Example (for three countries)
Co-occurrences in the Science Citation Index:
|
FRANCE - FRA FRANCE - UK: FRANCE - GER |
NCE: 250 UK - FR |
ANCE: 120 GERMANY - FRANCE: |
140 90 750 |
|
80 UK - U |
: 800 GERMANY - UK: | ||
|
MANY: 160 UK - GE |
RMANY: 110 GERMANY - GERMANY: | ||
|
Collaboration matrix:18 FRANCE FRANCE 250 UK 100 GERMANY 150 SUM 500 Frequency matrix: FRANCE FRANCE q11 = 0.10 UK q12 = 0.04 GERMANY q13 = 0.06 (q1. = 0.20) Tij-values: FRANCE FRANCE T11= ln(0.10/0.04)= 0.92 |
UK GERMANY SUM 100 150 500 800 100 1000 100 750 1000 1000 1000 2500 UK GERMANY q21 = 0.04 q31 = 0.06 (q.1 = 0.20) q22 = 0.32 q32 = 0.04 (q.2 = 0.40) q23 = 0.04 q33 = 0.30 (q.3 = 0.40) (q2. = 0.40) (q3. = 0.40) (q.. = 1.00) UK GERMANY T21= ln(0.04/0.08)= -0.69 T31= ln(0.06/0.08)= |
-0.29 | |
|
UK |
T12= ln(0.04/0.08)= -0.69 |
T22= ln(0.32/0.16)= 0.69 T32= ln(0.04/0.16)= |
-1.39 |
|
GERMANY |
T13= ln(0.06/0.08)= -0.29 |
T23= ln(0.04/0.16)= -1.39 T33= ln(0.30/0.16)= |
0.63 |
Integration indicators :
T = (0.10 ∙ 0.92) + (0.04 ∙ -0.69) + (0.06 ∙ -0.29) + (0.04 ∙ -0.69) + (0.32 ∙ 0.69) + (0.04 ∙ -1.39) + (0.06 ∙
-0.29) + (0.04 ∙ -1.39) + (0.30 ∙ 0.63) = 0.30
Ti=j = (1/0.72) ∙ ((0.10 ∙ 0.92) + (0.32 ∙ 0.69) + (0.30 ∙0. 63)) = 0.70
Ti j= (1/0.28) ∙ ((0.04 ∙ -0.69) + (0.06 ∙ -0.29) + (0.04 ∙ -0.69) + (0.04 ∙ -1.39) + (0.06 ∙ -0.29) + (0.04 ∙ -
1.39)) = -0.72
T1 = (1/0.2) ∙ ((0.10 ∙ 0.92) + (0.04 ∙ -0.69) + (0.06 ∙ -0.29)) = 0.23
T2 = (1/0.4) ∙ ((0.04 ∙ -0.69) + (0.32 ∙ 0.69) + (0.04 ∙ -1.39)) = 0.35
T3 = (1/0.4) ∙ ((0.06 ∙ -0.29) + (0.04 ∙ -1.39) + (0.30 ∙ 0.63)) = 0.29
Table 1. Example of application of integration indicators
18 An address that is listed before or after another address is treated in the same way. The share of
collaborations between two different countries is therefore computed as half the mean to obtain qij=qji.
19