This function calculates (local) market shares based on specified explanatory variables and their weighting parameters in a given MCI interaction matrix.
mci.shares(mcidataset, submarkets, suppliers, ..., mcitrans = "lc", interc = NULL)an interaction matrix which is a data.frame containing the submarkets, suppliers and the explanatory variables
the column in the interaction matrix mcidataset containing the submarkets
the column in the interaction matrix mcidataset containing the suppliers
the column(s) of the explanatory variable(s) (at least one), numeric and positive (or dummy [1,0]), and their weighting parameter(s). The parameter(s) must follow the particular variable(s): mcivariable1, parameter1, ...
defines if the regular multiplicative formula is used or the inverse log-centering transformation where the explanatory variables are MCI-transformed and linked by addition in an exponential function instead of multiplication. This transformation is necessary if an intercept is included in the model and/or if dummy variables are used as explanatories (default: mcitrans = "lc", which indicates the regular log-centering transformation)
if mcitrans = "ilc": logical argument that indicates if an intercept is included in the model (default interc = NULL)
The function mci.shares() returns the input interaction matrix (data.frame) with new variables/columns, where the last one (p_ij) is the one of interest, containing the (local) market shares of the \(j\) suppliers in the \(i\) submarkets (\(p_{ij}\)).
In this function, the input dataset (MCI interaction matrix) is used for a calculation of (local) market shares (\(p_{ij}\)), based on (at least one) given explanatory variable(s) and (a) given weighting parameter(s). If an intercept is included in the model and/or if dummy variables are used as explanatories, the inverse log-centering transformation by Nakanishi/Cooper (1982) has to be used for simulations (mcitrans = "ilc").
Huff, D. L./Batsell, R. R. (1975): “Conceptual and Operational Problems with Market Share Models of Consumer Spatial Behavior”. In: Advances in Consumer Research, 2, p. 165-172.
Huff, D. L./McCallum, D. (2008): “Calibrating the Huff Model Using ArcGIS Business Analyst”. ESRI White Paper, September 2008. https://www.esri.com/library/whitepapers/pdfs/calibrating-huff-model.pdf
Nakanishi, M./Cooper, L. G. (1974): “Parameter Estimation for a Multiplicative Competitive Interaction Model - Least Squares Approach”. In: Journal of Marketing Research, 11, 3, p. 303-311.
Nakanishi, M./Cooper, L. G. (1982): “Simplified Estimation Procedures for MCI Models”. In: Marketing Science, 1, 3, p. 314-322.
Wieland, T. (2013): “Einkaufsstaettenwahl, Einzelhandelscluster und raeumliche Versorgungsdisparitaeten - Modellierung von Marktgebieten im Einzelhandel unter Beruecksichtigung von Agglomerationseffekten”. In: Schrenk, M./Popovich, V./Zeile, P./Elisei, P. (eds.): REAL CORP 2013. Planning Times. Proceedings of 18th International Conference on Urban Planning, Regional Development and Information Society. Schwechat. p. 275-284. http://www.corp.at/archive/CORP2013_98.pdf
Wieland, T. (2015): “Raeumliches Einkaufsverhalten und Standortpolitik im Einzelhandel unter Beruecksichtigung von Agglomerationseffekten. Theoretische Erklaerungsansaetze, modellanalytische Zugaenge und eine empirisch-oekonometrische Marktgebietsanalyse anhand eines Fallbeispiels aus dem laendlichen Raum Ostwestfalens/Suedniedersachsens”. Geographische Handelsforschung, 23. 289 pages. Mannheim : MetaGIS.
# NOT RUN {
data(Freiburg1)
data(Freiburg2)
# Loads the data
mynewmatrix <- mci.shares(Freiburg1, "district", "store", "salesarea", 1, "distance", -2)
# Calculating shares based on two attractivity/utility variables
mynewmatrix_alldata <- merge(mynewmatrix, Freiburg2)
# Merge interaction matrix with district data (purchasing power)
shares.total (mynewmatrix_alldata, "district", "store", "p_ij", "ppower")
# Calculation of total sales
# }
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