MCI2 (version 1.1.2)

mci: Fitting the MCI model

Description

This function fits the MCI model based on a given MCI interaction matrix.

Usage

mci(mcimat, shares, ..., no.intercept = TRUE, 
mci.weighting = FALSE, mci.weights = NULL, 
show_proc = FALSE)

Arguments

mcimat

Object (list) created by the function mcimat.create (Creating an MCI interaction matrix based on raw data)

shares

Column containing the local market shares

…

Explanatory variables (partial utilites)

no.intercept

Logical argument that indicates if an intercept is included into the model

mci.weighting

Logical argument that indicates if weighted least squares (WLS) should be used for fitting the model

mci.weights

If mci.weighting = TRUE: optional weighting vector for the WLS fitting. If mci.weights = NULL, the reciprocals of the residuals are used as weightings

show_proc

Logical argument that indicates if the function prints messages about the state of process during the work

Value

A mcimodel list (invisible) containing the following components:

regdata

Log-centering transformed interaction matrix (data frame)

mcimodel_coef

A matrix containing the regression results (parameters, std. errors, t statistics,...)

mcimodel_stat

A matrix containing the regression model diagnostics (R-squared, adj. R-squared, F statistic,...)

Details

This function calculates a Multiplicative Competitive Interaction (MCI) Model based on a given interaction matrix.

References

Huff, D. L./Batsell, R. R. (1975): “Conceptual and Operational Problems with Market Share Models of Consumer Spatial Behavior”. In: Advances in Consumer Research, 2, p. 165-172.

Huff, D. L./McCallum, D. (2008): “Calibrating the Huff Model Using ArcGIS Business Analyst”. ESRI White Paper, September 2008. https://www.esri.com/library/whitepapers/pdfs/calibrating-huff-model.pdf

Nakanishi, M./Cooper, L. G. (1974): “Parameter Estimation for a Multiplicative Competitive Interaction Model - Least Squares Approach”. In: Journal of Marketing Research, 11, 3, p. 303-311.

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

Wieland, T. (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.

See Also

mcimat.create

Examples

# NOT RUN {
# 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)
# }