburg2)
# Loads the data

huff.shares (Freiburg1, "district", "store", "salesarea", "distance")
# Standard weighting (power function with gamma=1 and lambda=-2)

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