MCI (version 1.2.0)

mci.shares: MCI market share/market area simulations

Description

This function calculates (local) market shares based on specified explanatory variables and their weighting parameters in a given MCI interaction matrix.

Usage

mci.shares(mcidataset, submarkets, suppliers, ..., mcitrans = "lc", interc = NULL)

Arguments

mcidataset

an interaction matrix which is a data.frame containing the submarkets, suppliers and the explanatory variables

submarkets

the column in the interaction matrix mcidataset containing the submarkets

suppliers

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, ...

mcitrans

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)

interc

if mcitrans = "ilc": logical argument that indicates if an intercept is included in the model (default interc = NULL)

Value

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 ($p_{ij}$).

Details

The input dataset, a 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). In the MCI model the dependent variable is the market share of the $j$ suppliers in the $i$ submarkets ($p_{ij}$), in which the shares are logically consistent (that means: 0 < $p_{ij}$ < 1, $\sum_{j=1}^n{p_{ij} = 1}$). 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").

References

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.

See Also

mci.fit, mci.transmat, mci.transvar, shares.total

Examples

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