METHODOLOGICAL DEBATE ON THE ‘REGIONAL INNOVATION SCOREBOARD’. The centroid of the simplex , (��, ��,…,��) is the weight assigned by the European Commission in the RIS calculation, and therefore the expected value of the random variable � . 𝐸𝐸 𝜃𝜃 ! = 𝜃𝜃 ! = 1 𝑝𝑝 , para 𝑖𝑖 = 1 , 2 , … , 𝑝𝑝 .
METHODOLOGICAL DEBATE ON THE ‘REGIONAL INNOVATION SCOREBOARD’.
FIGURE 2A
Relationship between weights and number of variables
( 3 )
600
(3)
400
400
200
200
Each of the weights contained within therefore verify that:
0
0
0
0.5
1
0
0.5
1
FIGURE 1A
Standard simplex for p=3
1000
1000
500
500
0
0
0
0.5
1
0
0.5
1
Since the likelihood of observing a certain weighting decreases when moving away from zero, it is best to consider confidence intervals intersecting one end of the distribution. In this regard, if we intersect the weighting distribution � at 95% confidence, we can see in Figure 3A that each weighting will generally be contained in the interval (0, 0.14), approximately.
Figure 1A shows the simplex for the hypothetical case in which only three indicators (=3) are considered in the RIS. Each vertex of the simplex represents the situation in which all but one of the indicators are irrelevant. Since the expected value of each of the weights, (�)=1⁄, tends to zero as the number of indicators, , grows, the likelihood of observing a vector of weights in which all but one variable is irrelevant also tends to zero. The exercise in this paper consists of calculating R values for the vector , such that we have a sequence of vectors, with =1,..,. Figure 2A shows the weight distribution of a single indicator, �, for ten thousand random vectors, �, for different values of . The bottom right section of Figure 2A shows the case of the RIS, in which the number of indicators considered =21 and (��)=1/21=0.0476.
FIGURE 3A
Relationship between weights and number of variables
95% OF CONFIDENT
0
0.14
0.3
88
89
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