| Title: | Multiplicative Competitive Interaction (MCI) Model |
|---|---|
| Description: | Market area models are used to analyze and predict store choices and market areas concerning retail and service locations. This package implements two market area models (Huff Model, Multiplicative Competitive Interaction Model) into R, while the emphases lie on 1.) fitting these models based on empirical data via OLS regression and nonlinear techniques and 2.) data preparation and processing (esp. interaction matrices and data preparation for the MCI Model). |
| Authors: | Thomas Wieland |
| Maintainer: | Thomas Wieland <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.3.3 |
| Built: | 2024-07-27 06:11:03 UTC |
| Source: | CRAN |
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. Thus, 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 (interaction probabilities), which can be interpreted as market shares of the regarded locations () in the customer origins (), (local market shares). The model results can be regarded as an equilibrium solution (consumer equilibrium) with logically consistent market shares (0 < < 1, ). From a theoretical perspective, the model is based on an utility function with two explanatory variables ("attraction" of the locations, transport costs between origins and locations), which are weighted by an exponent: . The probability is calculated as the utility quotient: . The distance decay function reflecting the disutility of transport costs can also be exponential or logistic. The model can also be used for the estimation of market areas based on location sales or total patronage using nonlinear optimization algorithms. When the "real" local market shares were observed, the model can be parametrized by using the Multiplicative Competitive Interaction (MCI) Model.
The Multiplicative Competitive Interaction (MCI) Model (Nakanishi/Cooper 1974, 1982) is an econometric model for analyzing market shares and/or market areas in a competitive environment where the market is divided in submarkets (e.g. groups of customers, time periods or geographical regions) and served by suppliers (e.g. firms, brands or locations). The dependent variable of the model is , the market shares of in , which are logically consistent (0 < < 1, ). The market shares depend on the attraction/utility of the alternative in the choice situation/submarket , or . The model is nonlinear (multiplicative attractivity/utility function with exponential weighting) but can be transformed to be estimated by OLS (ordinary least squares) regression using the multi-step log-centering transformation. Before the log-centering transformation can be applied, which is required for fitting the model, also a re-arrangement of the raw data (e.g. household surveys) in an interaction matrix is necessary. An interaction matrix is a special case of table where every row is an x combination and the market shares of in () are saved in a new column (Linear table, the opposite of crosstable). The MCI model is a special case of market share model (which fulfills the requirement of logical consistency in the output), but can especially be used as a market area model (or spatial MCI model) in retail location analysis since it is an econometric approach to estimate the parameters of the Huff model mentioned above.
The functions in this package include fitting the MCI model, MCI shares simulations, the log-centering transformation of MCI datasets, creation of interaction matrices from empirical raw data and several tools for data preparation. Additionally, the package provides applications for the Huff model, including a nonlinear optimization algorithm to estimate market areas on condition that total market areas (customers, sales) of the stores/locations are known.
Thomas Wieland
Maintainer: Thomas Wieland [email protected]
Cooper, L. G./Nakanishi, M. (2010): “Market-Share Analysis: Evaluating competitive marketing effectiveness”. Boston, Dordrecht, London : Kluwer (first published 1988). E-book version from 2010: http://www.anderson.ucla.edu/faculty/lee.cooper/MCI_Book/BOOKI2010.pdf
Cliquet, G. (2006): “Retail Location Models”. In: Cliquet, G. (ed.): Geomarketing. Models and Strategies in Spatial Marketing. London : ISTE. p. 137-163.
Guessefeldt, J. (2002): “Zur Modellierung von raeumlichen Kaufkraftstroemen in unvollkommenen Maerkten”. In: Erdkunde, 56, 4, p. 351-370.
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.
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
Loeffler, G. (1998): “Market areas - a methodological reflection on their boundaries”. In: GeoJournal, 45, 4, p. 265-272.
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.
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
Preliminary stage of an interaction matrix: Distance matrix for 19 origins and six DIY (do-it-yourself) stores ( = 19 submarkets x = 6 suppliers) in a German research area.
data("DIY1")data("DIY1")
A data frame with 114 observations on the following 3 variables.
i_origina factor with 19 levels representing the origins
j_destinationa factor with six levels representing the DIY stores
t_ij_mina numeric vector containing the travel time (in minutes) from the origins to the stores
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.
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.
data(DIY1) data(DIY2) data(DIY3) # Loading the three DIY store datasets DIY_alldata <- merge (DIY1, DIY2, by.x = "j_destination", by.y = "j_destination") # Add store data to distance matrix huff_DIY <- huff.shares (DIY_alldata, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, lambda = -2) # Calculating Huff local market shares # Gamma = 1, Lambda = -2 huff_DIY <- merge (huff_DIY, DIY3, by.x = "i_origin", by.y = "district") # Add data for origins huff_DIY_total <- shares.total (huff_DIY, "i_origin", "j_destination", "p_ij", "population") # Calculating total market areas (=sums of customers) colnames(DIY3) <- c("district", "pop") # Change column name to "pop" (must be other name) huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "bisection", iterations = 10) # Iterative search for the best lambda value using bisection # Output: gamma and lambda huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "bisection", iterations = 10, output = "iterations", show_proc = TRUE) # Same procedure, output: single iterations huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "compare", iterations = 10, output = "iterations", show_proc = TRUE, plotVal = TRUE) # Using compare method, output: single iterations and plotdata(DIY1) data(DIY2) data(DIY3) # Loading the three DIY store datasets DIY_alldata <- merge (DIY1, DIY2, by.x = "j_destination", by.y = "j_destination") # Add store data to distance matrix huff_DIY <- huff.shares (DIY_alldata, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, lambda = -2) # Calculating Huff local market shares # Gamma = 1, Lambda = -2 huff_DIY <- merge (huff_DIY, DIY3, by.x = "i_origin", by.y = "district") # Add data for origins huff_DIY_total <- shares.total (huff_DIY, "i_origin", "j_destination", "p_ij", "population") # Calculating total market areas (=sums of customers) colnames(DIY3) <- c("district", "pop") # Change column name to "pop" (must be other name) huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "bisection", iterations = 10) # Iterative search for the best lambda value using bisection # Output: gamma and lambda huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "bisection", iterations = 10, output = "iterations", show_proc = TRUE) # Same procedure, output: single iterations huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "compare", iterations = 10, output = "iterations", show_proc = TRUE, plotVal = TRUE) # Using compare method, output: single iterations and plot
The six DIY stores in a German research area, their corresponding DIY chain and sales area.
data("DIY2")data("DIY2")
A data frame with 6 observations on the following 3 variables.
j_destinationa factor with six levels representing the DIY stores
j_chaina factor with five levels containing the store chain
A_j_salesarea_sqma numeric vector for the sales area of the DIY stores in sqm
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.
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.
data(DIY1) data(DIY2) data(DIY3) # Loading the three DIY store datasets DIY_alldata <- merge (DIY1, DIY2, by.x = "j_destination", by.y = "j_destination") # Add store data to distance matrix huff_DIY <- huff.shares (DIY_alldata, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, lambda = -2) # Calculating Huff local market shares # Gamma = 1, Lambda = -2 huff_DIY <- merge (huff_DIY, DIY3, by.x = "i_origin", by.y = "district") # Add data for origins huff_DIY_total <- shares.total (huff_DIY, "i_origin", "j_destination", "p_ij", "population") # Calculating total market areas (=sums of customers) colnames(DIY3) <- c("district", "pop") # Change column name to "pop" (must be other name) huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "bisection", iterations = 10) # Iterative search for the best lambda value using bisection # Output: gamma and lambda huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "bisection", iterations = 10, output = "iterations", show_proc = TRUE) # Same procedure, output: single iterations huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "compare", iterations = 10, output = "iterations", show_proc = TRUE, plotVal = TRUE) # Using compare method, output: single iterations and plotdata(DIY1) data(DIY2) data(DIY3) # Loading the three DIY store datasets DIY_alldata <- merge (DIY1, DIY2, by.x = "j_destination", by.y = "j_destination") # Add store data to distance matrix huff_DIY <- huff.shares (DIY_alldata, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, lambda = -2) # Calculating Huff local market shares # Gamma = 1, Lambda = -2 huff_DIY <- merge (huff_DIY, DIY3, by.x = "i_origin", by.y = "district") # Add data for origins huff_DIY_total <- shares.total (huff_DIY, "i_origin", "j_destination", "p_ij", "population") # Calculating total market areas (=sums of customers) colnames(DIY3) <- c("district", "pop") # Change column name to "pop" (must be other name) huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "bisection", iterations = 10) # Iterative search for the best lambda value using bisection # Output: gamma and lambda huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "bisection", iterations = 10, output = "iterations", show_proc = TRUE) # Same procedure, output: single iterations huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "compare", iterations = 10, output = "iterations", show_proc = TRUE, plotVal = TRUE) # Using compare method, output: single iterations and plot
The 19 origins and the resident population.
data("DIY3")data("DIY3")
A data frame with 19 observations on the following 2 variables.
districta factor with 19 levels representing the origins
populationa numeric vector containing the resident population (2012)
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.
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.
data(DIY1) data(DIY2) data(DIY3) # Loading the three DIY store datasets DIY_alldata <- merge (DIY1, DIY2, by.x = "j_destination", by.y = "j_destination") # Add store data to distance matrix huff_DIY <- huff.shares (DIY_alldata, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, lambda = -2) # Calculating Huff local market shares # Gamma = 1, Lambda = -2 huff_DIY <- merge (huff_DIY, DIY3, by.x = "i_origin", by.y = "district") # Add data for origins huff_DIY_total <- shares.total (huff_DIY, "i_origin", "j_destination", "p_ij", "population") # Calculating total market areas (=sums of customers) colnames(DIY3) <- c("district", "pop") # Change column name to "pop" (must be other name) huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "bisection", iterations = 10) # Iterative search for the best lambda value using bisection # Output: gamma and lambda huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "bisection", iterations = 10, output = "iterations", show_proc = TRUE) # Same procedure, output: single iterations huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "compare", iterations = 10, output = "iterations", show_proc = TRUE, plotVal = TRUE) # Using compare method, output: single iterations and plotdata(DIY1) data(DIY2) data(DIY3) # Loading the three DIY store datasets DIY_alldata <- merge (DIY1, DIY2, by.x = "j_destination", by.y = "j_destination") # Add store data to distance matrix huff_DIY <- huff.shares (DIY_alldata, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, lambda = -2) # Calculating Huff local market shares # Gamma = 1, Lambda = -2 huff_DIY <- merge (huff_DIY, DIY3, by.x = "i_origin", by.y = "district") # Add data for origins huff_DIY_total <- shares.total (huff_DIY, "i_origin", "j_destination", "p_ij", "population") # Calculating total market areas (=sums of customers) colnames(DIY3) <- c("district", "pop") # Change column name to "pop" (must be other name) huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "bisection", iterations = 10) # Iterative search for the best lambda value using bisection # Output: gamma and lambda huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "bisection", iterations = 10, output = "iterations", show_proc = TRUE) # Same procedure, output: single iterations huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "compare", iterations = 10, output = "iterations", show_proc = TRUE, plotVal = TRUE) # Using compare method, output: single iterations and plot
Preliminary stage of an interaction matrix: Distance matrix for all statistical 42 districts and all 63 grocery stores ( = 42 submarkets x = 63 suppliers) in Freiburg (Germany) including the size of the grocery stores.
data("Freiburg1")data("Freiburg1")
A data frame with 2646 observations on the following 4 variables.
districta numeric vector representing the 42 statistical districts of Freiburg
storea numeric vector identifying the store code of the mentioned grocery store in the study area
salesareaa numeric vector for the sales area of the grocery stores in sqm
distancea numeric vector for the distance from the places of residence (statistical districts) to the grocery stores in km
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
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
data(Freiburg1) data(Freiburg2) data(Freiburg3) # Loads the data huff_mat <- huff.shares (Freiburg1, "district", "store", "salesarea", "distance") # Market area estimation using the Huff Model with standard parameters # (gamma = 1, lambda = -2) huff_mat_pp <- merge (huff_mat, Freiburg2) # Adding the purchasing power data for the city districts huff_total <- shares.total (huff_mat_pp, "district", "store", "p_ij", "ppower") # Total expected sales and shares huff_total_control <- merge (huff_total, Freiburg3, by.x = "suppliers_single", by.y = "store") model.fit(huff_total_control$annualsales, huff_total_control$sum_E_j, plotVal = TRUE)data(Freiburg1) data(Freiburg2) data(Freiburg3) # Loads the data huff_mat <- huff.shares (Freiburg1, "district", "store", "salesarea", "distance") # Market area estimation using the Huff Model with standard parameters # (gamma = 1, lambda = -2) huff_mat_pp <- merge (huff_mat, Freiburg2) # Adding the purchasing power data for the city districts huff_total <- shares.total (huff_mat_pp, "district", "store", "p_ij", "ppower") # Total expected sales and shares huff_total_control <- merge (huff_total, Freiburg3, by.x = "suppliers_single", by.y = "store") model.fit(huff_total_control$annualsales, huff_total_control$sum_E_j, plotVal = TRUE)
The 42 statistical districts of Freiburg (Germany) and the estimated annual purchasing power for groceries, based on average expenditures and population.
data("Freiburg2")data("Freiburg2")
A data frame with 42 observations on the following 2 variables.
districta numeric vector representing the 42 statistical districts of Freiburg
ppowera numeric vector containing the estimated absolute value of annual purchasing power for groceries in the district in EUR
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
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
data(Freiburg1) data(Freiburg2) data(Freiburg3) # Loads the data huff_mat <- huff.shares (Freiburg1, "district", "store", "salesarea", "distance") # Market area estimation using the Huff Model with standard parameters # (gamma = 1, lambda = -2) huff_mat_pp <- merge (huff_mat, Freiburg2) # Adding the purchasing power data for the city districts huff_total <- shares.total (huff_mat_pp, "district", "store", "p_ij", "ppower") # Total expected sales and shares huff_total_control <- merge (huff_total, Freiburg3, by.x = "suppliers_single", by.y = "store") model.fit(huff_total_control$annualsales, huff_total_control$sum_E_j, plotVal = TRUE)data(Freiburg1) data(Freiburg2) data(Freiburg3) # Loads the data huff_mat <- huff.shares (Freiburg1, "district", "store", "salesarea", "distance") # Market area estimation using the Huff Model with standard parameters # (gamma = 1, lambda = -2) huff_mat_pp <- merge (huff_mat, Freiburg2) # Adding the purchasing power data for the city districts huff_total <- shares.total (huff_mat_pp, "district", "store", "p_ij", "ppower") # Total expected sales and shares huff_total_control <- merge (huff_total, Freiburg3, by.x = "suppliers_single", by.y = "store") model.fit(huff_total_control$annualsales, huff_total_control$sum_E_j, plotVal = TRUE)
The 63 grocery stores in Freiburg (Germany) and the estimated annual sales in EUR.
data("Freiburg3")data("Freiburg3")
A data frame with 63 observations on the following 2 variables.
storea numeric vector identifying the store code of the mentioned grocery store in the study area
annualsalesa numeric vector containing the estimated annual sales of the store in EUR
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
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
data(Freiburg1) data(Freiburg2) data(Freiburg3) # Loads the data huff_mat <- huff.shares (Freiburg1, "district", "store", "salesarea", "distance") # Market area estimation using the Huff Model with standard parameters # (gamma = 1, lambda = -2) huff_mat_pp <- merge (huff_mat, Freiburg2) # Adding the purchasing power data for the city districts huff_total <- shares.total (huff_mat_pp, "district", "store", "p_ij", "ppower") # Total expected sales and shares huff_total_control <- merge (huff_total, Freiburg3, by.x = "suppliers_single", by.y = "store") model.fit(huff_total_control$annualsales, huff_total_control$sum_E_j, plotVal = TRUE)data(Freiburg1) data(Freiburg2) data(Freiburg3) # Loads the data huff_mat <- huff.shares (Freiburg1, "district", "store", "salesarea", "distance") # Market area estimation using the Huff Model with standard parameters # (gamma = 1, lambda = -2) huff_mat_pp <- merge (huff_mat, Freiburg2) # Adding the purchasing power data for the city districts huff_total <- shares.total (huff_mat_pp, "district", "store", "p_ij", "ppower") # Total expected sales and shares huff_total_control <- merge (huff_total, Freiburg3, by.x = "suppliers_single", by.y = "store") model.fit(huff_total_control$annualsales, huff_total_control$sum_E_j, plotVal = TRUE)
Computes the geometric mean of a numeric vector.
geom(x)geom(x)
x |
A numeric vector |
The value of the geometric mean.
Thomas Wieland
numvec <- c(10,15,20,25,30) # Creates a numeric vector "numvec" mean(numvec) # Mean of numvec geom(numvec) # Geometric mean of numvecnumvec <- c(10,15,20,25,30) # Creates a numeric vector "numvec" mean(numvec) # Mean of numvec geom(numvec) # Geometric mean of numvec
Results from a POS survey in Goettingen (Germany) from June 2015 (raw data). Amongst other things, the participants were asked about their last grocery shopping trip (store choice and expenditures) and their place of residence (ZIP code). The survey dataset contains 179 cases/interviewed individuals. The survey is not representative and should be regarded as an example.
data("grocery1")data("grocery1")
A data frame with 179 observations on the following 5 variables.
interview_nra numeric vector, interview/individual identifier
store_codea factor with 32 levels (ALDI1, ALDI3, ..., EDEKA1, ... REWE1, ...), identifying the store code of the mentioned grocery store in the study area, data from Wieland (2011)
store_chaina factor with 11 levels (Aldi, Edeka, Kaufland, ...) for the store chain of the grocery stores in the study area, data from Wieland (2011)
trip_expena numeric vector containing the individual trip expenditures at the last visited grocery store
plz_submarketa factor with 7 levels (PLZ_37073, PLZ_37075, ...) representing the individuals' place of residence based on the five-digit ZIP codes in the study area
Wieland, T. (2011): “Nahversorgung mit Lebensmitteln in Goettingen 2011 - Eine Analyse der Angebotssituation im Goettinger Lebensmitteleinzelhandel unter besonderer Beruecksichtigung der Versorgungsqualitaet”. Goettinger Statistik Aktuell, 35. Goettingen. http://www.goesis.goettingen.de/pdf/Aktuell35.pdf
Primary empirical sources: POS (point of sale) survey in the authors' course (“Seminar Angewandte Geographie 1: Stadtentwicklung und Citymarketing an einem konkreten Fallbeispiel”, University of Goettingen/Institute of Geography, June 2015), own calculations
data(grocery1) # Loads the data ijmatrix.create (grocery1, "plz_submarket", "store_code") # Creates an interaction table with local market sharesdata(grocery1) # Loads the data ijmatrix.create (grocery1, "plz_submarket", "store_code") # Creates an interaction table with local market shares
Market areas of grocery stores in Goettingen, generated from a POS survey in Goettingen (Germany) from June 2015. The survey dataset contains 224 cases ( = 7 submarkets x = 32 suppliers). The data is the result of a survey that is not representative (see grocery1) and also biased due to the data preparation. The data should be regarded as an example.
data("grocery2")data("grocery2")
A data frame with 224 observations on the following 8 variables.
plz_submarketa factor with 7 levels (PLZ_37073,
PLZ_37075, ...) representing the submarkets (places of residence based
on the five-digit ZIP codes) in the study area
store_codea factor with 32 levels (ALDI1, ALDI3, ..., EDEKA1, ... REWE1, ...), identifying the store code of the mentioned grocery store in the study area, data from Wieland (2011)
store_chaina factor with 11 levels (Aldi, Edeka, ..., Kaufland, ...) for the store chain of the grocery stores in the study area, data from Wieland (2011)
store_typea factor with 3 levels for the store type (Biosup = bio-supermarkt, Disc = discounter, Sup = supermarket)
salesarea_qma numeric vector for the sales area of the grocery stores in sqm, data from Wieland (2011)
pricelevel_euroa numeric vector for the price level of the grocery chain (standardized basket in EUR), based on the data from DISQ (2015)
dist_kma numeric vector for the distance from the places of residence (ZIP codes) to the grocery stores in km
p_ij_obsa numeric vector for the empirically observed (and corrected) market shares () of the stores in the submarkets
DISQ (Deutsches Institut fuer Servicequalitaet) (2015) “Discounter guenstig, Vollsortimenter serviceorientiert. Studie Lebensmittelmaerkte (15.10.2015)”. http://disq.de/2015/20151015-Lebensmittelmaerkte.html
Wieland, T. (2011): “Nahversorgung mit Lebensmitteln in Goettingen 2011 - Eine Analyse der Angebotssituation im Goettinger Lebensmitteleinzelhandel unter besonderer Beruecksichtigung der Versorgungsqualitaet”. Goettinger Statistik Aktuell, 35. Goettingen. http://www.goesis.goettingen.de/pdf/Aktuell35.pdf
Primary empirical sources: POS (point of sale) survey in the authors' course (“Seminar Angewandte Geographie 1: Stadtentwicklung und Citymarketing an einem konkreten Fallbeispiel”, University of Goettingen/Institute of Geography, June 2015), own calculations
data(grocery2) # Loads the data mci.transmat (grocery2, "plz_submarket", "store_code", "p_ij_obs", "dist_km", "salesarea_qm") # Applies the log-centering transformation to the dataset using the function mci.transmatdata(grocery2) # Loads the data mci.transmat (grocery2, "plz_submarket", "store_code", "p_ij_obs", "dist_km", "salesarea_qm") # Applies the log-centering transformation to the dataset using the function mci.transmat
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)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 |
origins |
the column in the interaction matrix |
locations |
the column in the interaction matrix |
attrac |
the column in the interaction matrix |
dist |
the column in the interaction matrix |
lambda |
a single numeric value of |
dtype |
Type of distance weighting function: |
lambda2 |
if |
localmarket_dataset |
A |
origin_id |
the column in the dataset |
localmarket |
the column in the dataset |
location_dataset |
A |
location_id |
the column in the dataset |
location_total |
the column in the dataset |
tolerance |
accepted value of absolute percentage error between observed ( |
output |
Type of function output: |
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: |
check_df |
logical argument that indicates if the given dataset is checked for correct input, only for internal use, should not be deselected (default: |
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 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)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)
This function estimates a distance decay function from observed data and compares different function types
huff.decay(dataset, x, y, plotFunc = TRUE)huff.decay(dataset, x, y, plotFunc = TRUE)
dataset |
A |
x |
A numeric vector containing the independent variable, the transport costs (e.g. traveling time or street distance) |
y |
A numeric vector containing the dependent variable, the interaction measure (e.g. local market shares, trip volume, visitors per capita) |
plotFunc |
logical argument that indicates if the curves are plotted (default: |
The distance decay function is a classic concept in quantitative economic geography and describes the relationship between transport costs and trip volume between origins () and a destination (). The dependent variable is an indicator of trip volume, such as local market shares or visitors per capita etc., which are explained by the transport costs between all and the destination , .
The non-linear modeling of transport costs is a key concept of the Huff model (see the function huff.shares). This function estimates and compares different types of possible distance decay functions (linear, power, exponential, logistic) based on observed interaction data.
A data.frame containing the function parameters (Intercept, Slope), their p values in the regression function (p Intercept, p Slope) and fitting measures (R-Squared, Adj. R-Squared). Optionally, a plot of the four estimated functions and the observed data.
Thomas Wieland
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.
Isard, W. (1960): “Methods of Regional Analysis: an Introduction to Regional Science”. Cambridge.
Kanhaeusser, C. (2007): “Modellierung und Prognose von Marktgebieten am Beispiel des Moebeleinzelhandels”. In: Klein, R./Rauh, J. (eds.): Analysemethodik und Modellierung in der geographischen Handelsforschung. Geographische Handelsforschung, 13. Passau. p. 75-110.
Loeffler, G. (1998): “Market areas - a methodological reflection on their boundaries”. In: GeoJournal, 45, 4, p. 265-272.
huff.shares, huff.attrac, huff.fit, mci.fit
# Market area analysis based on the POS survey in shopping1 # data(shopping1) # The survey dataset data(shopping2) # Dataset with distances and travel times shopping1_adj <- shopping1[(shopping1$weekday != 3) & (shopping1$holiday != 1) & (shopping1$survey != "pretest"),] # Removing every case from tuesday, holidays and the ones belonging to the pretest ijmatrix_POS <- ijmatrix.create(shopping1_adj, "resid_code", "POS", "POS_expen") # Creates an interaction matrix based on the observed frequencies (automatically) # and the POS expenditures (Variable "POS_expen" separately stated) ijmatrix_POS_data <- merge(ijmatrix_POS, shopping2, by.x="interaction", by.y="route", all.x = TRUE) # Adding the distances and travel times ijmatrix_POS_data$freq_ij_abs_cor <- var.correct(ijmatrix_POS_data$freq_ij_abs, corr.mode = "inc", incby = 0.1) # Correcting the absolute values (frequencies) by increasing by 0.1 data(shopping3) ijmatrix_POS_data_residdata <- merge(ijmatrix_POS_data, shopping3) # Adding the information about the origins (places of residence) stored in shopping3 ijmatrix_POS_data_residdata$visitper1000 <- (ijmatrix_POS_data_residdata$ freq_ij_abs_cor/ijmatrix_POS_data_residdata$resid_pop2015)*1000 # Calculating the dependent variable # visitper1000: surveyed customers per 1.000 inhabitants of the origin ijmatrix_POS_data_residdata <- ijmatrix_POS_data_residdata[(!is.na(ijmatrix_POS_data_residdata$ visitper1000)) & (!is.na(ijmatrix_POS_data_residdata$d_time)),] # Removing NAs (data for some outlier origins and routes not available) ijmatrix_POS_data_residdata_POS1 <- ijmatrix_POS_data_residdata[ijmatrix_POS_data_residdata$POS=="POS1",] # Dataset for POS1 (town centre) ijmatrix_POS_data_residdata_POS2 <- ijmatrix_POS_data_residdata[ijmatrix_POS_data_residdata$POS=="POS2",] # Dataset for POS2 (out-of-town shopping centre) huff.decay(ijmatrix_POS_data_residdata_POS1, "d_km", "visitper1000") huff.decay(ijmatrix_POS_data_residdata_POS1, "d_time", "visitper1000") huff.decay(ijmatrix_POS_data_residdata_POS2, "d_km", "visitper1000") huff.decay(ijmatrix_POS_data_residdata_POS2, "d_time", "visitper1000")# Market area analysis based on the POS survey in shopping1 # data(shopping1) # The survey dataset data(shopping2) # Dataset with distances and travel times shopping1_adj <- shopping1[(shopping1$weekday != 3) & (shopping1$holiday != 1) & (shopping1$survey != "pretest"),] # Removing every case from tuesday, holidays and the ones belonging to the pretest ijmatrix_POS <- ijmatrix.create(shopping1_adj, "resid_code", "POS", "POS_expen") # Creates an interaction matrix based on the observed frequencies (automatically) # and the POS expenditures (Variable "POS_expen" separately stated) ijmatrix_POS_data <- merge(ijmatrix_POS, shopping2, by.x="interaction", by.y="route", all.x = TRUE) # Adding the distances and travel times ijmatrix_POS_data$freq_ij_abs_cor <- var.correct(ijmatrix_POS_data$freq_ij_abs, corr.mode = "inc", incby = 0.1) # Correcting the absolute values (frequencies) by increasing by 0.1 data(shopping3) ijmatrix_POS_data_residdata <- merge(ijmatrix_POS_data, shopping3) # Adding the information about the origins (places of residence) stored in shopping3 ijmatrix_POS_data_residdata$visitper1000 <- (ijmatrix_POS_data_residdata$ freq_ij_abs_cor/ijmatrix_POS_data_residdata$resid_pop2015)*1000 # Calculating the dependent variable # visitper1000: surveyed customers per 1.000 inhabitants of the origin ijmatrix_POS_data_residdata <- ijmatrix_POS_data_residdata[(!is.na(ijmatrix_POS_data_residdata$ visitper1000)) & (!is.na(ijmatrix_POS_data_residdata$d_time)),] # Removing NAs (data for some outlier origins and routes not available) ijmatrix_POS_data_residdata_POS1 <- ijmatrix_POS_data_residdata[ijmatrix_POS_data_residdata$POS=="POS1",] # Dataset for POS1 (town centre) ijmatrix_POS_data_residdata_POS2 <- ijmatrix_POS_data_residdata[ijmatrix_POS_data_residdata$POS=="POS2",] # Dataset for POS2 (out-of-town shopping centre) huff.decay(ijmatrix_POS_data_residdata_POS1, "d_km", "visitper1000") huff.decay(ijmatrix_POS_data_residdata_POS1, "d_time", "visitper1000") huff.decay(ijmatrix_POS_data_residdata_POS2, "d_km", "visitper1000") huff.decay(ijmatrix_POS_data_residdata_POS2, "d_time", "visitper1000")
This function fits the Huff model with a given interaction matrix by optimizing the attractivity values of suppliers/locations iteratively and calculates the market shares/market areas
huff.fit(huffdataset, origins, locations, attrac, dist, lambda = -2, dtype = "pow", lambda2 = NULL, localmarket_dataset, origin_id, localmarket, location_dataset, location_id, location_total, tolerance = 5, iterations = 3, output = "total", show_proc = FALSE, check_df = TRUE)huff.fit(huffdataset, origins, locations, attrac, dist, lambda = -2, dtype = "pow", lambda2 = NULL, localmarket_dataset, origin_id, localmarket, location_dataset, location_id, location_total, tolerance = 5, iterations = 3, output = "total", show_proc = FALSE, check_df = TRUE)
huffdataset |
an interaction matrix which is a |
origins |
the column in the interaction matrix |
locations |
the column in the interaction matrix |
attrac |
the column in the interaction matrix |
dist |
the column in the interaction matrix |
lambda |
a single numeric value of |
dtype |
Type of distance weighting function: |
lambda2 |
if |
localmarket_dataset |
A |
origin_id |
the column in the dataset |
localmarket |
the column in the dataset |
location_dataset |
A |
location_id |
the column in the dataset |
location_total |
the column in the dataset |
tolerance |
accepted value of absolute percentage error between observed ( |
iterations |
a single numeric value for the desired number of iterations |
output |
Type of function output: |
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: |
check_df |
logical argument that indicates if the given dataset is checked for correct input, only for internal use, should not be deselected (default: |
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 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. The fitting process in the huff.fit includes of given number of () iterations, while the fit gets better with every iteration. The algorithm results can be evaluated by several diagnosis criteria which have been frequently used to evaluate Huff model results: Besides the sum of squared residuals, the function also calculates a Pseudo-R-squared measure and the MAPE (mean average percentage error), both used by De Beule et al. (2014), and the global error used by Klein (1988).
The function output can be controlled by the function argument output. If output = "matrix" the function returns a Huff interaction matrix with the optimized attractivity values and the expected market shares/market areas. If output = "total", the old (observed) and the new (expected) total values are returned. If output = "diag", the diagnosis results (fitting measures) are returned. All results are data.frame.
Note that the iterations can be time-consuming and depend on the number of suppliers/locations. Use show_proc = TRUE for monitoring the iteration process.
Thomas Wieland
De Beule, M./Van den Poel, D./Van de Weghe, N. (2014): “An extended Huff-model for robustly benchmarking and predicting retail network performance”. In: Applied Geography, 46, 1, p. 80-89.
Guessefeldt, J. (2002): “Zur Modellierung von raeumlichen Kaufkraftstroemen in unvollkommenen Maerkten”. In: Erdkunde, 56, 4, p. 351-370.
Klein, R. (1988): “Der Lebensmittel-Einzelhandel im Raum Verden. Raeumliches Einkaufsverhalten unter sich wandelnden Bedingungen”. Flensburger Arbeitspapiere zur Landeskunde und Raumordnung, 6. Flensburg.
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.attrac, huff.shares, huff.decay
data(Freiburg1) data(Freiburg2) data(Freiburg3) # Loading the three Freiburg datasets # NOTE: This may take a while! # huff_total_opt2 <- huff.fit(Freiburg1, "district", "store", "salesarea", "distance", # lambda = -2, dtype= "pow", lambda2 = NULL, Freiburg2, "district", "ppower", # Freiburg3, "store", "annualsales", tolerance = 1, iterations = 2, output = "total", # show_proc = TRUE) # 2 iterations of the optimization algorithm with an accepted difference of +/- 1 % # Output of total sales/shares, stored in dataset huff_total_opt10 # model.fit(huff_total_opt2$total_obs, huff_total_opt2$sum_E_j, plotVal = TRUE) # total_obs = observed total values, originally from dataset Freiburg3 # sum_E_j = expected total valuesdata(Freiburg1) data(Freiburg2) data(Freiburg3) # Loading the three Freiburg datasets # NOTE: This may take a while! # huff_total_opt2 <- huff.fit(Freiburg1, "district", "store", "salesarea", "distance", # lambda = -2, dtype= "pow", lambda2 = NULL, Freiburg2, "district", "ppower", # Freiburg3, "store", "annualsales", tolerance = 1, iterations = 2, output = "total", # show_proc = TRUE) # 2 iterations of the optimization algorithm with an accepted difference of +/- 1 % # Output of total sales/shares, stored in dataset huff_total_opt10 # model.fit(huff_total_opt2$total_obs, huff_total_opt2$sum_E_j, plotVal = TRUE) # total_obs = observed total values, originally from dataset Freiburg3 # sum_E_j = expected total values
This function estimates a distance decay parameter from observed total store/location data (e.g. complete annual turnovers) using bisection or "trial and error"
huff.lambda(huffdataset, origins, locations, attrac, dist, gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -3, dtype = "pow", localmarket_dataset, origin_id, localmarket, location_dataset, location_id, location_total, method = "bisection", iterations = 10, output = "matrix", plotVal = FALSE, show_proc = FALSE, check_df = TRUE)huff.lambda(huffdataset, origins, locations, attrac, dist, gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -3, dtype = "pow", localmarket_dataset, origin_id, localmarket, location_dataset, location_id, location_total, method = "bisection", iterations = 10, output = "matrix", plotVal = FALSE, show_proc = FALSE, check_df = TRUE)
huffdataset |
an interaction matrix which is a |
origins |
the column in the interaction matrix |
locations |
the column in the interaction matrix |
attrac |
the column in the interaction matrix |
dist |
the column in the interaction matrix |
gamma |
a single numeric value of |
atype |
Type of attraction weighting function: |
gamma2 |
if |
lambda_startv |
Start value for |
lambda_endv |
End value for |
dtype |
Type of distance weighting function: |
localmarket_dataset |
A |
origin_id |
the column in the dataset |
localmarket |
the column in the dataset |
location_dataset |
A |
location_id |
the column in the dataset |
location_total |
the column in the dataset |
method |
If |
iterations |
a single numeric value for the desired number of iterations |
output |
If |
plotVal |
If |
show_proc |
logical argument that indicates if the function prints messages about the state of process during the work (e.g. “Processing variable xyz ...”). Default: |
check_df |
logical argument that indicates if the given dataset is checked for correct input, only for internal use, should not be deselected (default: |
In many cases, only total empirical values of the suppliers/locations (e.g. annual turnover) can be used for market area estimation. This function fits the Huff model by estimating the parameter iteratively using an optimization algorithm based on the idea of Klein (1988). The fitting process in the huff.lambda includes of given number of iterations, while the fit gets better with every iteration, measured using the sum of squared residuals of observed vs. expected total values. The iterative optimization can be done via bisection (see Kaw et al. 2011, ch. 03.03) or "trial and error" (see Fuelop et al. 2011).
The function output can be controlled by the function argument output. If output = "iterations", the results for every single iteration is shown (data.frame). If output = "total", total sales and market shares (or total market area) of the suppliers are shown (data.frame). The default output is a list with and .
Note that the iterations can be time-consuming and depend on the number of suppliers/locations. Use show_proc = TRUE for monitoring the iteration process.
Thomas Wieland
Fuelop, G./Kopetsch, T./Schoepe, P. (2011): “Catchment areas of medical practices and the role played by geographical distance in the patient's choice of doctor”. In: The Annals of Regional Science, 46, 3, p. 691-706.
Kaw, A. K./Kalu, E. E./Nguyen, D. (2011): “Numerical Methods with Applications”. http://nm.mathforcollege.com/topics/textbook_index.html
Klein, R. (1988): “Der Lebensmittel-Einzelhandel im Raum Verden. Raeumliches Einkaufsverhalten unter sich wandelnden Bedingungen”. Flensburger Arbeitspapiere zur Landeskunde und Raumordnung, 6. Flensburg.
huff.attrac, huff.shares, huff.decay, huff.fit
data(DIY1) data(DIY2) data(DIY3) # Loading the three DIY store datasets DIY_alldata <- merge (DIY1, DIY2, by.x = "j_destination", by.y = "j_destination") # Add store data to distance matrix huff_DIY <- huff.shares (DIY_alldata, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, lambda = -2) # Calculating Huff local market shares # Gamma = 1, Lambda = -2 huff_DIY <- merge (huff_DIY, DIY3, by.x = "i_origin", by.y = "district") # Add data for origins huff_DIY_total <- shares.total (huff_DIY, "i_origin", "j_destination", "p_ij", "population") # Calculating total market areas (=sums of customers) colnames(DIY3) <- c("district", "pop") # Change column name to "pop" (must be other name) huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "bisection", iterations = 10) # Iterative search for the best lambda value using bisection # Output: gamma and lambda huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "bisection", iterations = 10, output = "iterations", show_proc = TRUE) # Same procedure, output: single iterations huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "compare", iterations = 10, output = "iterations", show_proc = TRUE, plotVal = TRUE) # Using compare method, output: single iterations and plotdata(DIY1) data(DIY2) data(DIY3) # Loading the three DIY store datasets DIY_alldata <- merge (DIY1, DIY2, by.x = "j_destination", by.y = "j_destination") # Add store data to distance matrix huff_DIY <- huff.shares (DIY_alldata, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, lambda = -2) # Calculating Huff local market shares # Gamma = 1, Lambda = -2 huff_DIY <- merge (huff_DIY, DIY3, by.x = "i_origin", by.y = "district") # Add data for origins huff_DIY_total <- shares.total (huff_DIY, "i_origin", "j_destination", "p_ij", "population") # Calculating total market areas (=sums of customers) colnames(DIY3) <- c("district", "pop") # Change column name to "pop" (must be other name) huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "bisection", iterations = 10) # Iterative search for the best lambda value using bisection # Output: gamma and lambda huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "bisection", iterations = 10, output = "iterations", show_proc = TRUE) # Same procedure, output: single iterations huff.lambda (huff_DIY, "i_origin", "j_destination", "A_j_salesarea_sqm", "t_ij_min", gamma = 1, atype = "pow", gamma2 = NULL, lambda_startv = -1, lambda_endv = -2.5, dtype= "pow", DIY3, "district", "pop", huff_DIY_total, "suppliers_single", "sum_E_j", method = "compare", iterations = 10, output = "iterations", show_proc = TRUE, plotVal = TRUE) # Using compare method, output: single iterations and plot
Creation of an interaction matrix with market shares () of every supplier () in every submarket () based on the frequencies in the raw data (e.g. household or POS survey).
ijmatrix.create(rawdataset, submarkets, suppliers, ..., remNA = TRUE, remSing = FALSE, remSing.val = 1, remSingSupp.val = 1, correctVar = FALSE, correctVar.val = 1)ijmatrix.create(rawdataset, submarkets, suppliers, ..., remNA = TRUE, remSing = FALSE, remSing.val = 1, remSingSupp.val = 1, correctVar = FALSE, correctVar.val = 1)
rawdataset |
a |
submarkets |
the column in the dataset containing the submarkets (e.g. ZIP codes) |
suppliers |
the column in the dataset containing the suppliers (e.g. store codes) |
... |
other numeric variables in the raw data which were observed and shall be used to calculate market shares (e.g. expenditures) |
remNA |
logical argument that indicates if |
remSing |
logical argument that indicates if singular instances of the submarkets and suppliers are removed or not (default: |
remSing.val |
if |
remSingSupp.val |
if |
correctVar |
logical argument that indicates if the calculated market shares shall be corrected when they do not match the MCI standards ( |
correctVar.val |
if |
This function creates an interaction matrix for all submarkets (e.g. geographical regions) and all suppliers (e.g. store locations). The function calculates based on the frequencies and, optionally, further market shares calculated from other observed variables in the given raw dataset (e.g. expenditures from submarket at supplier ).
Single observations with missing submarket or supplier (NA) are removed from the data automatically (unless remNA = FALSE). Optionally, singular instances (e.g. some submarkets or suppliers are only represented once or twice in the whole dataset) can also be removed (remSing = TRUE), where the limit values for extraction can be set by remSing.val and remSingSupp.val (e.g. remSing.val = 2 and remSingSupp.val = 1 removes every submarket from the interaction matrix which was observed and every supplier observed ).
An interaction matrix which is a data.frame containing the x combinations ('interaction'), the submarkets (column is named as in raw data), the suppliers (column is named as in raw data), the observed absolute frequencies of every in every ('freq_ij_abs'), the observed absolute frequencies in every ('freq_i_total') and the observed market shares of every in every ('p_ij_obs'). If additional variables are stated (e.g. expenditures) which shall be turned into (local) market shares, the output interaction matrix contains absolute values for every interaction, total values for every submarket and market shares () for these variables, too, which are automatically named based on the given variable name (e.g. the market shares based on a raw data variable called expen is named p_ij_obs_expen). The first three variables of the output matrix are factors, the calculated values are numeric.
Thomas Wieland
Cooper, L. G./Nakanishi, M. (2010): “Market-Share Analysis: Evaluating competitive marketing effectiveness”. Boston, Dordrecht, London : Kluwer (first published 1988). E-book version from 2010: http://www.anderson.ucla.edu/faculty/lee.cooper/MCI_Book/BOOKI2010.pdf
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
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.
ijmatrix.shares, ijmatrix.crosstab
# Creating an interaction matrix based on the POS survey in grocery1 # data(grocery1) # Loads the data ijmatrix.create (grocery1, "plz_submarket", "store_code") # Creates an interaction matrix with local market shares based on frequencies mynewmcidata <- ijmatrix.create (grocery1, "plz_submarket", "store_code") # Save results directly in a new dataset ijmatrix.create (grocery1, "plz_submarket", "store_code", "trip_expen") # Creates an interaction matrix with local market shares based on frequencies # and expenditures (Variable "trip_expen") # MCI analysis for the grocery store market areas based on the POS survey in shopping1 # data(shopping1) # Loading the survey dataset data(shopping2) # Loading the distance/travel time dataset data(shopping3) # Loading the dataset containing information about the city districts data(shopping4) # Loading the grocery store data shopping1_KAeast <- shopping1[shopping1$resid_code %in% shopping3$resid_code[shopping3$KA_east == 1],] # Extracting only inhabitants of the eastern districts of Karlsruhe ijmatrix_gro_adj <- ijmatrix.create(shopping1_KAeast, "resid_code", "gro_purchase_code", "gro_purchase_expen", remSing = TRUE, remSing.val = 1, remSingSupp.val = 2, correctVar = TRUE, correctVar.val = 0.1) # Removing singular instances/outliers (remSing = TRUE) incorporating # only suppliers which are at least obtained three times (remSingSupp.val = 2) # Correcting the values (correctVar = TRUE) # by adding 0.1 to the absolute values (correctVar.val = 0.1) ijmatrix_gro_adj <- ijmatrix_gro_adj[(ijmatrix_gro_adj$gro_purchase_code != "REFORMHAUSBOESER") & (ijmatrix_gro_adj$gro_purchase_code != "WMARKT_DURLACH") & (ijmatrix_gro_adj$gro_purchase_code != "X_INCOMPLETE_STORE"),] # Remove non-regarded observations ijmatrix_gro_adj_dist <- merge (ijmatrix_gro_adj, shopping2, by.x="interaction", by.y="route") # Include the distances and travel times (shopping2) ijmatrix_gro_adj_dist_stores <- merge (ijmatrix_gro_adj_dist, shopping4, by.x = "gro_purchase_code", by.y = "location_code") # Adding the store information (shopping4) mci.transvar(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs") # Log-centering transformation of one variable (p_ij_obs) ijmatrix_gro_transf <- mci.transmat(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs", "d_time", "salesarea_qm") # Log-centering transformation of the interaction matrix mcimodel_gro_trips <- mci.fit(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs", "d_time", "salesarea_qm") # MCI model for the grocery store market areas # shares: "p_ij_obs", explanatory variables: "d_time", "salesarea_qm" summary(mcimodel_gro_trips) # Use like lm# Creating an interaction matrix based on the POS survey in grocery1 # data(grocery1) # Loads the data ijmatrix.create (grocery1, "plz_submarket", "store_code") # Creates an interaction matrix with local market shares based on frequencies mynewmcidata <- ijmatrix.create (grocery1, "plz_submarket", "store_code") # Save results directly in a new dataset ijmatrix.create (grocery1, "plz_submarket", "store_code", "trip_expen") # Creates an interaction matrix with local market shares based on frequencies # and expenditures (Variable "trip_expen") # MCI analysis for the grocery store market areas based on the POS survey in shopping1 # data(shopping1) # Loading the survey dataset data(shopping2) # Loading the distance/travel time dataset data(shopping3) # Loading the dataset containing information about the city districts data(shopping4) # Loading the grocery store data shopping1_KAeast <- shopping1[shopping1$resid_code %in% shopping3$resid_code[shopping3$KA_east == 1],] # Extracting only inhabitants of the eastern districts of Karlsruhe ijmatrix_gro_adj <- ijmatrix.create(shopping1_KAeast, "resid_code", "gro_purchase_code", "gro_purchase_expen", remSing = TRUE, remSing.val = 1, remSingSupp.val = 2, correctVar = TRUE, correctVar.val = 0.1) # Removing singular instances/outliers (remSing = TRUE) incorporating # only suppliers which are at least obtained three times (remSingSupp.val = 2) # Correcting the values (correctVar = TRUE) # by adding 0.1 to the absolute values (correctVar.val = 0.1) ijmatrix_gro_adj <- ijmatrix_gro_adj[(ijmatrix_gro_adj$gro_purchase_code != "REFORMHAUSBOESER") & (ijmatrix_gro_adj$gro_purchase_code != "WMARKT_DURLACH") & (ijmatrix_gro_adj$gro_purchase_code != "X_INCOMPLETE_STORE"),] # Remove non-regarded observations ijmatrix_gro_adj_dist <- merge (ijmatrix_gro_adj, shopping2, by.x="interaction", by.y="route") # Include the distances and travel times (shopping2) ijmatrix_gro_adj_dist_stores <- merge (ijmatrix_gro_adj_dist, shopping4, by.x = "gro_purchase_code", by.y = "location_code") # Adding the store information (shopping4) mci.transvar(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs") # Log-centering transformation of one variable (p_ij_obs) ijmatrix_gro_transf <- mci.transmat(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs", "d_time", "salesarea_qm") # Log-centering transformation of the interaction matrix mcimodel_gro_trips <- mci.fit(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs", "d_time", "salesarea_qm") # MCI model for the grocery store market areas # shares: "p_ij_obs", explanatory variables: "d_time", "salesarea_qm" summary(mcimodel_gro_trips) # Use like lm
This function converts a given interaction matrix with (local) market shares to a crosstable where the rows are the submarkets and the columns contain the market shares
ijmatrix.crosstab(mcidataset, submarkets, suppliers, shares)ijmatrix.crosstab(mcidataset, submarkets, suppliers, shares)
mcidataset |
The interaction matrix containing the submarkets/origins, suppliers/locations and local market shares |
submarkets |
the column in the dataset containing the submarkets (e.g. ZIP codes) |
suppliers |
the column in the dataset containing the suppliers (e.g. store codes) |
shares |
the column in the dataset containing the local market shares |
In many cases the results of a market area analysis shall be visualized in a map, e.g. by pie charts or contour lines which belongs to the standard map types in Geographical Information Systems (GIS). An interaction matrix can not be processed directly in a GIS due to its linear character. This function converts an interaction matrix into a special kind of crosstable where the rows contain the origins and the local market shares are represented by the columns. The submarkets/origins ID (rows) can be joined directly to the geodata (e.g. point shapefile) while the columns can be used for visualization.
A data.frame containing rows and columns (suppliers/locations and one column containing the submarkets/origins).
Thomas Wieland
Cooper, L. G./Nakanishi, M. (2010): “Market-Share Analysis: Evaluating competitive marketing effectiveness”. Boston, Dordrecht, London : Kluwer (first published 1988). E-book version from 2010: http://www.anderson.ucla.edu/faculty/lee.cooper/MCI_Book/BOOKI2010.pdf
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
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.
ijmatrix.create, ijmatrix.shares
data(grocery2) # Loads the data grocery2_cross <- ijmatrix.crosstab(grocery2, "plz_submarket", "store_code", "p_ij_obs") # Converts the market shares in the grocery2 dataset to a crosstabledata(grocery2) # Loads the data grocery2_cross <- ijmatrix.crosstab(grocery2, "plz_submarket", "store_code", "p_ij_obs") # Converts the market shares in the grocery2 dataset to a crosstable
Calculating the standardized (beta) regression coefficients of linear models
lm.beta(linmod, dummy.na = TRUE)lm.beta(linmod, dummy.na = TRUE)
linmod |
A |
dummy.na |
logical argument that indicates if dummy variables should be ignored when calculating the beta weights (default: |
Standardized coefficients (beta coefficients) show how many standard deviations a dependent variable will change when the regarded independent variable is increased by a standard deviation. The values are used in multiple linear regression models to compare the real effect (power) of the independent variables when they are measured in different units. Note that values do not make any sense for dummy variables since they cannot change by a standard deviation.
A list containing all independent variables and the corresponding standardized coefficients.
Thomas Wieland
Backhaus, K./Erichson, B./Plinke, W./Weiber, R. (2016): “Multivariate Analysemethoden: Eine anwendungsorientierte Einfuehrung”. Berlin: Springer.
x1 <- runif(100) x2 <- runif(100) # random values for two independent variables (x1, x2) y <- runif(100) # random values for the dependent variable (y) testmodel <- lm(y~x1+x2) # OLS regression summary(testmodel) # summary lm.beta(testmodel) # beta coefficientsx1 <- runif(100) x2 <- runif(100) # random values for two independent variables (x1, x2) y <- runif(100) # random values for the dependent variable (y) testmodel <- lm(y~x1+x2) # OLS regression summary(testmodel) # summary lm.beta(testmodel) # beta coefficients
This function fits the MCI model based on a given MCI interaction matrix.
mci.fit(mcidataset, submarkets, suppliers, shares, ..., origin = TRUE, show_proc = FALSE)mci.fit(mcidataset, submarkets, suppliers, shares, ..., origin = TRUE, show_proc = FALSE)
mcidataset |
an interaction matrix which is a |
submarkets |
the column in the interaction matrix |
suppliers |
the column in the interaction matrix |
shares |
the column in the interaction matrix |
... |
the column(s) of the explanatory variable(s) (at least one), numeric and positive (or dummy [1,0]) |
origin |
logical argument that indicates if an intercept is included in the model or it is a regression through the origin (default |
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: |
The function transforms the input dataset (MCI interaction matrix) to regression-ready-data with the log-centering transformation by Nakanishi/Cooper (1974) and, therefore, the data is fitted by a linear regression model. The return of the function mci.fit() can be treated exactly like the output of the lm() function. The column in the interaction matrix mcidataset containing the shares is the 4th parameter of the function (shares). The further arguments (...) are the columns with the explanatory variables (attractivity/utility values of the alternatives, characteristics of the submarkets). The function identifies dummy variables which are not transformed (because they do not have to be). Normally, in MCI analyzes no intercept is included into the transformed linear model due to the requirement of logically consistent market shares as model results (see above), so the default is a regression through the origin (origin = TRUE). Note: If an intercept is included (origin = FALSE) (and also if dummy variables are used as explanatories), the inverse log-centering transformation by Nakanishi/Cooper (1982) has to be used for simulations.
The function mci.fit() returns an object of class lm. The full information (estimates, significance, R-squared etc.) can be adressed by the function summary(). The explanatory variables are marked with a "_t" to indicate that they were transformed by log-centering transformation.
Thomas Wieland
Colome Perales, R. (2002): “Consumer Choice in Competitive Location Models”. Barcelona.
Gonzalez-Benito, O./Greatorex, M./Munos-Gallego, P. A. (2000): “Assessment of potential retail segmentation variables - An approach based on a subjective MCI resource allocation model”. In: Journal of Retailing and Consumer Services, 7, 3, p. 171-179.
Hartmann, M. (2005): “Gravitationsmodelle als Verfahren der Standortanalyse im Einzelhandel”. Statistik Regional Electronic Papers, 02/2005. Halle.
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.
Suarez-Vega, R./Gutierrez-Acuna, J. L./Rodriguez-Diaz, M. (2015): “Locating a supermarket using a locally calibrated Huff model”. In: International Journal of Geographical Information Science, 29, 2, p. 217-233.
Tihi, B./Oruc, N. (2012): “Competitive Location Assessment - the MCI Approach”. In: South East European Journal of Economics and Business, 7, 2, p. 35-49.
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.
mci.transmat, mci.transvar, mci.shares
# MCI analysis for the grocery store market areas based on the POS survey in shopping1 # data(shopping1) # Loading the survey dataset data(shopping2) # Loading the distance/travel time dataset data(shopping3) # Loading the dataset containing information about the city districts data(shopping4) # Loading the grocery store data shopping1_KAeast <- shopping1[shopping1$resid_code %in% shopping3$resid_code[shopping3$KA_east == 1],] # Extracting only inhabitants of the eastern districts of Karlsruhe ijmatrix_gro_adj <- ijmatrix.create(shopping1_KAeast, "resid_code", "gro_purchase_code", "gro_purchase_expen", remSing = TRUE, remSing.val = 1, remSingSupp.val = 2, correctVar = TRUE, correctVar.val = 0.1) # Removing singular instances/outliers (remSing = TRUE) incorporating # only suppliers which are at least obtained three times (remSingSupp.val = 2) # Correcting the values (correctVar = TRUE) # by adding 0.1 to the absolute values (correctVar.val = 0.1) ijmatrix_gro_adj <- ijmatrix_gro_adj[(ijmatrix_gro_adj$gro_purchase_code != "REFORMHAUSBOESER") & (ijmatrix_gro_adj$gro_purchase_code != "WMARKT_DURLACH") & (ijmatrix_gro_adj$gro_purchase_code != "X_INCOMPLETE_STORE"),] # Remove non-regarded observations ijmatrix_gro_adj_dist <- merge (ijmatrix_gro_adj, shopping2, by.x="interaction", by.y="route") # Include the distances and travel times (shopping2) ijmatrix_gro_adj_dist_stores <- merge (ijmatrix_gro_adj_dist, shopping4, by.x = "gro_purchase_code", by.y = "location_code") # Adding the store information (shopping4) mci.transvar(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs") # Log-centering transformation of one variable (p_ij_obs) ijmatrix_gro_transf <- mci.transmat(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs", "d_time", "salesarea_qm") # Log-centering transformation of the interaction matrix mcimodel_gro_trips <- mci.fit(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs", "d_time", "salesarea_qm") # MCI model for the grocery store market areas # shares: "p_ij_obs", explanatory variables: "d_time", "salesarea_qm" summary(mcimodel_gro_trips) # Use like lm# MCI analysis for the grocery store market areas based on the POS survey in shopping1 # data(shopping1) # Loading the survey dataset data(shopping2) # Loading the distance/travel time dataset data(shopping3) # Loading the dataset containing information about the city districts data(shopping4) # Loading the grocery store data shopping1_KAeast <- shopping1[shopping1$resid_code %in% shopping3$resid_code[shopping3$KA_east == 1],] # Extracting only inhabitants of the eastern districts of Karlsruhe ijmatrix_gro_adj <- ijmatrix.create(shopping1_KAeast, "resid_code", "gro_purchase_code", "gro_purchase_expen", remSing = TRUE, remSing.val = 1, remSingSupp.val = 2, correctVar = TRUE, correctVar.val = 0.1) # Removing singular instances/outliers (remSing = TRUE) incorporating # only suppliers which are at least obtained three times (remSingSupp.val = 2) # Correcting the values (correctVar = TRUE) # by adding 0.1 to the absolute values (correctVar.val = 0.1) ijmatrix_gro_adj <- ijmatrix_gro_adj[(ijmatrix_gro_adj$gro_purchase_code != "REFORMHAUSBOESER") & (ijmatrix_gro_adj$gro_purchase_code != "WMARKT_DURLACH") & (ijmatrix_gro_adj$gro_purchase_code != "X_INCOMPLETE_STORE"),] # Remove non-regarded observations ijmatrix_gro_adj_dist <- merge (ijmatrix_gro_adj, shopping2, by.x="interaction", by.y="route") # Include the distances and travel times (shopping2) ijmatrix_gro_adj_dist_stores <- merge (ijmatrix_gro_adj_dist, shopping4, by.x = "gro_purchase_code", by.y = "location_code") # Adding the store information (shopping4) mci.transvar(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs") # Log-centering transformation of one variable (p_ij_obs) ijmatrix_gro_transf <- mci.transmat(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs", "d_time", "salesarea_qm") # Log-centering transformation of the interaction matrix mcimodel_gro_trips <- mci.fit(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs", "d_time", "salesarea_qm") # MCI model for the grocery store market areas # shares: "p_ij_obs", explanatory variables: "d_time", "salesarea_qm" summary(mcimodel_gro_trips) # Use like lm
This function applies the log-centering transformation to the variables in a given MCI interaction matrix.
mci.transmat(mcidataset, submarkets, suppliers, mcivariable1, ..., show_proc = FALSE)mci.transmat(mcidataset, submarkets, suppliers, mcivariable1, ..., show_proc = FALSE)
mcidataset |
an interaction matrix which is a |
submarkets |
the column in the interaction matrix |
suppliers |
the column in the interaction matrix |
mcivariable1 |
the column of the first variable to be transformed, numeric and positive (or dummy [1,0]) |
... |
the columns of other variables to be transformed, numeric and positive (or dummy [1,0]) |
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: |
This function transformes the input dataset (MCI interaction matrix) to regression-ready data with the log-centering transformation by Nakanishi/Cooper (1974). The resulting data.frame can be fitted with the lm() function (to combine these two steps in one, use mci.fit()). The log-centering transformation can be regarded as the key concept of the MCI model because it enables the model to be estimated by OLS (ordinary least squares) regression. The function identifies dummy variables which are not transformed (because they do not have to be).
Returns a new data.frame with regression-ready data where the input variables are transformed by the the log-centering transformation. The names of the input variables are passed to the new data.frame marked with a "_t" to indicate that they were transformed (e.g. "shares_t" is the transformation of "shares").
Thomas Wieland
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.
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.
# MCI analysis for the grocery store market areas in grocery2 # data(grocery2) # Loads the data mci.transmat (grocery2, "plz_submarket", "store_code", "p_ij_obs", "dist_km", "salesarea_qm") # Applies the log-centering transformation to the dataset using the function mci.transmat # MCI analysis for the grocery store market areas based on the POS survey in shopping1 # data(shopping1) # Loading the survey dataset data(shopping2) # Loading the distance/travel time dataset data(shopping3) # Loading the dataset containing information about the city districts data(shopping4) # Loading the grocery store data shopping1_KAeast <- shopping1[shopping1$resid_code %in% shopping3$resid_code[shopping3$KA_east == 1],] # Extracting only inhabitants of the eastern districts of Karlsruhe ijmatrix_gro_adj <- ijmatrix.create(shopping1_KAeast, "resid_code", "gro_purchase_code", "gro_purchase_expen", remSing = TRUE, remSing.val = 1, remSingSupp.val = 2, correctVar = TRUE, correctVar.val = 0.1) # Removing singular instances/outliers (remSing = TRUE) incorporating # only suppliers which are at least obtained three times (remSingSupp.val = 2) # Correcting the values (correctVar = TRUE) # by adding 0.1 to the absolute values (correctVar.val = 0.1) ijmatrix_gro_adj <- ijmatrix_gro_adj[(ijmatrix_gro_adj$gro_purchase_code != "REFORMHAUSBOESER") & (ijmatrix_gro_adj$gro_purchase_code != "WMARKT_DURLACH") & (ijmatrix_gro_adj$gro_purchase_code != "X_INCOMPLETE_STORE"),] # Remove non-regarded observations ijmatrix_gro_adj_dist <- merge (ijmatrix_gro_adj, shopping2, by.x="interaction", by.y="route") # Include the distances and travel times (shopping2) ijmatrix_gro_adj_dist_stores <- merge (ijmatrix_gro_adj_dist, shopping4, by.x = "gro_purchase_code", by.y = "location_code") # Adding the store information (shopping4) mci.transvar(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs") # Log-centering transformation of one variable (p_ij_obs) ijmatrix_gro_transf <- mci.transmat(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs", "d_time", "salesarea_qm") # Log-centering transformation of the interaction matrix mcimodel_gro_trips <- mci.fit(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs", "d_time", "salesarea_qm") # MCI model for the grocery store market areas # shares: "p_ij_obs", explanatory variables: "d_time", "salesarea_qm" summary(mcimodel_gro_trips) # Use like lm# MCI analysis for the grocery store market areas in grocery2 # data(grocery2) # Loads the data mci.transmat (grocery2, "plz_submarket", "store_code", "p_ij_obs", "dist_km", "salesarea_qm") # Applies the log-centering transformation to the dataset using the function mci.transmat # MCI analysis for the grocery store market areas based on the POS survey in shopping1 # data(shopping1) # Loading the survey dataset data(shopping2) # Loading the distance/travel time dataset data(shopping3) # Loading the dataset containing information about the city districts data(shopping4) # Loading the grocery store data shopping1_KAeast <- shopping1[shopping1$resid_code %in% shopping3$resid_code[shopping3$KA_east == 1],] # Extracting only inhabitants of the eastern districts of Karlsruhe ijmatrix_gro_adj <- ijmatrix.create(shopping1_KAeast, "resid_code", "gro_purchase_code", "gro_purchase_expen", remSing = TRUE, remSing.val = 1, remSingSupp.val = 2, correctVar = TRUE, correctVar.val = 0.1) # Removing singular instances/outliers (remSing = TRUE) incorporating # only suppliers which are at least obtained three times (remSingSupp.val = 2) # Correcting the values (correctVar = TRUE) # by adding 0.1 to the absolute values (correctVar.val = 0.1) ijmatrix_gro_adj <- ijmatrix_gro_adj[(ijmatrix_gro_adj$gro_purchase_code != "REFORMHAUSBOESER") & (ijmatrix_gro_adj$gro_purchase_code != "WMARKT_DURLACH") & (ijmatrix_gro_adj$gro_purchase_code != "X_INCOMPLETE_STORE"),] # Remove non-regarded observations ijmatrix_gro_adj_dist <- merge (ijmatrix_gro_adj, shopping2, by.x="interaction", by.y="route") # Include the distances and travel times (shopping2) ijmatrix_gro_adj_dist_stores <- merge (ijmatrix_gro_adj_dist, shopping4, by.x = "gro_purchase_code", by.y = "location_code") # Adding the store information (shopping4) mci.transvar(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs") # Log-centering transformation of one variable (p_ij_obs) ijmatrix_gro_transf <- mci.transmat(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs", "d_time", "salesarea_qm") # Log-centering transformation of the interaction matrix mcimodel_gro_trips <- mci.fit(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs", "d_time", "salesarea_qm") # MCI model for the grocery store market areas # shares: "p_ij_obs", explanatory variables: "d_time", "salesarea_qm" summary(mcimodel_gro_trips) # Use like lm
This function applies the log-centering transformation to a variable in a given MCI interaction matrix.
mci.transvar(mcidataset, submarkets, suppliers, mcivariable, output_ij = FALSE, output_var = "numeric", show_proc = FALSE, check_df = TRUE)mci.transvar(mcidataset, submarkets, suppliers, mcivariable, output_ij = FALSE, output_var = "numeric", show_proc = FALSE, check_df = TRUE)
mcidataset |
an interaction matrix which is a |
submarkets |
the column in the interaction matrix |
suppliers |
the column in the interaction matrix |
mcivariable |
the column of the variable to be transformed, numeric and positive (or dummy [1,0]) |
output_ij |
logical argument that indicates if the function output has to be a |
output_var |
defines the mode of the function output if |
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: |
check_df |
logical argument that indicates if the input (dataset, column names) is checked (default: |
This function transforms one variable from the input dataset (MCI interaction matrix) to regression-ready data with the log-centering transformation by Nakanishi/Cooper (1974) (to transform a complete interaction matrix, use mci.transmat(), for transformation and fitting use mci.fit()). The log-centering transformation can be regarded as the key concept of the MCI model because it enables the model to be estimated by OLS (ordinary least squares) regression. The function identifies dummy variables which are not transformed (because they do not have to be).
The format of the output can be controlled by the last two arguments of the function (see above). Either a new data.frame with the transformed input variable and the submarkets/suppliers or a vector with the transformed values only. The name of the input variable is passed to the new data.frame marked with a "_t" to indicate that it was transformed (e.g. "shares_t" is the transformation of "shares").
Thomas Wieland
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.
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.
# MCI analysis for the grocery store market areas based on the POS survey in shopping1 # data(shopping1) # Loading the survey dataset data(shopping2) # Loading the distance/travel time dataset data(shopping3) # Loading the dataset containing information about the city districts data(shopping4) # Loading the grocery store data shopping1_KAeast <- shopping1[shopping1$resid_code %in% shopping3$resid_code[shopping3$KA_east == 1],] # Extracting only inhabitants of the eastern districts of Karlsruhe ijmatrix_gro_adj <- ijmatrix.create(shopping1_KAeast, "resid_code", "gro_purchase_code", "gro_purchase_expen", remSing = TRUE, remSing.val = 1, remSingSupp.val = 2, correctVar = TRUE, correctVar.val = 0.1) # Removing singular instances/outliers (remSing = TRUE) incorporating # only suppliers which are at least obtained three times (remSingSupp.val = 2) # Correcting the values (correctVar = TRUE) # by adding 0.1 to the absolute values (correctVar.val = 0.1) ijmatrix_gro_adj <- ijmatrix_gro_adj[(ijmatrix_gro_adj$gro_purchase_code != "REFORMHAUSBOESER") & (ijmatrix_gro_adj$gro_purchase_code != "WMARKT_DURLACH") & (ijmatrix_gro_adj$gro_purchase_code != "X_INCOMPLETE_STORE"),] # Remove non-regarded observations ijmatrix_gro_adj_dist <- merge (ijmatrix_gro_adj, shopping2, by.x="interaction", by.y="route") # Include the distances and travel times (shopping2) ijmatrix_gro_adj_dist_stores <- merge (ijmatrix_gro_adj_dist, shopping4, by.x = "gro_purchase_code", by.y = "location_code") # Adding the store information (shopping4) mci.transvar(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs") # Log-centering transformation of one variable (p_ij_obs) ijmatrix_gro_transf <- mci.transmat(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs", "d_time", "salesarea_qm") # Log-centering transformation of the interaction matrix mcimodel_gro_trips <- mci.fit(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs", "d_time", "salesarea_qm") # MCI model for the grocery store market areas # shares: "p_ij_obs", explanatory variables: "d_time", "salesarea_qm" summary(mcimodel_gro_trips) # Use like lm# MCI analysis for the grocery store market areas based on the POS survey in shopping1 # data(shopping1) # Loading the survey dataset data(shopping2) # Loading the distance/travel time dataset data(shopping3) # Loading the dataset containing information about the city districts data(shopping4) # Loading the grocery store data shopping1_KAeast <- shopping1[shopping1$resid_code %in% shopping3$resid_code[shopping3$KA_east == 1],] # Extracting only inhabitants of the eastern districts of Karlsruhe ijmatrix_gro_adj <- ijmatrix.create(shopping1_KAeast, "resid_code", "gro_purchase_code", "gro_purchase_expen", remSing = TRUE, remSing.val = 1, remSingSupp.val = 2, correctVar = TRUE, correctVar.val = 0.1) # Removing singular instances/outliers (remSing = TRUE) incorporating # only suppliers which are at least obtained three times (remSingSupp.val = 2) # Correcting the values (correctVar = TRUE) # by adding 0.1 to the absolute values (correctVar.val = 0.1) ijmatrix_gro_adj <- ijmatrix_gro_adj[(ijmatrix_gro_adj$gro_purchase_code != "REFORMHAUSBOESER") & (ijmatrix_gro_adj$gro_purchase_code != "WMARKT_DURLACH") & (ijmatrix_gro_adj$gro_purchase_code != "X_INCOMPLETE_STORE"),] # Remove non-regarded observations ijmatrix_gro_adj_dist <- merge (ijmatrix_gro_adj, shopping2, by.x="interaction", by.y="route") # Include the distances and travel times (shopping2) ijmatrix_gro_adj_dist_stores <- merge (ijmatrix_gro_adj_dist, shopping4, by.x = "gro_purchase_code", by.y = "location_code") # Adding the store information (shopping4) mci.transvar(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs") # Log-centering transformation of one variable (p_ij_obs) ijmatrix_gro_transf <- mci.transmat(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs", "d_time", "salesarea_qm") # Log-centering transformation of the interaction matrix mcimodel_gro_trips <- mci.fit(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs", "d_time", "salesarea_qm") # MCI model for the grocery store market areas # shares: "p_ij_obs", explanatory variables: "d_time", "salesarea_qm" summary(mcimodel_gro_trips) # Use like lm
This function calculates several goodness of fit values to evaluate how good the observed values fit the empirical observations.
model.fit(y_obs, y_exp, plotVal = FALSE)model.fit(y_obs, y_exp, plotVal = FALSE)
y_obs |
Observed values of the dependent variable |
y_exp |
Expected values of the dependent variable |
plotVal |
Logical argument that indicates if the function plots a graph comparing observed and expected values |
This function computes several goodness of fit statistics to evaluate the results of non-linear fitting procedures for the Huff model (see the functions huff.attrac and huff.fit). Besides the sum of squared residuals, the function also calculates a Pseudo-R-squared measure and the MAPE (mean average percentage error), both used by De Beule et al. (2014), and the global error used by Klein (1988).
list:
resids_sq_sum |
Sum of squared residuals |
pseudorsq |
Pseudo-R-squared |
globerr |
Global error |
mape |
Mean average percentage error |
Thomas Wieland
De Beule, M./Van den Poel, D./Van de Weghe, N. (2014): “An extended Huff-model for robustly benchmarking and predicting retail network performance”. In: Applied Geography, 46, 1, p. 80-89.
Klein, R. (1988): “Der Lebensmittel-Einzelhandel im Raum Verden. Raeumliches Einkaufsverhalten unter sich wandelnden Bedingungen”. Flensburger Arbeitspapiere zur Landeskunde und Raumordnung, 6. Flensburg.
# Controlling the fit of a Huff Model market area estimation # data(Freiburg1) data(Freiburg2) data(Freiburg3) # Loads the data huff_mat <- huff.shares (Freiburg1, "district", "store", "salesarea", "distance") # Market area estimation using the Huff Model with standard parameters # (gamma = 1, lambda = -2) huff_mat_pp <- merge (huff_mat, Freiburg2) # Adding the purchasing power data for the city districts huff_total <- shares.total (huff_mat_pp, "district", "store", "p_ij", "ppower") # Total expected sales and shares huff_total_control <- merge (huff_total, Freiburg3, by.x = "suppliers_single", by.y = "store") model.fit(huff_total_control$annualsales, huff_total_control$sum_E_j, plotVal = TRUE) # Observed vs. expected # Results can be adressed directly: huff_fit <- model.fit(huff_total_control$annualsales, huff_total_control$sum_E_j, plotVal = TRUE) huff_fit$mape# Controlling the fit of a Huff Model market area estimation # data(Freiburg1) data(Freiburg2) data(Freiburg3) # Loads the data huff_mat <- huff.shares (Freiburg1, "district", "store", "salesarea", "distance") # Market area estimation using the Huff Model with standard parameters # (gamma = 1, lambda = -2) huff_mat_pp <- merge (huff_mat, Freiburg2) # Adding the purchasing power data for the city districts huff_total <- shares.total (huff_mat_pp, "district", "store", "p_ij", "ppower") # Total expected sales and shares huff_total_control <- merge (huff_total, Freiburg3, by.x = "suppliers_single", by.y = "store") model.fit(huff_total_control$annualsales, huff_total_control$sum_E_j, plotVal = TRUE) # Observed vs. expected # Results can be adressed directly: huff_fit <- model.fit(huff_total_control$annualsales, huff_total_control$sum_E_j, plotVal = TRUE) huff_fit$mape
The dataset contains a point-of-sale (POS) survey conducted at two retail supply locations (town centre and planned shopping centre) in the east of Karlsruhe (Germany) from May 2016 (raw data). Amongst other things, the participants were asked about their last shopping trip with respect to groceries, clothing als consumer electronics (store choice and expenditures) and their place of residence (ZIP code and city district, respectively). The survey dataset contains 434 cases/interviewed individuals. The survey is not representative and should be regarded as an example.
data("shopping1")data("shopping1")
A data frame with 434 observations on the following 29 variables.
POSa factor indicating the survey location: POS1 (town centre) or POS2 (shopping centre)
timea numeric vector containing the code for the time period the interview was conducted
datea POSIXct containing the date the interview was conducted
POS_traffica numeric vector containing the code for the traffic mode the respondet used to come to the supply location
POS_staya numeric vector containing the respondents' duration of stay at the supply location
POS_expena numeric vector containing the respondents' expenditures at the supply location
POS1_freqa numeric vector containing the frequency of visiting the supply location POS1
POS2_freqa numeric vector containing the frequency of visiting the supply location POS2
gro_purchase_codea factor containing the destination of the last grocery shopping trip
gro_purchase_branda factor containing the brand (store chain) of the destination of the last grocery shopping trip
gro_purchase_channela factor containing the shopping channel of the destination of the last grocery shopping trip: ambulant, online and store
gro_purchase_expena numeric vector containing the expenditures corresponding to the last grocery shopping trip
cloth_purchase_codea factor containing the destination of the last clothing shopping trip
cloth_purchase_branda factor containing the brand (store chain) of the destination of the last clothing shopping trip
cloth_purchase_channela factor containing the shopping channel of the destination of the last clothing shopping trip: mail order, online or store
cloth_purchase_expena numeric vector containing the expenditures corresponding to the last clothing shopping trip
ce_purchase_codea factor containing the destination of the last shopping trip with respect to consumer electronics (CE)
ce_purchase_branda factor containing the brand (store chain) of the destination of the last CE shopping trip
ce_purchase_channela factor containing the shopping channel of the destination of the last CE shopping trip: online or store
ce_purchase_expena numeric vector containing the expenditures corresponding to the last CE shopping trip
resid_PLZa factor containing the customer origin (place of residence) as ZIP code
resid_namea factor containing the customer origin (place of residence) as name of the corresponding city or city district
resid_name_officiala factor containing the customer origin (place of residence) as official names of the corresponding city or city district
resid_codea factor containing the customer origin (place of residence) as internal code
age_cata numeric vector containing the age category of the respondent
sexa numeric vector containing the sex of the respondent
weekdaya numeric vector containing the weekday where the interview took place
holidaya numeric vector containing a dummy variable which indicates whether the interview was conducted on a holiday or not
surveya factor reflecting the mode of survey: main is the main survey while pretest marks the cases from the pretest
Primary empirical sources: POS (point of sale) survey in the authors' course (“Praktikum Empirische Sozialforschung: Stadtteilzentren als Einzelhandelsstandorte - Das Fallbeispiel Karlsruhe-Durlach”, Karlsruhe Institute of Technology, Institute for Geography and Geoecology, May 2016), own calculations
shopping2, shopping3, shopping4
# Market area segmentation based on the POS survey in shopping1 # data(shopping1) # The survey dataset data(shopping2) # Dataset with distances and travel times shopping1_adj <- shopping1[(shopping1$weekday != 3) & (shopping1$holiday != 1) & (shopping1$survey != "pretest"),] # Removing every case from tuesday, holidays and the ones belonging to the pretest ijmatrix_POS <- ijmatrix.create(shopping1_adj, "resid_code", "POS", "POS_expen") # Creates an interaction matrix based on the observed frequencies (automatically) # and the POS expenditures (Variable "POS_expen" separately stated) ijmatrix_POS_data <- merge(ijmatrix_POS, shopping2, by.x="interaction", by.y="route", all.x = TRUE) # Adding the distances and travel times ijmatrix_POS_data_segm_visit <- shares.segm(ijmatrix_POS_data, "resid_code", "POS", "d_time", "freq_ij_abs", 0,10,20,30) # Segmentation by travel time using the number of customers/visitors # Parameters: interaction matrix (data frame), columns with origins and destinations, # variable to divide in classes, absolute frequencies/expenditures, class segments ijmatrix_POS_data_segm_exp <- shares.segm(ijmatrix_POS_data, "resid_code", "POS", "d_time", "freq_ij_abs_POS_expen", 0,10,20,30) # Segmentation by travel time using the POS expenditures# Market area segmentation based on the POS survey in shopping1 # data(shopping1) # The survey dataset data(shopping2) # Dataset with distances and travel times shopping1_adj <- shopping1[(shopping1$weekday != 3) & (shopping1$holiday != 1) & (shopping1$survey != "pretest"),] # Removing every case from tuesday, holidays and the ones belonging to the pretest ijmatrix_POS <- ijmatrix.create(shopping1_adj, "resid_code", "POS", "POS_expen") # Creates an interaction matrix based on the observed frequencies (automatically) # and the POS expenditures (Variable "POS_expen" separately stated) ijmatrix_POS_data <- merge(ijmatrix_POS, shopping2, by.x="interaction", by.y="route", all.x = TRUE) # Adding the distances and travel times ijmatrix_POS_data_segm_visit <- shares.segm(ijmatrix_POS_data, "resid_code", "POS", "d_time", "freq_ij_abs", 0,10,20,30) # Segmentation by travel time using the number of customers/visitors # Parameters: interaction matrix (data frame), columns with origins and destinations, # variable to divide in classes, absolute frequencies/expenditures, class segments ijmatrix_POS_data_segm_exp <- shares.segm(ijmatrix_POS_data, "resid_code", "POS", "d_time", "freq_ij_abs_POS_expen", 0,10,20,30) # Segmentation by travel time using the POS expenditures
The dataset contains a distance matrix (OD matrix: Origins-Destinations matrix) including the street distance and the travel time from the customer origins to the shopping destinations, both stored in the dataset shopping1.
data("shopping2")data("shopping2")
A data frame with 3723 observations on the following 5 variables.
froma factor containing the customer origin (place of residence) as internal code
toa factor containing the shopping destination
d_kma numeric vector containing the street distance from the origins to the destinations in km
d_timea numeric vector containing the driving time from the origins to the destinations in km
routea factor containing the interaction/route code between origins and destinations (from-to)
Primary empirical sources: POS (point of sale) survey in the authors' course (“Praktikum Empirische Sozialforschung: Stadtteilzentren als Einzelhandelsstandorte - Das Fallbeispiel Karlsruhe-Durlach”, Karlsruhe Institute of Technology, Institute for Geography and Geoecology, May 2016), own calculations
The street distance and travel time was calculated using the package ggmap.
shopping1, shopping3, shopping4
# Market area segmentation based on the POS survey in shopping1 # data(shopping1) # The survey dataset data(shopping2) # Dataset with distances and travel times shopping1_adj <- shopping1[(shopping1$weekday != 3) & (shopping1$holiday != 1) & (shopping1$survey != "pretest"),] # Removing every case from tuesday, holidays and the ones belonging to the pretest ijmatrix_POS <- ijmatrix.create(shopping1_adj, "resid_code", "POS", "POS_expen") # Creates an interaction matrix based on the observed frequencies (automatically) # and the POS expenditures (Variable "POS_expen" separately stated) ijmatrix_POS_data <- merge(ijmatrix_POS, shopping2, by.x="interaction", by.y="route", all.x = TRUE) # Adding the distances and travel times ijmatrix_POS_data_segm_visit <- shares.segm(ijmatrix_POS_data, "resid_code", "POS", "d_time", "freq_ij_abs", 0,10,20,30) # Segmentation by travel time using the number of customers/visitors # Parameters: interaction matrix (data frame), columns with origins and destinations, # variable to divide in classes, absolute frequencies/expenditures, class segments ijmatrix_POS_data_segm_exp <- shares.segm(ijmatrix_POS_data, "resid_code", "POS", "d_time", "freq_ij_abs_POS_expen", 0,10,20,30) # Segmentation by travel time using the POS expenditures# Market area segmentation based on the POS survey in shopping1 # data(shopping1) # The survey dataset data(shopping2) # Dataset with distances and travel times shopping1_adj <- shopping1[(shopping1$weekday != 3) & (shopping1$holiday != 1) & (shopping1$survey != "pretest"),] # Removing every case from tuesday, holidays and the ones belonging to the pretest ijmatrix_POS <- ijmatrix.create(shopping1_adj, "resid_code", "POS", "POS_expen") # Creates an interaction matrix based on the observed frequencies (automatically) # and the POS expenditures (Variable "POS_expen" separately stated) ijmatrix_POS_data <- merge(ijmatrix_POS, shopping2, by.x="interaction", by.y="route", all.x = TRUE) # Adding the distances and travel times ijmatrix_POS_data_segm_visit <- shares.segm(ijmatrix_POS_data, "resid_code", "POS", "d_time", "freq_ij_abs", 0,10,20,30) # Segmentation by travel time using the number of customers/visitors # Parameters: interaction matrix (data frame), columns with origins and destinations, # variable to divide in classes, absolute frequencies/expenditures, class segments ijmatrix_POS_data_segm_exp <- shares.segm(ijmatrix_POS_data, "resid_code", "POS", "d_time", "freq_ij_abs_POS_expen", 0,10,20,30) # Segmentation by travel time using the POS expenditures
The dataset contains information about
data("shopping3")data("shopping3")
A data frame with 70 observations on the following 5 variables.
resid_namea factor containing the customer origin (place of residence) as name of the corresponding city or city district
resid_name_officala factor containing the customer origin (place of residence) as official names of the corresponding city or city district
resid_pop2015a numeric vector containing the population size of the area
KA_easta numeric vector containing a dummy variable indicating whether the area belongs to the east of Karlsruhe or not
resid_codea factor containing the customer origin (place of residence) as internal code
Primary empirical sources: POS (point of sale) survey in the authors' course (“Praktikum Empirische Sozialforschung: Stadtteilzentren als Einzelhandelsstandorte - Das Fallbeispiel Karlsruhe-Durlach”, Karlsruhe Institute of Technology, Institute for Geography and Geoecology, May 2016), own calculations
Stadt Karlsruhe, Amt fuer Stadtentwicklung (2016): “Die Karlsruher Bevoelkerung im Dezember 2015”. Stadt Karlsruhe.
shopping1, shopping2, shopping4
# Market area analysis based on the POS survey in shopping1 # data(shopping1) # The survey dataset data(shopping2) # Dataset with distances and travel times shopping1_adj <- shopping1[(shopping1$weekday != 3) & (shopping1$holiday != 1) & (shopping1$survey != "pretest"),] # Removing every case from tuesday, holidays and the ones belonging to the pretest ijmatrix_POS <- ijmatrix.create(shopping1_adj, "resid_code", "POS", "POS_expen") # Creates an interaction matrix based on the observed frequencies (automatically) # and the POS expenditures (Variable "POS_expen" separately stated) ijmatrix_POS_data <- merge(ijmatrix_POS, shopping2, by.x="interaction", by.y="route", all.x = TRUE) # Adding the distances and travel times ijmatrix_POS_data$freq_ij_abs_cor <- var.correct(ijmatrix_POS_data$freq_ij_abs, corr.mode = "inc", incby = 0.1) # Correcting the absolute values (frequencies) by increasing by 0.1 data(shopping3) ijmatrix_POS_data_residdata <- merge(ijmatrix_POS_data, shopping3) # Adding the information about the origins (places of residence) stored in shopping3 ijmatrix_POS_data_residdata$visitper1000 <- (ijmatrix_POS_data_residdata$ freq_ij_abs_cor/ijmatrix_POS_data_residdata$resid_pop2015)*1000 # Calculating the dependent variable # visitper1000: surveyed customers per 1.000 inhabitants of the origin ijmatrix_POS_data_residdata <- ijmatrix_POS_data_residdata[(!is.na(ijmatrix_POS_data_residdata$ visitper1000)) & (!is.na(ijmatrix_POS_data_residdata$d_time)),] # Removing NAs (data for some outlier origins and routes not available) ijmatrix_POS_data_residdata_POS1 <- ijmatrix_POS_data_residdata[ijmatrix_POS_data_residdata$POS=="POS1",] # Dataset for POS1 (town centre) ijmatrix_POS_data_residdata_POS2 <- ijmatrix_POS_data_residdata[ijmatrix_POS_data_residdata$POS=="POS2",] # Dataset for POS2 (out-of-town shopping centre) huff.decay(ijmatrix_POS_data_residdata_POS1, "d_km", "visitper1000") huff.decay(ijmatrix_POS_data_residdata_POS1, "d_time", "visitper1000") huff.decay(ijmatrix_POS_data_residdata_POS2, "d_km", "visitper1000") huff.decay(ijmatrix_POS_data_residdata_POS2, "d_time", "visitper1000")# Market area analysis based on the POS survey in shopping1 # data(shopping1) # The survey dataset data(shopping2) # Dataset with distances and travel times shopping1_adj <- shopping1[(shopping1$weekday != 3) & (shopping1$holiday != 1) & (shopping1$survey != "pretest"),] # Removing every case from tuesday, holidays and the ones belonging to the pretest ijmatrix_POS <- ijmatrix.create(shopping1_adj, "resid_code", "POS", "POS_expen") # Creates an interaction matrix based on the observed frequencies (automatically) # and the POS expenditures (Variable "POS_expen" separately stated) ijmatrix_POS_data <- merge(ijmatrix_POS, shopping2, by.x="interaction", by.y="route", all.x = TRUE) # Adding the distances and travel times ijmatrix_POS_data$freq_ij_abs_cor <- var.correct(ijmatrix_POS_data$freq_ij_abs, corr.mode = "inc", incby = 0.1) # Correcting the absolute values (frequencies) by increasing by 0.1 data(shopping3) ijmatrix_POS_data_residdata <- merge(ijmatrix_POS_data, shopping3) # Adding the information about the origins (places of residence) stored in shopping3 ijmatrix_POS_data_residdata$visitper1000 <- (ijmatrix_POS_data_residdata$ freq_ij_abs_cor/ijmatrix_POS_data_residdata$resid_pop2015)*1000 # Calculating the dependent variable # visitper1000: surveyed customers per 1.000 inhabitants of the origin ijmatrix_POS_data_residdata <- ijmatrix_POS_data_residdata[(!is.na(ijmatrix_POS_data_residdata$ visitper1000)) & (!is.na(ijmatrix_POS_data_residdata$d_time)),] # Removing NAs (data for some outlier origins and routes not available) ijmatrix_POS_data_residdata_POS1 <- ijmatrix_POS_data_residdata[ijmatrix_POS_data_residdata$POS=="POS1",] # Dataset for POS1 (town centre) ijmatrix_POS_data_residdata_POS2 <- ijmatrix_POS_data_residdata[ijmatrix_POS_data_residdata$POS=="POS2",] # Dataset for POS2 (out-of-town shopping centre) huff.decay(ijmatrix_POS_data_residdata_POS1, "d_km", "visitper1000") huff.decay(ijmatrix_POS_data_residdata_POS1, "d_time", "visitper1000") huff.decay(ijmatrix_POS_data_residdata_POS2, "d_km", "visitper1000") huff.decay(ijmatrix_POS_data_residdata_POS2, "d_time", "visitper1000")
This dataset contains information about the regarded grocery stores in the east of Karlsruhe, based on the POS survey stored in the dataset shopping1 and the related information in shopping2..
data("shopping4")data("shopping4")
A data frame with 11 observations on the following 4 variables.
location_codea factor containing the grocery store codes
salesarea_qma numeric vector containing the sales area of the stores in sqm
storetype_dca numeric vector containing a dummy variable that indicates if the store is a discounter or not
store_chaina factor containing the store chain
Primary empirical sources: POS (point of sale) survey in the authors' course (“Praktikum Empirische Sozialforschung: Stadtteilzentren als Einzelhandelsstandorte - Das Fallbeispiel Karlsruhe-Durlach”, Karlsruhe Institute of Technology, Institute for Geography and Geoecology, May 2016), own calculations
Mapping of grocery stores in the east of Karlsruhe in June 2016 with additional research
shopping1, shopping2, shopping3
# MCI analysis for the grocery store market areas based on the POS survey in shopping1 # data(shopping1) # Loading the survey dataset data(shopping2) # Loading the distance/travel time dataset data(shopping3) # Loading the dataset containing information about the city districts data(shopping4) # Loading the grocery store data shopping1_KAeast <- shopping1[shopping1$resid_code %in% shopping3$resid_code[shopping3$KA_east == 1],] # Extracting only inhabitants of the eastern districts of Karlsruhe ijmatrix_gro_adj <- ijmatrix.create(shopping1_KAeast, "resid_code", "gro_purchase_code", "gro_purchase_expen", remSing = TRUE, remSing.val = 1, remSingSupp.val = 2, correctVar = TRUE, correctVar.val = 0.1) # Removing singular instances/outliers (remSing = TRUE) incorporating # only suppliers which are at least obtained three times (remSingSupp.val = 2) # Correcting the values (correctVar = TRUE) # by adding 0.1 to the absolute values (correctVar.val = 0.1) ijmatrix_gro_adj <- ijmatrix_gro_adj[(ijmatrix_gro_adj$gro_purchase_code != "REFORMHAUSBOESER") & (ijmatrix_gro_adj$gro_purchase_code != "WMARKT_DURLACH") & (ijmatrix_gro_adj$gro_purchase_code != "X_INCOMPLETE_STORE"),] # Remove non-regarded observations ijmatrix_gro_adj_dist <- merge (ijmatrix_gro_adj, shopping2, by.x="interaction", by.y="route") # Include the distances and travel times (shopping2) ijmatrix_gro_adj_dist_stores <- merge (ijmatrix_gro_adj_dist, shopping4, by.x = "gro_purchase_code", by.y = "location_code") # Adding the store information (shopping4) mci.transvar(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs") # Log-centering transformation of one variable (p_ij_obs) ijmatrix_gro_transf <- mci.transmat(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs", "d_time", "salesarea_qm") # Log-centering transformation of the interaction matrix mcimodel_gro_trips <- mci.fit(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs", "d_time", "salesarea_qm") # MCI model for the grocery store market areas # shares: "p_ij_obs", explanatory variables: "d_time", "salesarea_qm" summary(mcimodel_gro_trips) # Use like lm# MCI analysis for the grocery store market areas based on the POS survey in shopping1 # data(shopping1) # Loading the survey dataset data(shopping2) # Loading the distance/travel time dataset data(shopping3) # Loading the dataset containing information about the city districts data(shopping4) # Loading the grocery store data shopping1_KAeast <- shopping1[shopping1$resid_code %in% shopping3$resid_code[shopping3$KA_east == 1],] # Extracting only inhabitants of the eastern districts of Karlsruhe ijmatrix_gro_adj <- ijmatrix.create(shopping1_KAeast, "resid_code", "gro_purchase_code", "gro_purchase_expen", remSing = TRUE, remSing.val = 1, remSingSupp.val = 2, correctVar = TRUE, correctVar.val = 0.1) # Removing singular instances/outliers (remSing = TRUE) incorporating # only suppliers which are at least obtained three times (remSingSupp.val = 2) # Correcting the values (correctVar = TRUE) # by adding 0.1 to the absolute values (correctVar.val = 0.1) ijmatrix_gro_adj <- ijmatrix_gro_adj[(ijmatrix_gro_adj$gro_purchase_code != "REFORMHAUSBOESER") & (ijmatrix_gro_adj$gro_purchase_code != "WMARKT_DURLACH") & (ijmatrix_gro_adj$gro_purchase_code != "X_INCOMPLETE_STORE"),] # Remove non-regarded observations ijmatrix_gro_adj_dist <- merge (ijmatrix_gro_adj, shopping2, by.x="interaction", by.y="route") # Include the distances and travel times (shopping2) ijmatrix_gro_adj_dist_stores <- merge (ijmatrix_gro_adj_dist, shopping4, by.x = "gro_purchase_code", by.y = "location_code") # Adding the store information (shopping4) mci.transvar(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs") # Log-centering transformation of one variable (p_ij_obs) ijmatrix_gro_transf <- mci.transmat(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs", "d_time", "salesarea_qm") # Log-centering transformation of the interaction matrix mcimodel_gro_trips <- mci.fit(ijmatrix_gro_adj_dist_stores, "resid_code", "gro_purchase_code", "p_ij_obs", "d_time", "salesarea_qm") # MCI model for the grocery store market areas # shares: "p_ij_obs", explanatory variables: "d_time", "salesarea_qm" summary(mcimodel_gro_trips) # Use like lm
This function creates a dataset of dummy variables based on an input character vector.
var.asdummy(x)var.asdummy(x)
x |
A character vector |
In MCI analyzes (as in OLS regression models generally) only quantitative information (that means: numeric) is allowed. Qualitative information (e.g. brands, companies, retail chains) can be added using dummy variables [1,0]. This function transforms a character vector x with characteristics to a set of dummy variables whose column names correspond to these characteristics marked with “_DUMMY”.
A data.frame with dummy variables corresponding to the levels of the input variable.
Thomas Wieland
Nakanishi, M./Cooper, L. G. (1982): “Simplified Estimation Procedures for MCI Models”. In: Marketing Science, 1, 3, p. 314-322.
Tihi, B./Oruc, N. (2012): “Competitive Location Assessment - the MCI Approach”. In: South East European Journal of Economics and Business, 7, 2, p. 35-49.
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.
charvec <- c("Peter", "Paul", "Peter", "Mary", "Peter", "Paul") # Creates a vector with three names (Peter, Paul, Mary) var.asdummy(charvec) # Returns a data frame with 3 dummy variables # (Mary_DUMMY, Paul_DUMMY, Peter_DUMMY) data(grocery2) # Loads the data dummyvars <- var.asdummy(grocery2$store_chain) # Save the dummy variable set into a new dataset mynewmcidata <- data.frame(grocery2, dummyvars) # Add the dummy dataset to the input datasetcharvec <- c("Peter", "Paul", "Peter", "Mary", "Peter", "Paul") # Creates a vector with three names (Peter, Paul, Mary) var.asdummy(charvec) # Returns a data frame with 3 dummy variables # (Mary_DUMMY, Paul_DUMMY, Peter_DUMMY) data(grocery2) # Loads the data dummyvars <- var.asdummy(grocery2$store_chain) # Save the dummy variable set into a new dataset mynewmcidata <- data.frame(grocery2, dummyvars) # Add the dummy dataset to the input dataset
This function corrects a numeric variable to match the MCI standards.
var.correct(x, corr.mode = "inc", incby = 1)var.correct(x, corr.mode = "inc", incby = 1)
x |
a numeric vector |
corr.mode |
character value for the mode of variable correction: |
incby |
value to increase the values with (default |
In the MCI model, only numeric variables with values greater than zero are accepted (From the theoretical perspective, a zero or negative attractivity/utility is just as impossible as negative market shares. In the log-centering transformation, those values cannot be processed.). This function corrects a numeric variable with zero and/or negative values to match the MCI standards. The most frequent case is that some absolute values which shall be used to calculate market shares (e.g. observed frequencies or expenditures) are equal to zero and must be increased by 1. Alternatively, they can be increased automatically by the absolute value of their minimum + incby. Another option which is especially designed to transform interval scale data (such as scoring in consumer surveys) is to apply a zeta-squared transformation (Cooper/Nakanishi 1983) to the numeric vector (corr.mode = "zetas").
Returns a numeric vector with the corrected values.
Thomas Wieland
Colome Perales, R. (2002): “Consumer Choice in Competitive Location Models”. Barcelona.
Cooper, L.G./Nakanishi, M. (1983): “Standardizing Variables in Multiplicative Choice Models”. In: Journal of Consumer Research, 10, 1, p. 96-108.
Cooper, L. G./Nakanishi, M. (2010): “Market-Share Analysis: Evaluating competitive marketing effectiveness”. Boston, Dordrecht, London : Kluwer (first published 1988). E-book version from 2010: http://www.anderson.ucla.edu/faculty/lee.cooper/MCI_Book/BOOKI2010.pdf
Hartmann, M. (2005): “Gravitationsmodelle als Verfahren der Standortanalyse im Einzelhandel”. Statistik Regional Electronic Papers, 02/2005. Halle.
Tihi, B./Oruc, N. (2012): “Competitive Location Assessment - the MCI Approach”. In: South East European Journal of Economics and Business, 7, 2, p. 35-49.
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.
var1 <- c(11, 17.5, 24.1, 0.9, 21.2, 0) # a vector containing one zero value var.correct(var1) # returns a vector with input values increased by 1 var2 <- -5:5 # a vector containing zero and negative values var.correct(var2, corr.mode = "incabs", incby = 1) # returns a vector with minimum value equal to 1 var.correct(var2, corr.mode = "zetas") # returns a vector only with positive values # (zeta-squared transformation)var1 <- c(11, 17.5, 24.1, 0.9, 21.2, 0) # a vector containing one zero value var.correct(var1) # returns a vector with input values increased by 1 var2 <- -5:5 # a vector containing zero and negative values var.correct(var2, corr.mode = "incabs", incby = 1) # returns a vector with minimum value equal to 1 var.correct(var2, corr.mode = "zetas") # returns a vector only with positive values # (zeta-squared transformation)