mcimat.create: Creation of a MCI interaction matrix
In MCI2: Market Area Models for Retail and Service Locations

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

Creation of an interaction matrix with local market shares (p_{ij}) of each location (j) in each customer origin (i) based on the frequencies in the raw data (e.g. household or POS survey).

mcimat.create(rawdata, origins.id, destinations.id, ..., tcmat, 
origvar.data = NULL, origvardata.id = NULL, 
destvar.data = NULL, destvardata.id = NULL, 
remOrig = NULL, remDest = NULL, corObserved = 0, 
remNA = TRUE)

`rawdata`	Raw data (`data.frame`), e.g. customer survey
`origins.id`	Vector of customer origins
`destinations.id`	Vector of destinations (stores, locations)
`...`	other numeric variables in the raw data which were observed and shall be used to calculate market shares (e.g. expenditures)
`tcmat`	Object (`list`) created by the function `tcmat.create` (Transportation costs matrix)
`origvar.data`	Optional: additional data (`data.frame`) concerning the customer origins
`origvardata.id`	Optional: customer origins in the additional origins data
`destvar.data`	Optional: additional data (`data.frame`) concerning the destinations
`destvardata.id`	Optional: destinations in the additional destinations data
`remOrig`	Optional: vector of origins to be removed from the analysis
`remDest`	Optional: vector of destinations to be removed from the analysis
`corObserved`	numeric value which is added to the absolute values before calculating market shares (default: 0)
`remNA`	Logical argument that indicates if `NA` values of the origins and destinations are removed or not

This function creates a Multiplicative Competitive Interaction (MCI) Model interaction matrix for further use in the function mci.

A mcimat list (invisible) containing the following components:

`mcimat`	MCI interaction matrix (`data frame`), also containing the local market shares (`p_ij`)
`coords`	A `list` containing the coordinates and additional information of the origins (`coords_origins`) and the destinations (`coords_destinations`), inherited from the `tcmat` object
`tc.mode`	A `list` containing information about the transportation costs matrix, inherited from the `tcmat` object
`mci.cormode`	A `list` containing information about the processing mode of the interaction matrix (removed origins/destinations etc.)

The function is a wrapper of ijmatrix.create from the MCI package. For further information see the MCI documentation and the corresponding RJ paper (Wieland 2017).

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.

Nakanishi, M./Cooper, L. G. (1982): “Simplified Estimation Procedures for MCI Models”. In: Marketing Science, 1, 3, p. 314-322.

Wieland, T. (2017): “Market Area Analysis for Retail and Service Locations with MCI”. In: The R Journal, 9, 1, p. 298-323. https://journal.r-project.org/archive/2017/RJ-2017-020/RJ-2017-020.pdf.

Wieland, T. (2018): “Competitive locations of grocery stores in the local supply context - The case of the urban district Freiburg-Haslach”. In: European Journal of Geography, 9, 3, p. 98-115.

mci, tcmat.create

# Compilation of tcmat list from existing datasets:
# (Results from the tcmat.create function)
data(Haslach_tcmatAirline)
# airline distances
data(Haslach_coords_origins)
# Coordinates of origins
data(Haslach_coords_destinations)
# Coordinates of destinationes

# Component "tc.mode":
Airline_tc.mode <- list()
Airline_tc.mode$tc.type = "airline"
Airline_tc.mode$tc.unit = "km"
Airline_tc.mode$tc.constant = 0

# tcmat with airline distances
# Compilation as a list:
tcmat_haslach_airline <- list(tcmat = Haslach_tcmatAirline,
coords_origins = Haslach_coords_origins,
coords_destinations = Haslach_coords_destinations,
tc.mode = Airline_tc.mode)

Drvtime_tc.mode <- list()
Drvtime_tc.mode$tc.type = "street"
Drvtime_tc.mode$tc.unit = "min"
Drvtime_tc.mode$tc.constant = 0

data(Haslach_tcmatDrvtime)
# car driving times

# tcmat with car driving times
# Compilation as a list:
tcmat_haslach_drvtime <- list(tcmat = Haslach_tcmatDrvtime,
coords_origins = Haslach_coords_origins,
coords_destinations = Haslach_coords_destinations,
tc.mode = Drvtime_tc.mode)

data(HaslachSurvey)
# survey raw data (Store choices and purchases)
data(HaslachDistricts)
# IDs and information about customer origins
data(HaslachStores)
# IDs and information about destinations (grocery stores)

# Preparing raw data (HaslachSurvey)
HaslachSurvey_prepared <- rawdata.prep (cols.below1 = 
list(HaslachSurvey$LM1_Text, HaslachSurvey$LM2_Text),
cols.below2 = list(HaslachSurvey$LM1E, HaslachSurvey$LM2E),
cols.keep = list(HaslachSurvey$WO),
colnames.new = c("LM", "LME", "Wohnort"))
# "WO" and "Wohnort" = origin ID
# "LM1_Text", "LM2_Text" and "LM" = destination IDs (grocery stores)
# "LM1E", "LM2E" and "LME" = grocery store purchases

# Creating a MCI interaction matrix
# based on raw data of a survey (HaslachSurvey_prepared)
# and a tcmat list object
mcimat_haslach <- mcimat.create(rawdata = HaslachSurvey_prepared, 
origins.id = "Wohnort", destinations.id = "LM", "LME", 
tcmat = tcmat_haslach_airline, 
remOrig = c("SBXXX", "SB613"), corObserved = 0.1,
origvar.data = HaslachDistricts, origvardata.id = "WO",
destvar.data = HaslachStores, destvardata.id = "LM")

# MCI model based on empirical local market shares
# two explanatory variables: distance (d_ij), store size (LM_VKF)
mcimodel_haslach <- mci (mcimat_haslach, "p_ij", "d_ij", "LM_VKF", 
show_proc = TRUE)