mci.transvar: Log-centering transformation of one variable in an MCI...
In MCI: Multiplicative Competitive Interaction (MCI) Model

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

This function applies the log-centering transformation to a variable in a given MCI interaction matrix.

1 2	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 `data.frame` containing the submarkets, suppliers and the regarded variables (e.g. the observed market shares, p_{ij}, and the explanatory variables)
`submarkets`	the column in the interaction matrix `mcidataset` containing the submarkets
`suppliers`	the column in the interaction matrix `mcidataset` containing the suppliers
`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 `data.frame` with three columns (submarkets, suppliers, transformed variable) or a vector only with the transformed values (default is `output_ij = FALSE`)
`output_var`	defines the mode of the function output if `output_ij = FALSE` (default is `output_var = "numeric"`, otherwise `"list"`)
`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: `show_proc = FALSE` (messages off)
`check_df`	logical argument that indicates if the input (dataset, column names) is checked (default: `check_df = TRUE` (should not be changed, only for internal use))

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.fit, 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

  [1]  0.5586409 -1.4456805  0.8119981  1.4633403 -1.4456805 -1.4456805
  [7] -0.4042878  0.1671033  0.7611454  0.8119981  0.1671033 -0.4297476
 [13]  0.6116451 -0.4297476  0.8924717 -0.4297476 -0.4297476 -0.4297476
 [19] -0.4297476  0.8924717  0.6116451 -0.4297476 -0.2148738 -0.2148738
 [25] -0.2148738  0.8265189 -0.2148738 -0.2148738 -0.2148738 -0.2148738
 [31]  1.1073455 -0.2148738 -0.2148738 -0.2148738 -0.2148738 -0.2148738
 [37]  1.1073455 -0.2148738 -0.2148738 -0.2148738 -0.2148738  0.8265189
 [43] -0.2148738 -0.2148738  0.1391845  0.1391845  0.4200111  0.8053619
 [49]  0.7105756 -0.9022082  0.5891535 -0.9022082  0.8053619 -0.9022082
 [55] -0.9022082 -0.1893441 -0.1893441 -0.1893441  0.8520486 -0.1893441
 [61] -0.1893441 -0.1893441 -0.1893441  0.8520486 -0.1893441 -0.1893441
 [67] -0.2768831 -0.2768831 -0.2768831  0.7645096 -0.2768831 -0.2768831
 [73] -0.2768831 -0.2768831  1.7274383 -0.2768831 -0.2768831 -0.1202018
 [79] -0.1202018 -0.1202018 -0.1202018 -0.1202018 -0.1202018 -0.1202018
 [85] -0.1202018  1.2020175 -0.1202018 -0.1202018 -0.3768671 -0.3768671
 [91]  0.6645256  1.2359167 -0.3768671 -0.3768671 -0.3768671 -0.3768671
 [97]  1.1144946 -0.3768671 -0.3768671 -0.3359608  0.7054318 -0.3359608
[103] -0.3359608 -0.3359608  0.7054318 -0.3359608 -0.3359608  1.2768230
[109] -0.3359608 -0.3359608 -0.2668185 -0.2668185 -0.2668185 -0.2668185
[115] -0.2668185  1.0554008 -0.2668185 -0.2668185  1.3459654 -0.2668185
[121] -0.2668185

Call:
lm(formula = mci_formula, data = mciworkfile)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.27457 -0.28725 -0.02391  0.32163  1.29351 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
d_time_t        -1.2443     0.2319  -5.367 4.02e-07 ***
salesarea_qm_t   0.9413     0.1158   8.132 4.59e-13 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.4458 on 119 degrees of freedom
Multiple R-squared:  0.4603,	Adjusted R-squared:  0.4512 
F-statistic: 50.74 on 2 and 119 DF,  p-value: < 2.2e-16