litzenberger2: Litzenberger-Sternberg Cluster Index

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

Description

Calculating the Cluster Index by Litzenberger and Sternberg for a given number of I industries and J regions

Usage

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litzenberger2(e_ij, industry.id, region.id, a_j, p_j, b_ij, 
CI.output = "mat", na.rm = TRUE)

Arguments

e_ij

a vector with the employment of industry i in region j

industry.id

a vector containing the IDs of the industries i

region.id

a vector containing the IDs of the regions j

a_j

a vector containing the areas of the regions j

p_j

a vector containing the populations of the regions j

b_ij

a vector containing the numbers of firms of industry i in region j

CI.output

Type of output: matrix (default: CI.output = "mat") or data frame (CI.output = "df")

na.rm

logical argument that indicates whether NA values should be excluded before computing results

Details

The Litzenberger-Sternberg Cluster Index is not standardized and depends on the number of regarded industries and regions.

Value

A matrix or data frame containing IxJ values of CI

Author(s)

Thomas Wieland

References

Farhauer, O./Kroell, A. (2014): “Standorttheorien: Regional- und Stadtoekonomik in Theorie und Praxis”. Wiesbaden : Springer.

Hoffmann J./Hirsch, S./Simons, J. (2017): “Identification of spatial agglomerations in the German food processing industry”. In: Papers in Regional Science, 96, 1, p. 139-162.

Litzenberger, T./Sternberg, R. (2006): “Der Clusterindex - eine Methodik zur Identifizierung regionaler Cluster am Beispiel deutscher Industriebranchen”. In: Geographische Zeitschrift, 94, 2, p. 209-224.

See Also

litzenberger, gini.conc, gini.spec, locq, locq2, ellison.a, ellison.a2, ellison.c, ellison.c2

Examples

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data (G.regions.industries)

lss <- litzenberger2(G.regions.industries$emp_all, 
G.regions.industries$ind_code, G.regions.industries$region_code,
G.regions.industries$area_sqkm, G.regions.industries$pop,
G.regions.industries$firms, CI.output = "df")
# output as data frame

lss_sort <- lss[order(lss$CI, decreasing = TRUE),]
# Sort decreasing by size of CI

lss_sort[1:5,]

Example output

Litzenberger-Sternberg cluster indices 
I = 17 industries, J = 16 regions 

    j_region i_industry           CI
1         BB     WZ08-B   0.57366920
2         BB     WZ08-C   0.16106787
3         BB     WZ08-D   0.22136272
4         BB     WZ08-E   0.88102599
5         BB     WZ08-F   0.71428882
6         BB     WZ08-G   0.27077871
7         BB     WZ08-H   0.43868777
8         BB     WZ08-I   0.26723360
9         BB     WZ08-J   0.11303259
10        BB     WZ08-K   0.15248253
11        BB     WZ08-L   0.25648136
12        BB     WZ08-M   0.16858953
13        BB     WZ08-N   0.42321660
14        BB     WZ08-P   0.20430232
15        BB     WZ08-Q   0.34456305
16        BB     WZ08-R   0.24509319
17        BB     WZ08-S   0.28911323
18        BE     WZ08-B   0.05611505
19        BE     WZ08-C   3.24717820
20        BE     WZ08-D   1.37720778
21        BE     WZ08-E  10.14891585
22        BE     WZ08-F  11.36434353
23        BE     WZ08-G  12.10626625
24        BE     WZ08-H  13.26265081
25        BE     WZ08-I  26.60020727
26        BE     WZ08-J  59.24931837
27        BE     WZ08-K  10.28664194
28        BE     WZ08-L  56.65943460
29        BE     WZ08-M  39.30149403
30        BE     WZ08-N  26.91532975
31        BE     WZ08-P  25.30839556
32        BE     WZ08-Q  21.86956483
33        BE     WZ08-R 104.73565741
34        BE     WZ08-S  24.71310833
35        BW     WZ08-B   0.80418127
36        BW     WZ08-C   2.62508051
37        BW     WZ08-D   1.70435052
38        BW     WZ08-E   0.82355174
39        BW     WZ08-F   1.23721079
40        BW     WZ08-G   1.39035316
41        BW     WZ08-H   1.09557469
42        BW     WZ08-I   1.40986571
43        BW     WZ08-J   1.43420374
44        BW     WZ08-K   1.47749805
45        BW     WZ08-L   0.95940926
46        BW     WZ08-M   1.53067987
47        BW     WZ08-N   1.02283263
48        BW     WZ08-P   1.36564094
49        BW     WZ08-Q   1.17702969
50        BW     WZ08-R   1.08397668
51        BW     WZ08-S   1.34355762
52        BY     WZ08-B   1.10734462
53        BY     WZ08-C   1.20434146
54        BY     WZ08-D   1.41782082
55        BY     WZ08-E   0.68902125
56        BY     WZ08-F   0.94422208
57        BY     WZ08-G   0.94046774
58        BY     WZ08-H   0.79820744
59        BY     WZ08-I   0.96330292
60        BY     WZ08-J   1.23935791
61        BY     WZ08-K   1.16924615
62        BY     WZ08-L   0.86956365
63        BY     WZ08-M   1.01104719
64        BY     WZ08-N   0.74718719
65        BY     WZ08-P   0.95090282
66        BY     WZ08-Q   0.78738769
67        BY     WZ08-R   0.78217786
68        BY     WZ08-S   0.95948817
69        HB     WZ08-B          NaN
70        HB     WZ08-C   5.11966880
71        HB     WZ08-D   4.17216154
72        HB     WZ08-E   6.70574394
73        HB     WZ08-F   3.49892111
74        HB     WZ08-G   7.13620546
75        HB     WZ08-H  22.65692351
76        HB     WZ08-I   8.48133822
77        HB     WZ08-J   8.68399837
78        HB     WZ08-K   6.65021283
79        HB     WZ08-L  11.83990010
80        HB     WZ08-M   9.41049808
81        HB     WZ08-N  10.79602732
82        HB     WZ08-P   7.32270897
83        HB     WZ08-Q   7.85088590
84        HB     WZ08-R  10.55536908
85        HB     WZ08-S   9.89368791
86        HE     WZ08-B   0.47450842
87        HE     WZ08-C   1.06030870
88        HE     WZ08-D   0.85413593
89        HE     WZ08-E   1.14272854
90        HE     WZ08-F   1.12250866
91        HE     WZ08-G   1.33610604
92        HE     WZ08-H   1.83582716
93        HE     WZ08-I   1.28802104
94        HE     WZ08-J   1.90248257
95        HE     WZ08-K   2.47390439
96        HE     WZ08-L   1.60999294
97        HE     WZ08-M   1.73024339
98        HE     WZ08-N   1.52658463
99        HE     WZ08-P   1.46278711
100       HE     WZ08-Q   1.21636237
101       HE     WZ08-R   1.04896722
102       HE     WZ08-S   1.54219030
103       HH     WZ08-B   2.31961082
104       HH     WZ08-C   4.00010393
105       HH     WZ08-D   1.67937102
106       HH     WZ08-E  11.12915599
107       HH     WZ08-F   5.52608299
108       HH     WZ08-G  15.62708966
109       HH     WZ08-H  44.37183557
110       HH     WZ08-I  14.79588537
111       HH     WZ08-J  59.72058402
112       HH     WZ08-K  26.18962266
113       HH     WZ08-L  33.17544287
114       HH     WZ08-M  44.43352692
115       HH     WZ08-N  23.25519505
116       HH     WZ08-P  14.29407491
117       HH     WZ08-Q  13.21191844
118       HH     WZ08-R  44.25621400
119       HH     WZ08-S  14.19515640
120       MV     WZ08-B   0.16000177
121       MV     WZ08-C   0.11993714
122       MV     WZ08-D   0.20954802
123       MV     WZ08-E   0.44055556
124       MV     WZ08-F   0.45291220
125       MV     WZ08-G   0.22665565
126       MV     WZ08-H   0.32192237
127       MV     WZ08-I   0.59842705
128       MV     WZ08-J   0.05895184
129       MV     WZ08-K   0.12112900
130       MV     WZ08-L   0.25167830
131       MV     WZ08-M   0.11657637
132       MV     WZ08-N   0.31231467
133       MV     WZ08-P   0.24008982
134       MV     WZ08-Q   0.38626491
135       MV     WZ08-R   0.20066782
136       MV     WZ08-S   0.27631480
137       NI     WZ08-B   1.50045303
138       NI     WZ08-C   0.50368383
139       NI     WZ08-D   0.88489563
140       NI     WZ08-E   0.64767974
141       NI     WZ08-F   0.62767914
142       NI     WZ08-G   0.68983593
143       NI     WZ08-H   0.64201456
144       NI     WZ08-I   0.63351256
145       NI     WZ08-J   0.29057685
146       NI     WZ08-K   0.56480501
147       NI     WZ08-L   0.52282483
148       NI     WZ08-M   0.44409589
149       NI     WZ08-N   0.52712928
150       NI     WZ08-P   0.72039527
151       NI     WZ08-Q   0.68774866
152       NI     WZ08-R   0.45088618
153       NI     WZ08-S   0.53648476
154       NW     WZ08-B   2.07473530
155       NW     WZ08-C   2.01075654
156       NW     WZ08-D   2.00170794
157       NW     WZ08-E   1.91519648
158       NW     WZ08-F   1.65638416
159       NW     WZ08-G   2.37736476
160       NW     WZ08-H   1.98049075
161       NW     WZ08-I   1.73196267
162       NW     WZ08-J   2.13979638
163       NW     WZ08-K   1.95396341
164       NW     WZ08-L   2.22385383
165       NW     WZ08-M   2.29730811
166       NW     WZ08-N   2.41335110
167       NW     WZ08-P   2.02297064
168       NW     WZ08-Q   2.26051779
169       NW     WZ08-R   2.19075182
170       NW     WZ08-S   1.94147014
171       RP     WZ08-B   1.19512657
172       RP     WZ08-C   0.96463511
173       RP     WZ08-D   0.60167149
174       RP     WZ08-E   0.86168906
175       RP     WZ08-F   0.89731616
176       RP     WZ08-G   0.81158172
177       RP     WZ08-H   0.70873414
178       RP     WZ08-I   1.05729958
179       RP     WZ08-J   0.51429532
180       RP     WZ08-K   0.71049294
181       RP     WZ08-L   0.53496408
182       RP     WZ08-M   0.49616108
183       RP     WZ08-N   0.55375095
184       RP     WZ08-P   0.97049749
185       RP     WZ08-Q   0.77709797
186       RP     WZ08-R   0.52872904
187       RP     WZ08-S   0.79962906
188       SH     WZ08-B   0.31190909
189       SH     WZ08-C   0.40085979
190       SH     WZ08-D   1.29891053
191       SH     WZ08-E   0.81010869
192       SH     WZ08-F   0.80556617
193       SH     WZ08-G   0.90082874
194       SH     WZ08-H   0.72059610
195       SH     WZ08-I   1.03613892
196       SH     WZ08-J   0.44271796
197       SH     WZ08-K   0.57588183
198       SH     WZ08-L   0.85875875
199       SH     WZ08-M   0.44561194
200       SH     WZ08-N   0.73480679
201       SH     WZ08-P   0.69377918
202       SH     WZ08-Q   0.84262534
203       SH     WZ08-R   0.66942726
204       SH     WZ08-S   0.92388157
205       SL     WZ08-B   0.36730896
206       SL     WZ08-C   1.83487126
207       SL     WZ08-D   0.96432626
208       SL     WZ08-E   1.99394611
209       SL     WZ08-F   1.32451524
210       SL     WZ08-G   1.75280779
211       SL     WZ08-H   1.10991515
212       SL     WZ08-I   1.78711625
213       SL     WZ08-J   0.89846793
214       SL     WZ08-K   1.55059281
215       SL     WZ08-L   0.81707232
216       SL     WZ08-M   1.01371510
217       SL     WZ08-N   1.39402977
218       SL     WZ08-P   1.23313897
219       SL     WZ08-Q   1.85512660
220       SL     WZ08-R   0.84777016
221       SL     WZ08-S   1.61389554
222       SN     WZ08-B   1.11791105
223       SN     WZ08-C   1.03117225
224       SN     WZ08-D   0.45340294
225       SN     WZ08-E   1.55541252
226       SN     WZ08-F   1.81672627
227       SN     WZ08-G   0.76446952
228       SN     WZ08-H   0.92970532
229       SN     WZ08-I   0.71195666
230       SN     WZ08-J   0.49270301
231       SN     WZ08-K   0.59805883
232       SN     WZ08-L   0.82267731
233       SN     WZ08-M   0.64898684
234       SN     WZ08-N   1.24926584
235       SN     WZ08-P   0.78005314
236       SN     WZ08-Q   1.07490000
237       SN     WZ08-R   0.86664784
238       SN     WZ08-S   0.86005193
239       ST     WZ08-B   1.49064630
240       ST     WZ08-C   0.32128528
241       ST     WZ08-D   0.29391783
242       ST     WZ08-E   1.09973945
243       ST     WZ08-F   0.68075807
244       ST     WZ08-G   0.31005922
245       ST     WZ08-H   0.42973342
246       ST     WZ08-I   0.29998391
247       ST     WZ08-J   0.08046178
248       ST     WZ08-K   0.21942805
249       ST     WZ08-L   0.21044244
250       ST     WZ08-M   0.15797219
251       ST     WZ08-N   0.42285503
252       ST     WZ08-P   0.31406013
253       ST     WZ08-Q   0.48353914
254       ST     WZ08-R   0.21562997
255       ST     WZ08-S   0.34624522
256       TH     WZ08-B   0.45627298
257       TH     WZ08-C   0.78923598
258       TH     WZ08-D   0.20860415
259       TH     WZ08-E   1.18157264
260       TH     WZ08-F   1.03137492
261       TH     WZ08-G   0.43133055
262       TH     WZ08-H   0.48816435
263       TH     WZ08-I   0.40129099
264       TH     WZ08-J   0.20871737
265       TH     WZ08-K   0.31604325
266       TH     WZ08-L   0.28860684
267       TH     WZ08-M   0.24934581
268       TH     WZ08-N   0.59353287
269       TH     WZ08-P   0.43896755
270       TH     WZ08-Q   0.58547874
271       TH     WZ08-R   0.29193000
272       TH     WZ08-S   0.53697655
    j_region i_industry        CI
33        BE     WZ08-R 104.73566
111       HH     WZ08-J  59.72058
26        BE     WZ08-J  59.24932
28        BE     WZ08-L  56.65943
114       HH     WZ08-M  44.43353

REAT documentation built on Sept. 5, 2021, 5:18 p.m.