ijmatrix.create {MCI}

Interaction matrix with market shares

Description

Creation of an interaction matrix with market shares (p_{ij}) of every supplier (j) in every submarket (i) based on the frequencies in the raw data (e.g. household or POS survey).

Usage

ijmatrix.create(rawdataset, submarkets, suppliers, ..., remNA = TRUE, 
remSing = FALSE, remSing.val = 1, remSingSupp.val = 1, 
correctVar = FALSE, correctVar.val = 1)

Arguments

rawdataset

a data.frame containing the raw data

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 NA values of the submarkets and suppliers are removed or not (default: remNA = TRUE, otherwise: remNA = FALSE, which means that NA are considered in the interaction matrix, recoded as factor 99999)

remSing

logical argument that indicates if singular instances of the submarkets and suppliers are removed or not (default: remSing = FALSE)

remSing.val

if remSing = TRUE: numeric value that indicates the limit value of singular instances in the submarket set to be removed from the data

remSingSupp.val

if remSing = TRUE: numeric value that indicates the limit value of singular instances in the supplier set to be removed from the data

correctVar

logical argument that indicates if the calculated market shares shall be corrected when they do not match the MCI standards (p_{ij} = 0) (default: correctVar = FALSE)

correctVar.val

if correctVar = TRUE: numeric value which is added to the absolute values before calculating market shares (default: 1)

Details

This function creates an interaction matrix for all i submarkets (e.g. geographical regions) and all j suppliers (e.g. store locations). The function calculates p_{ij} based on the frequencies and, optionally, further market shares calculated from other observed variables in the given raw dataset (e.g. expenditures from submarket i at supplier j).

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 \le 2 and every supplier observed \le 1).

Value

An interaction matrix which is a data.frame containing the i x j 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 j in every i ('freq_ij_abs'), the observed absolute frequencies in every i ('freq_i_total') and the observed market shares of every j in every i ('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 i submarket and market shares (p_{ij}) 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.

Author(s)

Thomas Wieland

References

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.

See Also

ijmatrix.shares, ijmatrix.crosstab

Examples

# 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