mci.shares: MCI market share/market area simulations
In MCI: Multiplicative Competitive Interaction (MCI) Model

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

This function calculates (local) market shares based on specified explanatory variables and their weighting parameters in a given MCI interaction matrix.

1	mci.shares(mcidataset, submarkets, suppliers, ..., mcitrans = "lc", interc = NULL)

`mcidataset`	an interaction matrix which is a `data.frame` containing the submarkets, suppliers 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
`...`	the column(s) of the explanatory variable(s) (at least one), numeric and positive (or dummy [1,0]), and their weighting parameter(s). The parameter(s) must follow the particular variable(s): `mcivariable1, parameter1, ...`
`mcitrans`	defines if the regular multiplicative formula is used or the inverse log-centering transformation where the explanatory variables are MCI-transformed and linked by addition in an exponential function instead of multiplication. This transformation is necessary if an intercept is included in the model and/or if dummy variables are used as explanatories (default: `mcitrans = "lc"`, which indicates the regular log-centering transformation)
`interc`	if `mcitrans = "ilc"`: logical argument that indicates if an intercept is included in the model (default `interc = NULL`)

In this function, the input dataset (MCI interaction matrix) is used for a calculation of (local) market shares (p_{ij}), based on (at least one) given explanatory variable(s) and (a) given weighting parameter(s). If an intercept is included in the model and/or if dummy variables are used as explanatories, the inverse log-centering transformation by Nakanishi/Cooper (1982) has to be used for simulations (mcitrans = "ilc").

The function mci.shares() returns the input interaction matrix (data.frame) with new variables/columns, where the last one (p_ij) is the one of interest, containing the (local) market shares of the j suppliers in the i submarkets (p_{ij}).

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. (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.transvar, shares.total

data(Freiburg1)
data(Freiburg2)
# Loads the data

mynewmatrix <- mci.shares(Freiburg1, "district", "store", "salesarea", 1, "distance", -2)
# Calculating shares based on two attractivity/utility variables

mynewmatrix_alldata <- merge(mynewmatrix, Freiburg2)
# Merge interaction matrix with district data (purchasing power)

shares.total (mynewmatrix_alldata, "district", "store", "p_ij", "ppower")
# Calculation of total sales

   suppliers_single  sum_E_j     share_j
1                 1  4057591 0.010759819
2                10  5809861 0.015406444
3                11  1289847 0.003420383
4                12  7103210 0.018836115
5                13  3476313 0.009218400
6                14  7264438 0.019263657
7                15  7667744 0.020333134
8                16  5836249 0.015476420
9                17  2093917 0.005552598
10               18  3717873 0.009858963
11               19  1836516 0.004870028
12                2  4163924 0.011041789
13               20  7193956 0.019076753
14               21  4587982 0.012166296
15               22  7219367 0.019144137
16               23  3511346 0.009311301
17               24  7529751 0.019967205
18               25  8959078 0.023757460
19               26 18002697 0.047739105
20               27  3118085 0.008268460
21               28  3247581 0.008611856
22               29 21478569 0.056956335
23                3  6936748 0.018394695
24               30  5087282 0.013490329
25               31  6333310 0.016794514
26               32  2555499 0.006776608
27               33  3659372 0.009703833
28               34  3660671 0.009707275
29               35  2439080 0.006467893
30               36  5843828 0.015496517
31               37  3687732 0.009779035
32               38  3329573 0.008829279
33               39  1412032 0.003744392
34                4  3890181 0.010315885
35               40  4837267 0.012827345
36               41  2996955 0.007947250
37               42  1747369 0.004633629
38               43  1307060 0.003466029
39               44  6414607 0.017010096
40               45 20704568 0.054903858
41               46 22209552 0.058894739
42               47  9658730 0.025612779
43               48 10347232 0.027438534
44               49  6232115 0.016526168
45                5  3272610 0.008678225
46               50 10234404 0.027139338
47               51 10456838 0.027729182
48               52  4877062 0.012932873
49               53 13217387 0.035049538
50               54  4402544 0.011674556
51               55  6433646 0.017060583
52               56  2437403 0.006463444
53               57  4097990 0.010866947
54               58  6495891 0.017225641
55               59  3502213 0.009287082
56                6  6880875 0.018246533
57               60  5747010 0.015239778
58               61  2760915 0.007321325
59               62  2458063 0.006518231
60               63  2860499 0.007585401
61                7  4027402 0.010679766
62                8  6245398 0.016561391
63                9  2241074 0.005942826