huff.attrac: Local optimization of attraction values in the Huff Model
In MCI: Multiplicative Competitive Interaction (MCI) Model

Description Usage Arguments Details Value Author(s) References See Also Examples

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

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)

`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 λ 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 λ 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`)

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 λ 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).

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.

Thomas Wieland

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

huff.fit, huff.shares, huff.decay

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)