mci.transmat: Log-centering transformation of an MCI interaction matrix
In MCI: Multiplicative Competitive Interaction (MCI) Model
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
This function applies the log-centering transformation to the variables in a given MCI interaction matrix.
Usage
1
mci.transmat(mcidataset, submarkets, suppliers, mcivariable1, ..., show_proc = FALSE)
Arguments
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
mcivariable1
the column of the first variable to be transformed, numeric and positive (or dummy [1,0])
...
the columns of other variables to be transformed, numeric and positive (or dummy [1,0])
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)
Details
This function transformes the input dataset (MCI interaction matrix) to regression-ready data with the log-centering transformation by Nakanishi/Cooper (1974). The resulting data.frame can be fitted with the lm() function (to combine these two steps in one, 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).
Value
Returns a new data.frame with regression-ready data where the input variables are transformed by the the log-centering transformation. The names of the input variables are passed to the new data.frame marked with a "_t" to indicate that they were transformed (e.g. "shares_t" is the transformation of "shares").
Author(s)
Thomas Wieland
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.
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.
See Also
Examples
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# MCI analysis for the grocery store market areas in grocery2 #
data(grocery2)
# Loads the data
mci.transmat (grocery2, "plz_submarket", "store_code", "p_ij_obs", "dist_km", "salesarea_qm")
# Applies the log-centering transformation to the dataset using the function 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
Example output
plz_submarket store_code p_ij_obs_t dist_km_t salesarea_qm_t
1 PLZ_37073 ALDI1 -0.21478211 0.181616655 -0.15794353
2 PLZ_37073 ALDI3 -0.21478211 0.145112207 -0.16922454
3 PLZ_37073 ALDI6 -0.21478211 0.215378611 -0.09579563
4 PLZ_37073 ALDI7 0.08624789 0.336859862 -0.13096004
5 PLZ_37073 ALNATURA 0.26233915 -0.721997320 -0.33403479
6 PLZ_37073 EDEKA1 0.08624789 -0.116939911 0.25099186
7 PLZ_37073 EDEKA2 -0.21478211 0.438517839 -0.44797814
8 PLZ_37073 EDEKA3 -0.21478211 0.200018092 0.02914311
9 PLZ_37073 EDEKA4 -0.21478211 -0.178663577 -0.27188689
10 PLZ_37073 EDEKA5 -0.21478211 -0.117763504 -0.44797814
11 PLZ_37073 KAUFLAND1 -0.21478211 0.247502848 0.79194667
12 PLZ_37073 KAUFLAND2 0.86439914 -0.680666343 0.43426170
13 PLZ_37073 LIDL1 0.08624789 -0.063366459 -0.05003814
14 PLZ_37073 LIDL2 -0.21478211 0.253315501 -0.05003814
15 PLZ_37073 NAHKAUF1 -0.21478211 0.375630990 -0.17497687
16 PLZ_37073 NAHKAUF4 -0.21478211 -0.019313504 -0.57291688
17 PLZ_37073 NAHKAUF5 -0.21478211 0.158306586 -0.44797814
18 PLZ_37073 NETTO1 0.56336914 -0.897356519 -0.27188689
19 PLZ_37073 NETTO6 -0.21478211 -0.150573125 -0.14694815
20 PLZ_37073 PENNY1 -0.21478211 0.034819010 -0.30574515
21 PLZ_37073 PENNY2 -0.21478211 -0.144526863 -0.33907502
22 PLZ_37073 REAL1 0.08624789 0.227251582 1.01228056
23 PLZ_37073 REAL2 -0.21478211 0.330373786 0.80626773
24 PLZ_37073 REWE1 0.73946040 -0.102688478 0.28401330
25 PLZ_37073 REWE2 -0.21478211 -0.755617172 -0.47600687
26 PLZ_37073 REWE3 0.38727788 -0.087920984 0.44661480
27 PLZ_37073 REWE4 0.26233915 0.131495832 0.20523437
28 PLZ_37073 REWE6 -0.21478211 0.190362357 0.02147567
29 PLZ_37073 TEGUT1 0.78521789 -0.066441493 0.23303684
30 PLZ_37073 TEGUT2 0.08624789 0.173400864 0.12518366
31 PLZ_37073 TEGUT3 -0.21478211 0.308285850 0.14475362
32 PLZ_37073 TEGUT4 -0.21478211 0.155586779 0.10620805
33 PLZ_37075 ALDI1 0.35814513 -0.299366621 -0.15794353
34 PLZ_37075 ALDI3 -0.24391487 0.265244859 -0.16922454
35 PLZ_37075 ALDI6 -0.24391487 0.224522614 -0.09579563
36 PLZ_37075 ALDI7 -0.24391487 0.383879117 -0.13096004
37 PLZ_37075 ALNATURA 0.35814513 0.017886455 -0.33403479
38 PLZ_37075 EDEKA1 -0.24391487 -0.395758981 0.25099186
39 PLZ_37075 EDEKA2 -0.24391487 0.266575899 -0.44797814
40 PLZ_37075 EDEKA3 -0.24391487 0.144924876 0.02914311
41 PLZ_37075 EDEKA4 0.23320639 -0.061494497 -0.27188689
42 PLZ_37075 EDEKA5 -0.24391487 0.183093060 -0.44797814
43 PLZ_37075 KAUFLAND1 -0.24391487 0.216384188 0.79194667
44 PLZ_37075 KAUFLAND2 0.45505514 0.024444780 0.43426170
45 PLZ_37075 LIDL1 0.23320639 -0.595477885 -0.05003814
46 PLZ_37075 LIDL2 -0.24391487 0.256407273 -0.05003814
47 PLZ_37075 NAHKAUF1 -0.24391487 0.044905066 -0.17497687
48 PLZ_37075 NAHKAUF4 -0.24391487 0.197236070 -0.57291688
49 PLZ_37075 NAHKAUF5 -0.24391487 0.300609112 -0.44797814
50 PLZ_37075 NETTO1 0.05711513 -0.049764072 -0.27188689
51 PLZ_37075 NETTO6 0.05711513 -0.305547680 -0.14694815
52 PLZ_37075 PENNY1 0.35814513 -1.094601196 -0.30574515
53 PLZ_37075 PENNY2 -0.24391487 0.162652010 -0.33907502
54 PLZ_37075 REAL1 0.05711513 -0.185731025 1.01228056
55 PLZ_37075 REAL2 0.23320639 0.379014949 0.80626773
56 PLZ_37075 REWE1 0.23320639 0.099862279 0.28401330
57 PLZ_37075 REWE2 -0.24391487 0.012928046 -0.47600687
58 PLZ_37075 REWE3 0.79747782 -0.434157964 0.44661480
59 PLZ_37075 REWE4 0.05711513 0.304984853 0.20523437
60 PLZ_37075 REWE6 -0.24391487 0.303364273 0.02147567
61 PLZ_37075 TEGUT1 0.60118317 -0.575195827 0.23303684
62 PLZ_37075 TEGUT2 0.05711513 -0.426336574 0.12518366
63 PLZ_37075 TEGUT3 -0.24391487 0.362587905 0.14475362
64 PLZ_37075 TEGUT4 -0.24391487 0.271924640 0.10620805
65 PLZ_37077 ALDI1 -0.10172727 -0.615197054 -0.15794353
66 PLZ_37077 ALDI3 -0.10172727 0.233871871 -0.16922454
67 PLZ_37077 ALDI6 -0.10172727 0.136000825 -0.09579563
68 PLZ_37077 ALDI7 -0.10172727 0.304523236 -0.13096004
69 PLZ_37077 ALNATURA -0.10172727 0.058946520 -0.33403479
70 PLZ_37077 EDEKA1 0.19930273 -0.173318638 0.25099186
71 PLZ_37077 EDEKA2 0.19930273 0.091617476 -0.44797814
72 PLZ_37077 EDEKA3 -0.10172727 -0.003081685 0.02914311
73 PLZ_37077 EDEKA4 -0.10172727 0.003978282 -0.27188689
74 PLZ_37077 EDEKA5 -0.10172727 0.174403182 -0.44797814
75 PLZ_37077 KAUFLAND1 -0.10172727 0.077577427 0.79194667
76 PLZ_37077 KAUFLAND2 0.19930273 0.063272563 0.43426170
77 PLZ_37077 LIDL1 -0.10172727 -0.240067193 -0.05003814
78 PLZ_37077 LIDL2 -0.10172727 0.164130035 -0.05003814
79 PLZ_37077 NAHKAUF1 0.37539399 -0.406342851 -0.17497687
80 PLZ_37077 NAHKAUF4 -0.10172727 0.183640529 -0.57291688
81 PLZ_37077 NAHKAUF5 -0.10172727 0.264046203 -0.44797814
82 PLZ_37077 NETTO1 -0.10172727 0.015641639 -0.27188689
83 PLZ_37077 NETTO6 -0.10172727 -0.131835358 -0.14694815
84 PLZ_37077 PENNY1 -0.10172727 -0.346826349 -0.30574515
85 PLZ_37077 PENNY2 -0.10172727 0.159415854 -0.33907502
86 PLZ_37077 REAL1 0.59724274 -0.607205701 1.01228056
87 PLZ_37077 REAL2 -0.10172727 0.313064405 0.80626773
88 PLZ_37077 REWE1 -0.10172727 0.110747271 0.28401330
89 PLZ_37077 REWE2 -0.10172727 0.055690614 -0.47600687
90 PLZ_37077 REWE3 -0.10172727 -0.186610872 0.44661480
91 PLZ_37077 REWE4 -0.10172727 0.267492237 0.20523437
92 PLZ_37077 REWE6 -0.10172727 0.263511396 0.02147567
93 PLZ_37077 TEGUT1 0.59724274 -0.244098063 0.23303684
94 PLZ_37077 TEGUT2 0.37539399 -0.537163208 0.12518366
95 PLZ_37077 TEGUT3 -0.10172727 0.311102192 0.14475362
96 PLZ_37077 TEGUT4 -0.10172727 0.239073215 0.10620805
97 PLZ_37079 ALDI1 -0.09957473 0.006863408 -0.15794353
98 PLZ_37079 ALDI3 -0.09957473 0.262644245 -0.16922454
99 PLZ_37079 ALDI6 -0.09957473 -0.397022834 -0.09579563
100 PLZ_37079 ALDI7 -0.09957473 -0.117874073 -0.13096004
101 PLZ_37079 ALNATURA 0.20145527 0.073430624 -0.33403479
102 PLZ_37079 EDEKA1 -0.09957473 0.015334607 0.25099186
103 PLZ_37079 EDEKA2 -0.09957473 0.324895820 -0.44797814
104 PLZ_37079 EDEKA3 0.37754653 -0.477838167 0.02914311
105 PLZ_37079 EDEKA4 -0.09957473 0.115997117 -0.27188689
106 PLZ_37079 EDEKA5 -0.09957473 0.174006948 -0.44797814
107 PLZ_37079 KAUFLAND1 0.20145527 -0.783354459 0.79194667
108 PLZ_37079 KAUFLAND2 0.20145527 0.077135132 0.43426170
109 PLZ_37079 LIDL1 -0.09957473 0.054664654 -0.05003814
110 PLZ_37079 LIDL2 -0.09957473 -0.444118569 -0.05003814
111 PLZ_37079 NAHKAUF1 -0.09957473 0.168439503 -0.17497687
112 PLZ_37079 NAHKAUF4 0.20145527 0.026658124 -0.57291688
113 PLZ_37079 NAHKAUF5 -0.09957473 0.268084943 -0.44797814
114 PLZ_37079 NETTO1 -0.09957473 0.022827323 -0.27188689
115 PLZ_37079 NETTO6 -0.09957473 0.001707982 -0.14694815
116 PLZ_37079 PENNY1 -0.09957473 0.084302974 -0.30574515
117 PLZ_37079 PENNY2 -0.09957473 0.166327883 -0.33907502
118 PLZ_37079 REAL1 0.20145527 -0.008153394 1.01228056
119 PLZ_37079 REAL2 0.50248527 -0.098145168 0.80626773
120 PLZ_37079 REWE1 -0.09957473 -0.119876006 0.28401330
121 PLZ_37079 REWE2 0.20145527 0.070646010 -0.47600687
122 PLZ_37079 REWE3 -0.09957473 0.042926533 0.44661480
123 PLZ_37079 REWE4 -0.09957473 0.252937988 0.20523437
124 PLZ_37079 REWE6 -0.09957473 -0.087058039 0.02147567
125 PLZ_37079 TEGUT1 -0.09957473 0.049692313 0.23303684
126 PLZ_37079 TEGUT2 0.20145527 0.061781705 0.12518366
127 PLZ_37079 TEGUT3 -0.09957473 -0.054820608 0.14475362
128 PLZ_37079 TEGUT4 -0.09957473 0.266955480 0.10620805
129 PLZ_37081 ALDI1 -0.10667609 0.199183392 -0.15794353
130 PLZ_37081 ALDI3 -0.10667609 0.236021642 -0.16922454
131 PLZ_37081 ALDI6 0.19435390 -0.396608465 -0.09579563
132 PLZ_37081 ALDI7 -0.10667609 -0.183594854 -0.13096004
133 PLZ_37081 ALNATURA -0.10667609 -0.045938140 -0.33403479
134 PLZ_37081 EDEKA1 -0.10667609 0.007796204 0.25099186
135 PLZ_37081 EDEKA2 -0.10667609 0.409798383 -0.44797814
136 PLZ_37081 EDEKA3 -0.10667609 -0.078348020 0.02914311
137 PLZ_37081 EDEKA4 -0.10667609 0.102188519 -0.27188689
138 PLZ_37081 EDEKA5 -0.10667609 0.107977380 -0.44797814
139 PLZ_37081 KAUFLAND1 0.19435390 -0.080205019 0.79194667
140 PLZ_37081 KAUFLAND2 0.19435390 -0.039715028 0.43426170
141 PLZ_37081 LIDL1 -0.10667609 0.058346751 -0.05003814
142 PLZ_37081 LIDL2 0.19435390 -0.310434636 -0.05003814
143 PLZ_37081 NAHKAUF1 -0.10667609 0.336585298 -0.17497687
144 PLZ_37081 NAHKAUF4 -0.10667609 -0.175298432 -0.57291688
145 PLZ_37081 NAHKAUF5 -0.10667609 0.243088985 -0.44797814
146 PLZ_37081 NETTO1 0.37044516 -0.072788503 -0.27188689
147 PLZ_37081 NETTO6 -0.10667609 -0.010035235 -0.14694815
148 PLZ_37081 PENNY1 -0.10667609 0.116882823 -0.30574515
149 PLZ_37081 PENNY2 -0.10667609 0.098441665 -0.33907502
150 PLZ_37081 REAL1 -0.10667609 0.188493478 1.01228056
151 PLZ_37081 REAL2 -0.10667609 -0.198478013 0.80626773
152 PLZ_37081 REWE1 0.37044516 -0.505428583 0.28401330
153 PLZ_37081 REWE2 -0.10667609 -0.050639905 -0.47600687
154 PLZ_37081 REWE3 -0.10667609 0.043395245 0.44661480
155 PLZ_37081 REWE4 -0.10667609 0.198380684 0.20523437
156 PLZ_37081 REWE6 0.37044516 -0.443600165 0.02147567
157 PLZ_37081 TEGUT1 0.37044516 0.052026692 0.23303684
158 PLZ_37081 TEGUT2 -0.10667609 0.202111347 0.12518366
159 PLZ_37081 TEGUT3 0.19435390 -0.251483393 0.14475362
160 PLZ_37081 TEGUT4 -0.10667609 0.241877901 0.10620805
161 PLZ_37083 ALDI1 -0.16130697 0.220547032 -0.15794353
162 PLZ_37083 ALDI3 0.13972303 -0.159335078 -0.16922454
163 PLZ_37083 ALDI6 -0.16130697 0.235820448 -0.09579563
164 PLZ_37083 ALDI7 -0.16130697 0.302932598 -0.13096004
165 PLZ_37083 ALNATURA -0.16130697 -0.300909392 -0.33403479
166 PLZ_37083 EDEKA1 -0.16130697 0.045497839 0.25099186
167 PLZ_37083 EDEKA2 -0.16130697 0.389668922 -0.44797814
168 PLZ_37083 EDEKA3 -0.16130697 0.238248223 0.02914311
169 PLZ_37083 EDEKA4 -0.16130697 -0.042640350 -0.27188689
170 PLZ_37083 EDEKA5 0.31581429 -1.183823899 -0.44797814
171 PLZ_37083 KAUFLAND1 0.44075302 0.270552897 0.79194667
172 PLZ_37083 KAUFLAND2 0.61684428 -0.345493586 0.43426170
173 PLZ_37083 LIDL1 0.13972303 0.073222913 -0.05003814
174 PLZ_37083 LIDL2 -0.16130697 0.262582041 -0.05003814
175 PLZ_37083 NAHKAUF1 -0.16130697 0.359105058 -0.17497687
176 PLZ_37083 NAHKAUF4 -0.16130697 -0.041410053 -0.57291688
177 PLZ_37083 NAHKAUF5 -0.16130697 -0.227969855 -0.44797814
178 PLZ_37083 NETTO1 0.13972303 -0.171235479 -0.27188689
179 PLZ_37083 NETTO6 -0.16130697 0.028935859 -0.14694815
180 PLZ_37083 PENNY1 -0.16130697 0.128289239 -0.30574515
181 PLZ_37083 PENNY2 0.31581429 -0.546528578 -0.33907502
182 PLZ_37083 REAL1 -0.16130697 0.251523989 1.01228056
183 PLZ_37083 REAL2 0.13972303 0.297822161 0.80626773
184 PLZ_37083 REWE1 0.13972303 0.040953713 0.28401330
185 PLZ_37083 REWE2 -0.16130697 -0.317976426 -0.47600687
186 PLZ_37083 REWE3 -0.16130697 0.060310783 0.44661480
187 PLZ_37083 REWE4 0.68379107 -0.388165864 0.20523437
188 PLZ_37083 REWE6 -0.16130697 0.135513666 0.02147567
189 PLZ_37083 TEGUT1 0.31581429 0.071586937 0.23303684
190 PLZ_37083 TEGUT2 -0.16130697 0.195748283 0.12518366
191 PLZ_37083 TEGUT3 -0.16130697 0.280541664 0.14475362
192 PLZ_37083 TEGUT4 -0.16130697 -0.163915704 0.10620805
193 PLZ_37085 ALDI1 -0.19436922 0.181542457 -0.15794353
194 PLZ_37085 ALDI3 -0.19436922 -0.838223266 -0.16922454
195 PLZ_37085 ALDI6 -0.19436922 0.203808390 -0.09579563
196 PLZ_37085 ALDI7 -0.19436922 0.272194155 -0.13096004
197 PLZ_37085 ALNATURA 0.10666078 -0.136797067 -0.33403479
198 PLZ_37085 EDEKA1 -0.19436922 0.065170808 0.25099186
199 PLZ_37085 EDEKA2 -0.19436922 0.212375537 -0.44797814
200 PLZ_37085 EDEKA3 -0.19436922 0.204426114 0.02914311
201 PLZ_37085 EDEKA4 0.28275204 -0.154655825 -0.27188689
202 PLZ_37085 EDEKA5 -0.19436922 -0.219310104 -0.44797814
203 PLZ_37085 KAUFLAND1 0.28275204 0.229363658 0.79194667
204 PLZ_37085 KAUFLAND2 0.50460079 -0.157858978 0.43426170
205 PLZ_37085 LIDL1 0.10666078 0.061132810 -0.05003814
206 PLZ_37085 LIDL2 -0.19436922 0.224353232 -0.05003814
207 PLZ_37085 NAHKAUF1 -0.19436922 0.268878221 -0.17497687
208 PLZ_37085 NAHKAUF4 -0.19436922 0.046293539 -0.57291688
209 PLZ_37085 NAHKAUF5 0.40769077 -0.401119319 -0.44797814
210 PLZ_37085 NETTO1 0.40769077 -0.069046064 -0.27188689
211 PLZ_37085 NETTO6 -0.19436922 0.054033413 -0.14694815
212 PLZ_37085 PENNY1 -0.19436922 0.087498448 -0.30574515
213 PLZ_37085 PENNY2 -0.19436922 -0.245529065 -0.33907502
214 PLZ_37085 REAL1 0.10666078 0.208826142 1.01228056
215 PLZ_37085 REAL2 0.10666078 0.268316014 0.80626773
216 PLZ_37085 REWE1 0.40769077 0.063812642 0.28401330
217 PLZ_37085 REWE2 -0.19436922 -0.144994438 -0.47600687
218 PLZ_37085 REWE3 -0.19436922 0.074772559 0.44661480
219 PLZ_37085 REWE4 0.28275204 -0.116845433 0.20523437
220 PLZ_37085 REWE6 -0.19436922 0.173490410 0.02147567
221 PLZ_37085 TEGUT1 0.28275204 0.082994425 0.23303684
222 PLZ_37085 TEGUT2 0.10666078 0.115728257 0.12518366
223 PLZ_37085 TEGUT3 -0.19436922 0.255284573 0.14475362
224 PLZ_37085 TEGUT4 0.10666078 -0.869916245 0.10620805
[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
MCI documentation built on May 2, 2019, 6:02 a.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
This function applies the log-centering transformation to the variables in a given MCI interaction matrix.
Usage
1 | mci.transmat(mcidataset, submarkets, suppliers, mcivariable1, ..., show_proc = FALSE)
|
Arguments
mcidataset |
an interaction matrix which is a |
submarkets |
the column in the interaction matrix |
suppliers |
the column in the interaction matrix |
mcivariable1 |
the column of the first variable to be transformed, numeric and positive (or dummy [1,0]) |
... |
the columns of other variables to be transformed, numeric and positive (or dummy [1,0]) |
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: |
Details
This function transformes the input dataset (MCI interaction matrix) to regression-ready data with the log-centering transformation by Nakanishi/Cooper (1974). The resulting data.frame can be fitted with the lm() function (to combine these two steps in one, 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).
Value
Returns a new data.frame with regression-ready data where the input variables are transformed by the the log-centering transformation. The names of the input variables are passed to the new data.frame marked with a "_t" to indicate that they were transformed (e.g. "shares_t" is the transformation of "shares").
Author(s)
Thomas Wieland
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.
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.
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 | # MCI analysis for the grocery store market areas in grocery2 #
data(grocery2)
# Loads the data
mci.transmat (grocery2, "plz_submarket", "store_code", "p_ij_obs", "dist_km", "salesarea_qm")
# Applies the log-centering transformation to the dataset using the function 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
|
Example output
plz_submarket store_code p_ij_obs_t dist_km_t salesarea_qm_t
1 PLZ_37073 ALDI1 -0.21478211 0.181616655 -0.15794353
2 PLZ_37073 ALDI3 -0.21478211 0.145112207 -0.16922454
3 PLZ_37073 ALDI6 -0.21478211 0.215378611 -0.09579563
4 PLZ_37073 ALDI7 0.08624789 0.336859862 -0.13096004
5 PLZ_37073 ALNATURA 0.26233915 -0.721997320 -0.33403479
6 PLZ_37073 EDEKA1 0.08624789 -0.116939911 0.25099186
7 PLZ_37073 EDEKA2 -0.21478211 0.438517839 -0.44797814
8 PLZ_37073 EDEKA3 -0.21478211 0.200018092 0.02914311
9 PLZ_37073 EDEKA4 -0.21478211 -0.178663577 -0.27188689
10 PLZ_37073 EDEKA5 -0.21478211 -0.117763504 -0.44797814
11 PLZ_37073 KAUFLAND1 -0.21478211 0.247502848 0.79194667
12 PLZ_37073 KAUFLAND2 0.86439914 -0.680666343 0.43426170
13 PLZ_37073 LIDL1 0.08624789 -0.063366459 -0.05003814
14 PLZ_37073 LIDL2 -0.21478211 0.253315501 -0.05003814
15 PLZ_37073 NAHKAUF1 -0.21478211 0.375630990 -0.17497687
16 PLZ_37073 NAHKAUF4 -0.21478211 -0.019313504 -0.57291688
17 PLZ_37073 NAHKAUF5 -0.21478211 0.158306586 -0.44797814
18 PLZ_37073 NETTO1 0.56336914 -0.897356519 -0.27188689
19 PLZ_37073 NETTO6 -0.21478211 -0.150573125 -0.14694815
20 PLZ_37073 PENNY1 -0.21478211 0.034819010 -0.30574515
21 PLZ_37073 PENNY2 -0.21478211 -0.144526863 -0.33907502
22 PLZ_37073 REAL1 0.08624789 0.227251582 1.01228056
23 PLZ_37073 REAL2 -0.21478211 0.330373786 0.80626773
24 PLZ_37073 REWE1 0.73946040 -0.102688478 0.28401330
25 PLZ_37073 REWE2 -0.21478211 -0.755617172 -0.47600687
26 PLZ_37073 REWE3 0.38727788 -0.087920984 0.44661480
27 PLZ_37073 REWE4 0.26233915 0.131495832 0.20523437
28 PLZ_37073 REWE6 -0.21478211 0.190362357 0.02147567
29 PLZ_37073 TEGUT1 0.78521789 -0.066441493 0.23303684
30 PLZ_37073 TEGUT2 0.08624789 0.173400864 0.12518366
31 PLZ_37073 TEGUT3 -0.21478211 0.308285850 0.14475362
32 PLZ_37073 TEGUT4 -0.21478211 0.155586779 0.10620805
33 PLZ_37075 ALDI1 0.35814513 -0.299366621 -0.15794353
34 PLZ_37075 ALDI3 -0.24391487 0.265244859 -0.16922454
35 PLZ_37075 ALDI6 -0.24391487 0.224522614 -0.09579563
36 PLZ_37075 ALDI7 -0.24391487 0.383879117 -0.13096004
37 PLZ_37075 ALNATURA 0.35814513 0.017886455 -0.33403479
38 PLZ_37075 EDEKA1 -0.24391487 -0.395758981 0.25099186
39 PLZ_37075 EDEKA2 -0.24391487 0.266575899 -0.44797814
40 PLZ_37075 EDEKA3 -0.24391487 0.144924876 0.02914311
41 PLZ_37075 EDEKA4 0.23320639 -0.061494497 -0.27188689
42 PLZ_37075 EDEKA5 -0.24391487 0.183093060 -0.44797814
43 PLZ_37075 KAUFLAND1 -0.24391487 0.216384188 0.79194667
44 PLZ_37075 KAUFLAND2 0.45505514 0.024444780 0.43426170
45 PLZ_37075 LIDL1 0.23320639 -0.595477885 -0.05003814
46 PLZ_37075 LIDL2 -0.24391487 0.256407273 -0.05003814
47 PLZ_37075 NAHKAUF1 -0.24391487 0.044905066 -0.17497687
48 PLZ_37075 NAHKAUF4 -0.24391487 0.197236070 -0.57291688
49 PLZ_37075 NAHKAUF5 -0.24391487 0.300609112 -0.44797814
50 PLZ_37075 NETTO1 0.05711513 -0.049764072 -0.27188689
51 PLZ_37075 NETTO6 0.05711513 -0.305547680 -0.14694815
52 PLZ_37075 PENNY1 0.35814513 -1.094601196 -0.30574515
53 PLZ_37075 PENNY2 -0.24391487 0.162652010 -0.33907502
54 PLZ_37075 REAL1 0.05711513 -0.185731025 1.01228056
55 PLZ_37075 REAL2 0.23320639 0.379014949 0.80626773
56 PLZ_37075 REWE1 0.23320639 0.099862279 0.28401330
57 PLZ_37075 REWE2 -0.24391487 0.012928046 -0.47600687
58 PLZ_37075 REWE3 0.79747782 -0.434157964 0.44661480
59 PLZ_37075 REWE4 0.05711513 0.304984853 0.20523437
60 PLZ_37075 REWE6 -0.24391487 0.303364273 0.02147567
61 PLZ_37075 TEGUT1 0.60118317 -0.575195827 0.23303684
62 PLZ_37075 TEGUT2 0.05711513 -0.426336574 0.12518366
63 PLZ_37075 TEGUT3 -0.24391487 0.362587905 0.14475362
64 PLZ_37075 TEGUT4 -0.24391487 0.271924640 0.10620805
65 PLZ_37077 ALDI1 -0.10172727 -0.615197054 -0.15794353
66 PLZ_37077 ALDI3 -0.10172727 0.233871871 -0.16922454
67 PLZ_37077 ALDI6 -0.10172727 0.136000825 -0.09579563
68 PLZ_37077 ALDI7 -0.10172727 0.304523236 -0.13096004
69 PLZ_37077 ALNATURA -0.10172727 0.058946520 -0.33403479
70 PLZ_37077 EDEKA1 0.19930273 -0.173318638 0.25099186
71 PLZ_37077 EDEKA2 0.19930273 0.091617476 -0.44797814
72 PLZ_37077 EDEKA3 -0.10172727 -0.003081685 0.02914311
73 PLZ_37077 EDEKA4 -0.10172727 0.003978282 -0.27188689
74 PLZ_37077 EDEKA5 -0.10172727 0.174403182 -0.44797814
75 PLZ_37077 KAUFLAND1 -0.10172727 0.077577427 0.79194667
76 PLZ_37077 KAUFLAND2 0.19930273 0.063272563 0.43426170
77 PLZ_37077 LIDL1 -0.10172727 -0.240067193 -0.05003814
78 PLZ_37077 LIDL2 -0.10172727 0.164130035 -0.05003814
79 PLZ_37077 NAHKAUF1 0.37539399 -0.406342851 -0.17497687
80 PLZ_37077 NAHKAUF4 -0.10172727 0.183640529 -0.57291688
81 PLZ_37077 NAHKAUF5 -0.10172727 0.264046203 -0.44797814
82 PLZ_37077 NETTO1 -0.10172727 0.015641639 -0.27188689
83 PLZ_37077 NETTO6 -0.10172727 -0.131835358 -0.14694815
84 PLZ_37077 PENNY1 -0.10172727 -0.346826349 -0.30574515
85 PLZ_37077 PENNY2 -0.10172727 0.159415854 -0.33907502
86 PLZ_37077 REAL1 0.59724274 -0.607205701 1.01228056
87 PLZ_37077 REAL2 -0.10172727 0.313064405 0.80626773
88 PLZ_37077 REWE1 -0.10172727 0.110747271 0.28401330
89 PLZ_37077 REWE2 -0.10172727 0.055690614 -0.47600687
90 PLZ_37077 REWE3 -0.10172727 -0.186610872 0.44661480
91 PLZ_37077 REWE4 -0.10172727 0.267492237 0.20523437
92 PLZ_37077 REWE6 -0.10172727 0.263511396 0.02147567
93 PLZ_37077 TEGUT1 0.59724274 -0.244098063 0.23303684
94 PLZ_37077 TEGUT2 0.37539399 -0.537163208 0.12518366
95 PLZ_37077 TEGUT3 -0.10172727 0.311102192 0.14475362
96 PLZ_37077 TEGUT4 -0.10172727 0.239073215 0.10620805
97 PLZ_37079 ALDI1 -0.09957473 0.006863408 -0.15794353
98 PLZ_37079 ALDI3 -0.09957473 0.262644245 -0.16922454
99 PLZ_37079 ALDI6 -0.09957473 -0.397022834 -0.09579563
100 PLZ_37079 ALDI7 -0.09957473 -0.117874073 -0.13096004
101 PLZ_37079 ALNATURA 0.20145527 0.073430624 -0.33403479
102 PLZ_37079 EDEKA1 -0.09957473 0.015334607 0.25099186
103 PLZ_37079 EDEKA2 -0.09957473 0.324895820 -0.44797814
104 PLZ_37079 EDEKA3 0.37754653 -0.477838167 0.02914311
105 PLZ_37079 EDEKA4 -0.09957473 0.115997117 -0.27188689
106 PLZ_37079 EDEKA5 -0.09957473 0.174006948 -0.44797814
107 PLZ_37079 KAUFLAND1 0.20145527 -0.783354459 0.79194667
108 PLZ_37079 KAUFLAND2 0.20145527 0.077135132 0.43426170
109 PLZ_37079 LIDL1 -0.09957473 0.054664654 -0.05003814
110 PLZ_37079 LIDL2 -0.09957473 -0.444118569 -0.05003814
111 PLZ_37079 NAHKAUF1 -0.09957473 0.168439503 -0.17497687
112 PLZ_37079 NAHKAUF4 0.20145527 0.026658124 -0.57291688
113 PLZ_37079 NAHKAUF5 -0.09957473 0.268084943 -0.44797814
114 PLZ_37079 NETTO1 -0.09957473 0.022827323 -0.27188689
115 PLZ_37079 NETTO6 -0.09957473 0.001707982 -0.14694815
116 PLZ_37079 PENNY1 -0.09957473 0.084302974 -0.30574515
117 PLZ_37079 PENNY2 -0.09957473 0.166327883 -0.33907502
118 PLZ_37079 REAL1 0.20145527 -0.008153394 1.01228056
119 PLZ_37079 REAL2 0.50248527 -0.098145168 0.80626773
120 PLZ_37079 REWE1 -0.09957473 -0.119876006 0.28401330
121 PLZ_37079 REWE2 0.20145527 0.070646010 -0.47600687
122 PLZ_37079 REWE3 -0.09957473 0.042926533 0.44661480
123 PLZ_37079 REWE4 -0.09957473 0.252937988 0.20523437
124 PLZ_37079 REWE6 -0.09957473 -0.087058039 0.02147567
125 PLZ_37079 TEGUT1 -0.09957473 0.049692313 0.23303684
126 PLZ_37079 TEGUT2 0.20145527 0.061781705 0.12518366
127 PLZ_37079 TEGUT3 -0.09957473 -0.054820608 0.14475362
128 PLZ_37079 TEGUT4 -0.09957473 0.266955480 0.10620805
129 PLZ_37081 ALDI1 -0.10667609 0.199183392 -0.15794353
130 PLZ_37081 ALDI3 -0.10667609 0.236021642 -0.16922454
131 PLZ_37081 ALDI6 0.19435390 -0.396608465 -0.09579563
132 PLZ_37081 ALDI7 -0.10667609 -0.183594854 -0.13096004
133 PLZ_37081 ALNATURA -0.10667609 -0.045938140 -0.33403479
134 PLZ_37081 EDEKA1 -0.10667609 0.007796204 0.25099186
135 PLZ_37081 EDEKA2 -0.10667609 0.409798383 -0.44797814
136 PLZ_37081 EDEKA3 -0.10667609 -0.078348020 0.02914311
137 PLZ_37081 EDEKA4 -0.10667609 0.102188519 -0.27188689
138 PLZ_37081 EDEKA5 -0.10667609 0.107977380 -0.44797814
139 PLZ_37081 KAUFLAND1 0.19435390 -0.080205019 0.79194667
140 PLZ_37081 KAUFLAND2 0.19435390 -0.039715028 0.43426170
141 PLZ_37081 LIDL1 -0.10667609 0.058346751 -0.05003814
142 PLZ_37081 LIDL2 0.19435390 -0.310434636 -0.05003814
143 PLZ_37081 NAHKAUF1 -0.10667609 0.336585298 -0.17497687
144 PLZ_37081 NAHKAUF4 -0.10667609 -0.175298432 -0.57291688
145 PLZ_37081 NAHKAUF5 -0.10667609 0.243088985 -0.44797814
146 PLZ_37081 NETTO1 0.37044516 -0.072788503 -0.27188689
147 PLZ_37081 NETTO6 -0.10667609 -0.010035235 -0.14694815
148 PLZ_37081 PENNY1 -0.10667609 0.116882823 -0.30574515
149 PLZ_37081 PENNY2 -0.10667609 0.098441665 -0.33907502
150 PLZ_37081 REAL1 -0.10667609 0.188493478 1.01228056
151 PLZ_37081 REAL2 -0.10667609 -0.198478013 0.80626773
152 PLZ_37081 REWE1 0.37044516 -0.505428583 0.28401330
153 PLZ_37081 REWE2 -0.10667609 -0.050639905 -0.47600687
154 PLZ_37081 REWE3 -0.10667609 0.043395245 0.44661480
155 PLZ_37081 REWE4 -0.10667609 0.198380684 0.20523437
156 PLZ_37081 REWE6 0.37044516 -0.443600165 0.02147567
157 PLZ_37081 TEGUT1 0.37044516 0.052026692 0.23303684
158 PLZ_37081 TEGUT2 -0.10667609 0.202111347 0.12518366
159 PLZ_37081 TEGUT3 0.19435390 -0.251483393 0.14475362
160 PLZ_37081 TEGUT4 -0.10667609 0.241877901 0.10620805
161 PLZ_37083 ALDI1 -0.16130697 0.220547032 -0.15794353
162 PLZ_37083 ALDI3 0.13972303 -0.159335078 -0.16922454
163 PLZ_37083 ALDI6 -0.16130697 0.235820448 -0.09579563
164 PLZ_37083 ALDI7 -0.16130697 0.302932598 -0.13096004
165 PLZ_37083 ALNATURA -0.16130697 -0.300909392 -0.33403479
166 PLZ_37083 EDEKA1 -0.16130697 0.045497839 0.25099186
167 PLZ_37083 EDEKA2 -0.16130697 0.389668922 -0.44797814
168 PLZ_37083 EDEKA3 -0.16130697 0.238248223 0.02914311
169 PLZ_37083 EDEKA4 -0.16130697 -0.042640350 -0.27188689
170 PLZ_37083 EDEKA5 0.31581429 -1.183823899 -0.44797814
171 PLZ_37083 KAUFLAND1 0.44075302 0.270552897 0.79194667
172 PLZ_37083 KAUFLAND2 0.61684428 -0.345493586 0.43426170
173 PLZ_37083 LIDL1 0.13972303 0.073222913 -0.05003814
174 PLZ_37083 LIDL2 -0.16130697 0.262582041 -0.05003814
175 PLZ_37083 NAHKAUF1 -0.16130697 0.359105058 -0.17497687
176 PLZ_37083 NAHKAUF4 -0.16130697 -0.041410053 -0.57291688
177 PLZ_37083 NAHKAUF5 -0.16130697 -0.227969855 -0.44797814
178 PLZ_37083 NETTO1 0.13972303 -0.171235479 -0.27188689
179 PLZ_37083 NETTO6 -0.16130697 0.028935859 -0.14694815
180 PLZ_37083 PENNY1 -0.16130697 0.128289239 -0.30574515
181 PLZ_37083 PENNY2 0.31581429 -0.546528578 -0.33907502
182 PLZ_37083 REAL1 -0.16130697 0.251523989 1.01228056
183 PLZ_37083 REAL2 0.13972303 0.297822161 0.80626773
184 PLZ_37083 REWE1 0.13972303 0.040953713 0.28401330
185 PLZ_37083 REWE2 -0.16130697 -0.317976426 -0.47600687
186 PLZ_37083 REWE3 -0.16130697 0.060310783 0.44661480
187 PLZ_37083 REWE4 0.68379107 -0.388165864 0.20523437
188 PLZ_37083 REWE6 -0.16130697 0.135513666 0.02147567
189 PLZ_37083 TEGUT1 0.31581429 0.071586937 0.23303684
190 PLZ_37083 TEGUT2 -0.16130697 0.195748283 0.12518366
191 PLZ_37083 TEGUT3 -0.16130697 0.280541664 0.14475362
192 PLZ_37083 TEGUT4 -0.16130697 -0.163915704 0.10620805
193 PLZ_37085 ALDI1 -0.19436922 0.181542457 -0.15794353
194 PLZ_37085 ALDI3 -0.19436922 -0.838223266 -0.16922454
195 PLZ_37085 ALDI6 -0.19436922 0.203808390 -0.09579563
196 PLZ_37085 ALDI7 -0.19436922 0.272194155 -0.13096004
197 PLZ_37085 ALNATURA 0.10666078 -0.136797067 -0.33403479
198 PLZ_37085 EDEKA1 -0.19436922 0.065170808 0.25099186
199 PLZ_37085 EDEKA2 -0.19436922 0.212375537 -0.44797814
200 PLZ_37085 EDEKA3 -0.19436922 0.204426114 0.02914311
201 PLZ_37085 EDEKA4 0.28275204 -0.154655825 -0.27188689
202 PLZ_37085 EDEKA5 -0.19436922 -0.219310104 -0.44797814
203 PLZ_37085 KAUFLAND1 0.28275204 0.229363658 0.79194667
204 PLZ_37085 KAUFLAND2 0.50460079 -0.157858978 0.43426170
205 PLZ_37085 LIDL1 0.10666078 0.061132810 -0.05003814
206 PLZ_37085 LIDL2 -0.19436922 0.224353232 -0.05003814
207 PLZ_37085 NAHKAUF1 -0.19436922 0.268878221 -0.17497687
208 PLZ_37085 NAHKAUF4 -0.19436922 0.046293539 -0.57291688
209 PLZ_37085 NAHKAUF5 0.40769077 -0.401119319 -0.44797814
210 PLZ_37085 NETTO1 0.40769077 -0.069046064 -0.27188689
211 PLZ_37085 NETTO6 -0.19436922 0.054033413 -0.14694815
212 PLZ_37085 PENNY1 -0.19436922 0.087498448 -0.30574515
213 PLZ_37085 PENNY2 -0.19436922 -0.245529065 -0.33907502
214 PLZ_37085 REAL1 0.10666078 0.208826142 1.01228056
215 PLZ_37085 REAL2 0.10666078 0.268316014 0.80626773
216 PLZ_37085 REWE1 0.40769077 0.063812642 0.28401330
217 PLZ_37085 REWE2 -0.19436922 -0.144994438 -0.47600687
218 PLZ_37085 REWE3 -0.19436922 0.074772559 0.44661480
219 PLZ_37085 REWE4 0.28275204 -0.116845433 0.20523437
220 PLZ_37085 REWE6 -0.19436922 0.173490410 0.02147567
221 PLZ_37085 TEGUT1 0.28275204 0.082994425 0.23303684
222 PLZ_37085 TEGUT2 0.10666078 0.115728257 0.12518366
223 PLZ_37085 TEGUT3 -0.19436922 0.255284573 0.14475362
224 PLZ_37085 TEGUT4 0.10666078 -0.869916245 0.10620805
[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
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