huff.attrac {MCI}

Local optimization of attraction values in the Huff Model

Description

This function optimizes the attraction values of suppliers/location in a given Huff interaction matrix to fit empirically observed total values (e.g. annual sales) and calculates market shares/market areas

Usage

huff.attrac(huffdataset, origins, locations, attrac, dist, 
lambda = -2, dtype = "pow", lambda2 = NULL, 
localmarket_dataset, origin_id, localmarket, 
location_dataset, location_id, location_total, 
tolerance = 5, output = "matrix", show_proc = FALSE, 
check_df = TRUE)

Arguments

huffdataset

an interaction matrix which is a data.frame containing the origins, locations and the explanatory variables (attraction, 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 attraction variable (e.g. sales area)

dist

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

lambda

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

dtype

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

lambda2

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

localmarket_dataset

A data.frame containing the origins saved in a column which has the same name as in huffdataset and another column containing the local market potential

origin_id

the column in the dataset localmarket_dataset containing the origins (e.g. statistical districts, ZIP codes)

localmarket

the column in the dataset localmarket_dataset containing the local market potential (e.g. purchasing power, number of customers)

location_dataset

A data.frame containing the suppliers/locations and their observed total values

location_id

the column in the dataset location_dataset containing the locations (e.g. store codes), j, according to the codes in huffdataset

location_total

the column in the dataset location_dataset containing the observed total values of suppliers/locations, T_{j,obs} (e.g. annual sales, total number of customers)

tolerance

accepted value of absolute percentage error between observed (T_{j,obs}) and modeled total values (T_{j,exp}) to skip a local optimization of location/supplier j

output

Type of function output: output = "matrix" returns a Huff interaction matrix with the optimized attraction values and the expected market shares/market areas. If output = "total", the old (observed) and the new (expected) total values are returned. If output = "attrac", the optimized attraction values are returned.

show_proc

logical argument that indicates if the function prints messages about the state of process during the work (e.g. “Processing variable xyz ...” or “Variable xyz is regarded as dummy variable”). Default: show_proc = FALSE (messages off)

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)

Details

In many cases, only total empirical values of the suppliers/locations can be used for market area estimation. This function fits the Huff model not by estimating the parameters but by optimizing the attraction variable (transport cost weighting by \lambda is given) using an optimization algorithm based on the idea of the local optimization of attraction algorithm developed by Guessefeldt (2002) and other model fit approaches. This function consists of a single optimization of every supplier/location. Note that the best results can be achieved by repeating the algorithm while evaluating the results (see the function huff.fit(), which extends this algorithm to a given number of iterations).

Value

The function output can be controlled by the function argument output. If output = "matrix" the function returns a Huff interaction matrix with the optimized attraction values and the expected market shares/market areas. If output = "total", the old (observed) and the new (expected) total values are returned. If output = "attrac", the optimized attraction values are returned. All results are data.frame.

Author(s)

Thomas Wieland

References

Guessefeldt, J. (2002): “Zur Modellierung von raeumlichen Kaufkraftstroemen in unvollkommenen Maerkten”. In: Erdkunde, 56, 4, p. 351-370.

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

See Also

huff.fit, huff.shares, huff.decay

Examples

data(Freiburg1)
data(Freiburg2)
data(Freiburg3)
# Loading the three Freiburg datasets

# NOTE: This may take a while!
# huff.attrac(Freiburg1, "district", "store", "salesarea", "distance", lambda = -2, dtype= "pow",
# lambda2 = NULL, Freiburg2, "district", "ppower", Freiburg3, "store", "annualsales", 
# tolerance = 5, output = "total")
# Local optimization of store attraction using the function huff.attrac()
# returns a data frame with total values (observed and expected after optimization)