measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf ·...
TRANSCRIPT
![Page 1: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/1.jpg)
Measuring scientific production Ranking
Measuring and ranking scientific production
Nicolas Carayol
Observatoire des Sciences et Techniques, Paris
Dimetic, July 2010, Pecs 2010
![Page 2: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/2.jpg)
Measuring scientific production Ranking
Bibliometrics
A field born with the its object : scientific production.
A distributional approach : with Bradford, Zipf and Lotka1926-> 35
RK Merton influence : measuring production and credit.
D. J. de Solla Price
E. Garfield
A connection with economics through Stigler’s influence
![Page 3: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/3.jpg)
Measuring scientific production Ranking
Bibliometrics
A field born with the its object : scientific production.
A distributional approach : with Bradford, Zipf and Lotka1926-> 35
RK Merton influence : measuring production and credit.
D. J. de Solla Price
E. Garfield
A connection with economics through Stigler’s influence
![Page 4: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/4.jpg)
Measuring scientific production Ranking
Bibliometrics
A field born with the its object : scientific production.
A distributional approach : with Bradford, Zipf and Lotka1926-> 35
RK Merton influence : measuring production and credit.
D. J. de Solla Price
E. Garfield
A connection with economics through Stigler’s influence
![Page 5: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/5.jpg)
Measuring scientific production Ranking
Bibliometrics
A field born with the its object : scientific production.
A distributional approach : with Bradford, Zipf and Lotka1926-> 35
RK Merton influence : measuring production and credit.
D. J. de Solla Price
E. Garfield
A connection with economics through Stigler’s influence
![Page 6: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/6.jpg)
Measuring scientific production Ranking
Bibliometrics
A field born with the its object : scientific production.
A distributional approach : with Bradford, Zipf and Lotka1926-> 35
RK Merton influence : measuring production and credit.
D. J. de Solla Price
E. Garfield
A connection with economics through Stigler’s influence
![Page 7: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/7.jpg)
Measuring scientific production Ranking
Bibliometrics
A field born with the its object : scientific production.
A distributional approach : with Bradford, Zipf and Lotka1926-> 35
RK Merton influence : measuring production and credit.
D. J. de Solla Price
E. Garfield
A connection with economics through Stigler’s influence
![Page 8: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/8.jpg)
Measuring scientific production Ranking
Bibliometrics
Measuring scientific production
How to rank ?
![Page 9: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/9.jpg)
Measuring scientific production Ranking
Bibliometrics
Measuring scientific production
How to rank ?
![Page 10: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/10.jpg)
Measuring scientific production Ranking
Sections :
1 Measuring scientific productionVolumeImpactInfluenceMeasures for both quality and quantity
2 RankingThe axiomatic approachThe extended stochastic dominance approach
Core background theoryIllustrative Results
![Page 11: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/11.jpg)
Measuring scientific production Ranking
Bibliometrics
Define the agent ?
Q : quantity
q : quality
![Page 12: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/12.jpg)
Measuring scientific production Ranking
Bibliometrics
Define the agent ?
Q : quantity
q : quality
![Page 13: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/13.jpg)
Measuring scientific production Ranking
Bibliometrics
Define the agent ?
Q : quantity
q : quality
![Page 14: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/14.jpg)
Measuring scientific production Ranking
Volume
The basic data
The structured set of i ’s publications is given by
Si := (s1, s2, ..., s′a, ..., sa, ..., sni ),
with ni the number of articles to be associated to agent i .
![Page 15: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/15.jpg)
Measuring scientific production Ranking
Volume
Ground zero
Total counts :
Ti ,a = # {i mentioned in a}
Total counts by domain :
T ki ,a = # {i mentioned in a} × 1 {j(a) associated to k}
with j(a) is the journal in which a were published.
![Page 16: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/16.jpg)
Measuring scientific production Ranking
Volume
Ground zero
Total counts :
Ti ,a = # {i mentioned in a}
Total counts by domain :
T ki ,a = # {i mentioned in a} × 1 {j(a) associated to k}
with j(a) is the journal in which a were published.
![Page 17: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/17.jpg)
Measuring scientific production Ranking
Volume
Accounting for coauthorship
An article a, referencing at least one address associated toinstitution i , brings a score of :
pki ,a =
# {i mentioned in a}# { j | j mentioned in a}
× 1 {j(a) associated to k} ,
where 1 {.} is the indicator function and # {.} denotes thecardinal of the set defined into brackets.
![Page 18: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/18.jpg)
Measuring scientific production Ranking
Volume
Allocate over disciplines
An article a, referencing at least one address associated toinstitution i , brings a score of :
pki ,a =
# {i mentioned in a}# { j | j mentioned in a}
× 1 {j(a) associated to k}# {k | j(a) associated to k}
,
where 1 {.} is the indicator function and # {.} denotes thecardinal of the set defined into brackets. j(a) is the journal inwhich a were published.
![Page 19: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/19.jpg)
Measuring scientific production Ranking
Volume
Other basic corrections
# pages
...
![Page 20: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/20.jpg)
Measuring scientific production Ranking
Volume
Other basic corrections
# pages
...
![Page 21: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/21.jpg)
Measuring scientific production Ranking
Volume
Authors’ rank
(Assimakis & Adam, scientometrics forthcoming)The linearcontribution index :
lpia = c − δria,
where ria the rank of author i among the na authors of articlea and with c a normalization parameter c = na+1
2 δ + 1na
sothat authros contribution sum to one.
The geometriccontribution index
gpia = κ · λ−na+ri ,
with 0 < λ < 1, and κ he normalization parameter.
![Page 22: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/22.jpg)
Measuring scientific production Ranking
Volume
Authors’ rank
(Assimakis & Adam, scientometrics forthcoming)The linearcontribution index :
lpia = c − δria,
where ria the rank of author i among the na authors of articlea and with c a normalization parameter c = na+1
2 δ + 1na
sothat authros contribution sum to one.The geometriccontribution index
gpia = κ · λ−na+ri ,
with 0 < λ < 1, and κ he normalization parameter.
![Page 23: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/23.jpg)
Measuring scientific production Ranking
Impact
Quality is critical
Rely on peer review
Rely on citation data
![Page 24: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/24.jpg)
Measuring scientific production Ranking
Impact
Quality is critical
Rely on peer review
Rely on citation data
![Page 25: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/25.jpg)
Measuring scientific production Ranking
Impact
Counting citations
The Number of direct citations received :
sa = # { j | tj ∈ w(a) and j cites a} ,
with tj the year of publication of j , and w(a) the citationwindow of article a.
![Page 26: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/26.jpg)
Measuring scientific production Ranking
Impact
The impact Factor
Impact Factor of the journal :
s ′a =# { j | tj ∈ w(a) and j cites i ∈ j(a)}
# { i | i ∈ j(a)}.
![Page 27: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/27.jpg)
Measuring scientific production Ranking
Impact
Correction across fields
Relative Impact Factor of the journal :
s ′′a =s ′a
〈s ′a〉subfield of a
.
![Page 28: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/28.jpg)
Measuring scientific production Ranking
Influence
Prestige centrality
Narin & Pinski 1976
Leibowitz and Palmer 1986
Page rank (Page & al, 1998)
Katz → prestige
![Page 29: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/29.jpg)
Measuring scientific production Ranking
Influence
Prestige centrality
Narin & Pinski 1976
Leibowitz and Palmer 1986
Page rank (Page & al, 1998)
Katz → prestige
![Page 30: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/30.jpg)
Measuring scientific production Ranking
Influence
Prestige centrality
Narin & Pinski 1976
Leibowitz and Palmer 1986
Page rank (Page & al, 1998)
Katz → prestige
![Page 31: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/31.jpg)
Measuring scientific production Ranking
Influence
Prestige centrality
Narin & Pinski 1976
Leibowitz and Palmer 1986
Page rank (Page & al, 1998)
Katz → prestige
![Page 32: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/32.jpg)
Measuring scientific production Ranking
Influence
A unified writing of centrality
A = (ai ) with ai the number of articles published in/of i .
C = (cij) with cij the number of citations i received from j (orthe number of references made in j to i).
The counting method of Bush, Hamelman & Staaf (1974) :
φi = λ
∑j cij/ai∑
k
∑j ckj/ak
.
value is proportional to the average number of citations madeto its articles
The counting modified method :
φi = λ
∑j cij/ai × φj∑
k
∑j ckj/ak × φj
.
value is proportional to the average number of citations madeto its articles
![Page 33: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/33.jpg)
Measuring scientific production Ranking
Influence
A unified writing of centrality
A = (ai ) with ai the number of articles published in/of i .
C = (cij) with cij the number of citations i received from j (orthe number of references made in j to i).
The counting method of Bush, Hamelman & Staaf (1974) :
φi = λ
∑j cij/ai∑
k
∑j ckj/ak
.
value is proportional to the average number of citations madeto its articles
The counting modified method :
φi = λ
∑j cij/ai × φj∑
k
∑j ckj/ak × φj
.
value is proportional to the average number of citations madeto its articles
![Page 34: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/34.jpg)
Measuring scientific production Ranking
Influence
A unified writing of centrality
A = (ai ) with ai the number of articles published in/of i .
C = (cij) with cij the number of citations i received from j (orthe number of references made in j to i).
The counting method of Bush, Hamelman & Staaf (1974) :
φi = λ
∑j cij/ai∑
k
∑j ckj/ak
.
value is proportional to the average number of citations madeto its articles
The counting modified method :
φi = λ
∑j cij/ai × φj∑
k
∑j ckj/ak × φj
.
value is proportional to the average number of citations madeto its articles
![Page 35: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/35.jpg)
Measuring scientific production Ranking
Influence
A unified writing of centrality
A = (ai ) with ai the number of articles published in/of i .
C = (cij) with cij the number of citations i received from j (orthe number of references made in j to i).
The counting method of Bush, Hamelman & Staaf (1974) :
φi = λ
∑j cij/ai∑
k
∑j ckj/ak
.
value is proportional to the average number of citations madeto its articles
The counting modified method :
φi = λ
∑j cij/ai × φj∑
k
∑j ckj/ak × φj
.
value is proportional to the average number of citations madeto its articles
![Page 36: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/36.jpg)
Measuring scientific production Ranking
Influence
A unified writing of centrality
The Leibowitz and Palmer (1986) method :
φi = λ
∑j 6=i cij/ai∑
k
∑j 6=k ckj/ak
,
the value is proportional to the average number of citationsmade to its articles.
In matrix form, this becomes :
φ = λA−1Cφ
‖A−1Cφ‖
with ‖X‖ =∑
k ‖xk‖ the 1 norm of X .
![Page 37: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/37.jpg)
Measuring scientific production Ranking
Influence
A unified writing of centrality
The Leibowitz and Palmer (1986) method :
φi = λ
∑j 6=i cij/ai∑
k
∑j 6=k ckj/ak
,
the value is proportional to the average number of citationsmade to its articles.
In matrix form, this becomes :
φ = λA−1Cφ
‖A−1Cφ‖
with ‖X‖ =∑
k ‖xk‖ the 1 norm of X .
![Page 38: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/38.jpg)
Measuring scientific production Ranking
Influence
A unified writing of centrality
The Narin and Pinski (1976) method :
φi = λ∑j 6=i
cij/ai
cj/ajφj ,
the value is a weighted average of the centrality of thejournals citing it.
In matrix form, this becomes :
φ = λA−1CD−1C Aφ
with DC the diagonal matrix having the sum of the of thereferences in the diagonal (ci ). The matrix CD−1
C is thenormalized matrix of C and is a stochastic matrix (sums toone in each column).
![Page 39: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/39.jpg)
Measuring scientific production Ranking
Influence
A unified writing of centrality
The Narin and Pinski (1976) method :
φi = λ∑j 6=i
cij/ai
cj/ajφj ,
the value is a weighted average of the centrality of thejournals citing it.
In matrix form, this becomes :
φ = λA−1CD−1C Aφ
with DC the diagonal matrix having the sum of the of thereferences in the diagonal (ci ). The matrix CD−1
C is thenormalized matrix of C and is a stochastic matrix (sums toone in each column).
![Page 40: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/40.jpg)
Measuring scientific production Ranking
Influence
Prestige centrality (reminder)
Prestige depends of the average prestige of its neighbors asystem of equations :
pi (g) =∑j 6=i
gij
ηj (g)pj (g) .
![Page 41: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/41.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
Quantity and quality
The number of articles published ni , the average 〈s〉i and thetotal number 〈s〉i ni of citations received.
The first synthetic measure of both quality and quantity wasproposed by (Lindsay, 1978) :
Qi = 〈s〉i × (〈s〉i ni )1/2 = 〈s〉3/2
i n1/2i .
![Page 42: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/42.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
Quantity and quality
The number of articles published ni , the average 〈s〉i and thetotal number 〈s〉i ni of citations received.
The first synthetic measure of both quality and quantity wasproposed by (Lindsay, 1978) :
Qi = 〈s〉i × (〈s〉i ni )1/2 = 〈s〉3/2
i n1/2i .
![Page 43: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/43.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
The h-index
Each article published is denoted by an index a ∈ N\ {0} andis characterized by an associated impact measure (herecitations) sa ∈ R+ (here sa ∈ N).
The structured set of agent i ’s publications isSi := (s1, s2, ..., s
′a, ..., sa, ..., sni ), a vector assumed to be
(decreasingly) ordered according to the number of citationsreceived : a > a′ → s ′a ≤ sa.
![Page 44: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/44.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
The h-index
Each article published is denoted by an index a ∈ N\ {0} andis characterized by an associated impact measure (herecitations) sa ∈ R+ (here sa ∈ N).
The structured set of agent i ’s publications isSi := (s1, s2, ..., s
′a, ..., sa, ..., sni ), a vector assumed to be
(decreasingly) ordered according to the number of citationsreceived : a > a′ → s ′a ≤ sa.
![Page 45: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/45.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
The h-index
Hirsch (2005) proposes the h-index as a synthetic a uniquemeasure for both the # of citations and the # ofpublications. More, it a basic measure for the wholepublication/citation sequence.
The h-index of agent i is a measure computed from her/hisstructured set Si as follows :
h := maxa
(a ≤ sa).
![Page 46: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/46.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
The h-index
Hirsch (2005) proposes the h-index as a synthetic a uniquemeasure for both the # of citations and the # ofpublications. More, it a basic measure for the wholepublication/citation sequence.
The h-index of agent i is a measure computed from her/hisstructured set Si as follows :
h := maxa
(a ≤ sa).
![Page 47: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/47.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
The h-index
Example : ni = 7, Si = (8, 6, 5, 4, 2, 2, 1).
S
rank 1 2 3 4 5 6 7
8
S
rank 1 2 3 4 5 6 7
8
h=4
sh=
![Page 48: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/48.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
The h-index
Example : ni = 7, Si = (8, 6, 5, 4, 2, 2, 1).
S
rank 1 2 3 4 5 6 7
8
S
rank 1 2 3 4 5 6 7
8
h=4
sh=
![Page 49: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/49.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
The h-index
Example : ni = 7, Si = (8, 6, 5, 4, 2, 2, 1).
S
rank 1 2 3 4 5 6 7
8
S
rank 1 2 3 4 5 6 7
8
h=4
sh=
![Page 50: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/50.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
The h-index and beyond
Main shortcoming of the h-index : citations have no impact onthe index outside the h-core
The derivatives :
the g-index (Egghe, 2006) : g := maxa a2 ≤∑
j=1...a sj
the r-index (Jin et al., 2007)the tapered h-index (Anderson et al., 2008)the w-index (Woeringer, 2008)...
![Page 51: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/51.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
The h-index and beyond
Main shortcoming of the h-index : citations have no impact onthe index outside the h-core
The derivatives :
the g-index (Egghe, 2006) : g := maxa a2 ≤∑
j=1...a sj
the r-index (Jin et al., 2007)the tapered h-index (Anderson et al., 2008)the w-index (Woeringer, 2008)...
![Page 52: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/52.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
The h-index and beyond
Main shortcoming of the h-index : citations have no impact onthe index outside the h-core
The derivatives :
the g-index (Egghe, 2006) : g := maxa a2 ≤∑
j=1...a sj
the r-index (Jin et al., 2007)the tapered h-index (Anderson et al., 2008)the w-index (Woeringer, 2008)...
![Page 53: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/53.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
The h-index and beyond
Main shortcoming of the h-index : citations have no impact onthe index outside the h-core
The derivatives :
the g-index (Egghe, 2006) : g := maxa a2 ≤∑
j=1...a sj
the r-index (Jin et al., 2007)
the tapered h-index (Anderson et al., 2008)the w-index (Woeringer, 2008)...
![Page 54: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/54.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
The h-index and beyond
Main shortcoming of the h-index : citations have no impact onthe index outside the h-core
The derivatives :
the g-index (Egghe, 2006) : g := maxa a2 ≤∑
j=1...a sj
the r-index (Jin et al., 2007)the tapered h-index (Anderson et al., 2008)
the w-index (Woeringer, 2008)...
![Page 55: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/55.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
The h-index and beyond
Main shortcoming of the h-index : citations have no impact onthe index outside the h-core
The derivatives :
the g-index (Egghe, 2006) : g := maxa a2 ≤∑
j=1...a sj
the r-index (Jin et al., 2007)the tapered h-index (Anderson et al., 2008)the w-index (Woeringer, 2008)
...
![Page 56: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/56.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
The h-index and beyond
Main shortcoming of the h-index : citations have no impact onthe index outside the h-core
The derivatives :
the g-index (Egghe, 2006) : g := maxa a2 ≤∑
j=1...a sj
the r-index (Jin et al., 2007)the tapered h-index (Anderson et al., 2008)the w-index (Woeringer, 2008)...
![Page 57: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/57.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
The h-index and beyond
Hirsch self defense :
He argues his aim is precisely to NOT consider both i) lowimpact papers (is intended to capture a maintained flow ofinfluential contributions) AND ii) the high volume of citationsthat some papers sometime receive (could unduly grant someco-authors of highly cited papers).Hirsch argues the h-index has a strong predictive power on thearrival of future citations (Hirsch, 2007).
Main implicit advantage : easy to compute and thereforerobust to errors.
From a theoretical point of view, it is not a defense of theimplicit value judgements it incorporates.
![Page 58: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/58.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
The h-index and beyond
Hirsch self defense :
He argues his aim is precisely to NOT consider both i) lowimpact papers (is intended to capture a maintained flow ofinfluential contributions) AND ii) the high volume of citationsthat some papers sometime receive (could unduly grant someco-authors of highly cited papers).
Hirsch argues the h-index has a strong predictive power on thearrival of future citations (Hirsch, 2007).
Main implicit advantage : easy to compute and thereforerobust to errors.
From a theoretical point of view, it is not a defense of theimplicit value judgements it incorporates.
![Page 59: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/59.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
The h-index and beyond
Hirsch self defense :
He argues his aim is precisely to NOT consider both i) lowimpact papers (is intended to capture a maintained flow ofinfluential contributions) AND ii) the high volume of citationsthat some papers sometime receive (could unduly grant someco-authors of highly cited papers).Hirsch argues the h-index has a strong predictive power on thearrival of future citations (Hirsch, 2007).
Main implicit advantage : easy to compute and thereforerobust to errors.
From a theoretical point of view, it is not a defense of theimplicit value judgements it incorporates.
![Page 60: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/60.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
The h-index and beyond
Hirsch self defense :
He argues his aim is precisely to NOT consider both i) lowimpact papers (is intended to capture a maintained flow ofinfluential contributions) AND ii) the high volume of citationsthat some papers sometime receive (could unduly grant someco-authors of highly cited papers).Hirsch argues the h-index has a strong predictive power on thearrival of future citations (Hirsch, 2007).
Main implicit advantage : easy to compute and thereforerobust to errors.
From a theoretical point of view, it is not a defense of theimplicit value judgements it incorporates.
![Page 61: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/61.jpg)
Measuring scientific production Ranking
Measures for both quality and quantity
The h-index and beyond
Hirsch self defense :
He argues his aim is precisely to NOT consider both i) lowimpact papers (is intended to capture a maintained flow ofinfluential contributions) AND ii) the high volume of citationsthat some papers sometime receive (could unduly grant someco-authors of highly cited papers).Hirsch argues the h-index has a strong predictive power on thearrival of future citations (Hirsch, 2007).
Main implicit advantage : easy to compute and thereforerobust to errors.
From a theoretical point of view, it is not a defense of theimplicit value judgements it incorporates.
![Page 62: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/62.jpg)
Measuring scientific production Ranking
Sections :
1 Measuring scientific productionVolumeImpactInfluenceMeasures for both quality and quantity
2 RankingThe axiomatic approachThe extended stochastic dominance approach
Core background theoryIllustrative Results
![Page 63: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/63.jpg)
Measuring scientific production Ranking
Ranking : what for ?
Any ranking incorporate value judgements.
An axiomatic approach which renders explicit the valuejudgements incorporated in any ranking based on some index(as Arrow 1955).
A normative approach directly applied to the structured set ofpublications (as Rothshild and Stiglitz 1969, Atkinson, 1970).
![Page 64: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/64.jpg)
Measuring scientific production Ranking
Ranking : what for ?
Any ranking incorporate value judgements.
An axiomatic approach which renders explicit the valuejudgements incorporated in any ranking based on some index(as Arrow 1955).
A normative approach directly applied to the structured set ofpublications (as Rothshild and Stiglitz 1969, Atkinson, 1970).
![Page 65: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/65.jpg)
Measuring scientific production Ranking
Ranking : what for ?
Any ranking incorporate value judgements.
An axiomatic approach which renders explicit the valuejudgements incorporated in any ranking based on some index(as Arrow 1955).
A normative approach directly applied to the structured set ofpublications (as Rothshild and Stiglitz 1969, Atkinson, 1970).
![Page 66: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/66.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
→ An axiomatic approach which renders explicit the valuejudgements incorporated in measures :
Palacios Huerta & Volij 2004 (econometrica) →axiomatization of Pinski & Narin influence measure and someothers
Woeringer 2008 (math soc science) & Marchant 2009(scientometrics) → axiomatization of h-index and some othermeasures
![Page 67: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/67.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
→ An axiomatic approach which renders explicit the valuejudgements incorporated in measures :
Palacios Huerta & Volij 2004 (econometrica) →axiomatization of Pinski & Narin influence measure and someothers
Woeringer 2008 (math soc science) & Marchant 2009(scientometrics) → axiomatization of h-index and some othermeasures
![Page 68: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/68.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
Palacios Huerta & Volij 2004 :
Let J be the set of ranked agents
Axioms :
1 Invariance with respect to reference intensity : the ranking isnot modified by any modification of the reference intensity ofagents (each one has a vote one) : for any diagonal matrix Λwith strictly positive diagonal entries λj , if C ′ = C Λ, theranking is unchanged.
2 Weak homogeneity : in a two agents ranking problem issueonly, for any two agents with identical number of references(ai = aj) : φi
φj=
cij
cji.
![Page 69: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/69.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
Palacios Huerta & Volij 2004 :
Let J be the set of ranked agents
Axioms :
1 Invariance with respect to reference intensity : the ranking isnot modified by any modification of the reference intensity ofagents (each one has a vote one) : for any diagonal matrix Λwith strictly positive diagonal entries λj , if C ′ = C Λ, theranking is unchanged.
2 Weak homogeneity : in a two agents ranking problem issueonly, for any two agents with identical number of references(ai = aj) : φi
φj=
cij
cji.
![Page 70: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/70.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
Palacios Huerta & Volij 2004 :
Let J be the set of ranked agents
Axioms :
1 Invariance with respect to reference intensity : the ranking isnot modified by any modification of the reference intensity ofagents (each one has a vote one) : for any diagonal matrix Λwith strictly positive diagonal entries λj , if C ′ = C Λ, theranking is unchanged.
2 Weak homogeneity : in a two agents ranking problem issueonly, for any two agents with identical number of references(ai = aj) : φi
φj=
cij
cji.
![Page 71: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/71.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
Palacios Huerta & Volij 2004 :
Let J be the set of ranked agents
Axioms :
1 Invariance with respect to reference intensity : the ranking isnot modified by any modification of the reference intensity ofagents (each one has a vote one) : for any diagonal matrix Λwith strictly positive diagonal entries λj , if C ′ = C Λ, theranking is unchanged.
2 Weak homogeneity : in a two agents ranking problem issueonly, for any two agents with identical number of references(ai = aj) : φi
φj=
cij
cji.
![Page 72: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/72.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
Palacios Huerta & Volij 2004 :
Let J be the set of ranked agents
Axioms :
1 Invariance with respect to reference intensity : the ranking isnot modified by any modification of the reference intensity ofagents (each one has a vote one) : for any diagonal matrix Λwith strictly positive diagonal entries λj , if C ′ = C Λ, theranking is unchanged.
2 Weak homogeneity : in a two agents ranking problem issueonly, for any two agents with identical number of references(ai = aj) : φi
φj=
cij
cji.
![Page 73: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/73.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
3 Weak consistency : if for any set of agents with identicalnumber of references (ai = aj ,∀i , j ∈ J) :
∀k ∈ J, φiφj
=φk
i
φkj
, ∀i , j ∈ J\ {k}, with φki the rank of i with the
modified citation matrix C k such thatckij = cij + ckj
cik∑h∈J\{k} chk
. (the relative valuations shall be
proportional of the relative influences without any otheragent, the influences of which are redistributed to the agentsit cites (proportionally).
![Page 74: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/74.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
4 Invariance to the splitting of agents : if for all rankingproblems, and any splitting of agent i∈ J into nj identicalagents (same profile of citation and references :
anj
j = aj/nj , cninj
ij = cij/(ninj)) : φiφj
=φ
nii
φnjj
, ∀ni , nj .
![Page 75: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/75.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
Theorem
The Narin and Pinski (1976) measure of centrality is the uniquemeasure that may rank any set of agents while satisfying the 4axioms.
![Page 76: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/76.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
Woeringer 2008 axiomatization of h − index and some othermeasures
Si := (s1, s2, ..., s′a, ..., sa, ..., sni )
S ∈ Ψ the set of all possible positive entry vectors ofdimension 1× n(n > 0).
An index is a function φ : Ψ→ N with φ(0, 0, ..., 0) = 0
![Page 77: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/77.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
Woeringer 2008 axiomatization of h − index and some othermeasures
Si := (s1, s2, ..., s′a, ..., sa, ..., sni )
S ∈ Ψ the set of all possible positive entry vectors ofdimension 1× n(n > 0).
An index is a function φ : Ψ→ N with φ(0, 0, ..., 0) = 0
![Page 78: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/78.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
Woeringer 2008 axiomatization of h − index and some othermeasures
Si := (s1, s2, ..., s′a, ..., sa, ..., sni )
S ∈ Ψ the set of all possible positive entry vectors ofdimension 1× n(n > 0).
An index is a function φ : Ψ→ N with φ(0, 0, ..., 0) = 0
![Page 79: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/79.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
Woeringer 2008 axiomatization of h − index and some othermeasures
Si := (s1, s2, ..., s′a, ..., sa, ..., sni )
S ∈ Ψ the set of all possible positive entry vectors ofdimension 1× n(n > 0).
An index is a function φ : Ψ→ N with φ(0, 0, ..., 0) = 0
![Page 80: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/80.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
Axioms
a Monotonicity : for all vectors S of size 1× n and S ′ of size m,such that m ≤ n and sk ≥ s ′k ,∀k ≤ m then φ(S) > φ(S ′).
b If the vector S of size 1× (n + 1) can be built from vector S ′
of size 1× n by simply adding a paper with φ(S) citations,then φ(S ′) ≤ φ(S).
![Page 81: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/81.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
Axioms
a Monotonicity : for all vectors S of size 1× n and S ′ of size m,such that m ≤ n and sk ≥ s ′k ,∀k ≤ m then φ(S) > φ(S ′).
b If the vector S of size 1× (n + 1) can be built from vector S ′
of size 1× n by simply adding a paper with φ(S) citations,then φ(S ′) ≤ φ(S).
![Page 82: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/82.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
Axioms
a Monotonicity : for all vectors S of size 1× n and S ′ of size m,such that m ≤ n and sk ≥ s ′k ,∀k ≤ m then φ(S) > φ(S ′).
b If the vector S of size 1× (n + 1) can be built from vector S ′
of size 1× n by simply adding a paper with φ(S) citations,then φ(S ′) ≤ φ(S).
![Page 83: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/83.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
Axioms
c If the vector S of size 1× n can be built from vector S ′ of size1× n by simply adding a citation to a paper (∃h ≤ n sts ′h = sh + 1 and ∀k ≤ n st k 6= h then s ′h = sh) thenφ(S) ≤ φ(S ′) + 1.
d If the vector S of size 1× (n + 1) can be built from vector S ′
of size 1× n by simply adding an article with φ(S) citations,and then increasing the number of citations of paper by atleast one (∀h ≤ n st sh ≥ s ′h) then φ(S) > φ(S ′).
![Page 84: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/84.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
Axioms
c If the vector S of size 1× n can be built from vector S ′ of size1× n by simply adding a citation to a paper (∃h ≤ n sts ′h = sh + 1 and ∀k ≤ n st k 6= h then s ′h = sh) thenφ(S) ≤ φ(S ′) + 1.
d If the vector S of size 1× (n + 1) can be built from vector S ′
of size 1× n by simply adding an article with φ(S) citations,and then increasing the number of citations of paper by atleast one (∀h ≤ n st sh ≥ s ′h) then φ(S) > φ(S ′).
![Page 85: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/85.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
Axioms
c If the vector S of size 1× n can be built from vector S ′ of size1× n by simply adding a citation to a paper (∃h ≤ n sts ′h = sh + 1 and ∀k ≤ n st k 6= h then s ′h = sh) thenφ(S) ≤ φ(S ′) + 1.
d If the vector S of size 1× (n + 1) can be built from vector S ′
of size 1× n by simply adding an article with φ(S) citations,and then increasing the number of citations of paper by atleast one (∀h ≤ n st sh ≥ s ′h) then φ(S) > φ(S ′).
![Page 86: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/86.jpg)
Measuring scientific production Ranking
The axiomatic approach
The axiomatic approach
Theorem
An index φ : Ψ→ N satisfies the four axioms a, b, c and d if andonly if it is the h-index.
![Page 87: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/87.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
→ A normative approach directly applied to the structured set ofpublications.
![Page 88: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/88.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
→ A normative approach directly applied to the structured set ofpublications.
![Page 89: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/89.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
The main goal
There is a well known concept often used in economics :stochastic dominance.
Applied to the theory of choice under uncertainty (Stiglitz &Rothschild, 1970) and income distribution (Atkinson 1970).
But :
This is designed to compare distributions only (care only aboutquality and quality distribution).The assumptions associated to second order stochasticdominance (concavity) will not be systematically consistent.
→ A need an adaptation of the technique which would value bothimpact and volume of publication.
![Page 90: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/90.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
The main goal
There is a well known concept often used in economics :stochastic dominance.
Applied to the theory of choice under uncertainty (Stiglitz &Rothschild, 1970) and income distribution (Atkinson 1970).
But :
This is designed to compare distributions only (care only aboutquality and quality distribution).The assumptions associated to second order stochasticdominance (concavity) will not be systematically consistent.
→ A need an adaptation of the technique which would value bothimpact and volume of publication.
![Page 91: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/91.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
The main goal
There is a well known concept often used in economics :stochastic dominance.
Applied to the theory of choice under uncertainty (Stiglitz &Rothschild, 1970) and income distribution (Atkinson 1970).
But :
This is designed to compare distributions only (care only aboutquality and quality distribution).The assumptions associated to second order stochasticdominance (concavity) will not be systematically consistent.
→ A need an adaptation of the technique which would value bothimpact and volume of publication.
![Page 92: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/92.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
The main goal
There is a well known concept often used in economics :stochastic dominance.
Applied to the theory of choice under uncertainty (Stiglitz &Rothschild, 1970) and income distribution (Atkinson 1970).
But :
This is designed to compare distributions only (care only aboutquality and quality distribution).
The assumptions associated to second order stochasticdominance (concavity) will not be systematically consistent.
→ A need an adaptation of the technique which would value bothimpact and volume of publication.
![Page 93: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/93.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
The main goal
There is a well known concept often used in economics :stochastic dominance.
Applied to the theory of choice under uncertainty (Stiglitz &Rothschild, 1970) and income distribution (Atkinson 1970).
But :
This is designed to compare distributions only (care only aboutquality and quality distribution).The assumptions associated to second order stochasticdominance (concavity) will not be systematically consistent.
→ A need an adaptation of the technique which would value bothimpact and volume of publication.
![Page 94: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/94.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
The main goal
There is a well known concept often used in economics :stochastic dominance.
Applied to the theory of choice under uncertainty (Stiglitz &Rothschild, 1970) and income distribution (Atkinson 1970).
But :
This is designed to compare distributions only (care only aboutquality and quality distribution).The assumptions associated to second order stochasticdominance (concavity) will not be systematically consistent.
→ A need an adaptation of the technique which would value bothimpact and volume of publication.
![Page 95: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/95.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
The main goal
There is a well known concept often used in economics :stochastic dominance.
Applied to the theory of choice under uncertainty (Stiglitz &Rothschild, 1970) and income distribution (Atkinson 1970).
But :
This is designed to compare distributions only (care only aboutquality and quality distribution).The assumptions associated to second order stochasticdominance (concavity) will not be systematically consistent.
→ A need an adaptation of the technique which would value bothimpact and volume of publication.
![Page 96: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/96.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
The main goal
→ we hereby introduce a theory and develop a methodologyto compare the scientific production of institutions.
1 Dominance relations are established.
2 Dominance relations are used to build dominance networks,rankings and reference classes.
![Page 97: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/97.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
The main goal
→ we hereby introduce a theory and develop a methodologyto compare the scientific production of institutions.
1 Dominance relations are established.
2 Dominance relations are used to build dominance networks,rankings and reference classes.
![Page 98: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/98.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
The main goal
→ we hereby introduce a theory and develop a methodologyto compare the scientific production of institutions.
1 Dominance relations are established.
2 Dominance relations are used to build dominance networks,rankings and reference classes.
![Page 99: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/99.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
General problem
→ in principle that theory could apply to the comparison ofthe outcome of a set agents for which :
1 The outcome is composite,
2 Each element can be described by a “quality” index,
3 The modeler is concerned by both quantity and quality,
4 The modeler does not know exactly the function whichtransforms the “quality” in valued outcome, and thusrefers to classes of functions.
![Page 100: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/100.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
General problem
→ in principle that theory could apply to the comparison ofthe outcome of a set agents for which :
1 The outcome is composite,
2 Each element can be described by a “quality” index,
3 The modeler is concerned by both quantity and quality,
4 The modeler does not know exactly the function whichtransforms the “quality” in valued outcome, and thusrefers to classes of functions.
![Page 101: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/101.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
General problem
→ in principle that theory could apply to the comparison ofthe outcome of a set agents for which :
1 The outcome is composite,
2 Each element can be described by a “quality” index,
3 The modeler is concerned by both quantity and quality,
4 The modeler does not know exactly the function whichtransforms the “quality” in valued outcome, and thusrefers to classes of functions.
![Page 102: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/102.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
General problem
→ in principle that theory could apply to the comparison ofthe outcome of a set agents for which :
1 The outcome is composite,
2 Each element can be described by a “quality” index,
3 The modeler is concerned by both quantity and quality,
4 The modeler does not know exactly the function whichtransforms the “quality” in valued outcome, and thusrefers to classes of functions.
![Page 103: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/103.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
General problem
→ in principle that theory could apply to the comparison ofthe outcome of a set agents for which :
1 The outcome is composite,
2 Each element can be described by a “quality” index,
3 The modeler is concerned by both quantity and quality,
4 The modeler does not know exactly the function whichtransforms the “quality” in valued outcome, and thusrefers to classes of functions.
![Page 104: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/104.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
General problem : Potential applictions
Departments of economics
Museums
Social clubs
Night clubs
...
![Page 105: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/105.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
General problem : Potential applictions
Departments of economics
Museums
Social clubs
Night clubs
...
![Page 106: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/106.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
General problem : Potential applictions
Departments of economics
Museums
Social clubs
Night clubs
...
![Page 107: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/107.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
General problem : Potential applictions
Departments of economics
Museums
Social clubs
Night clubs
...
![Page 108: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/108.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
General problem : Potential applictions
Departments of economics
Museums
Social clubs
Night clubs
...
![Page 109: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/109.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Implicit to explicit valuation of the scientific output
Let f ki (s) :=
∑j=1,...,ni
1 {sj = s} be the publicationperformance of i with “impact” s in discipline k .
0 1 2 3 4 s
f(0)
f(1) f(2)
f(3)
![Page 110: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/110.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
The scientific output : articles and citations
Then the vector of structured publication outcome ofinstitution i in domain k is computed by summing over allarticles a and filtering out the article scores in the sum on theright side of previous equation. It gives :
f ki (s) =
∑j=1,...,ni
pki ,a × 1 {sj = s} .
Assume the exists some s such that ∀i , f ki (s) = 0 if s ≥ s.
The “value” (for the agent, the consumer, the holder, thesponsor...) of the whole publication production of institution iin domain k is assumed to be symmetric and additiveseparable given by :
V k (Si ) = ωk
∫ s
0v(s)f k
i (s) ds,
with ωk the discipline dependent normalization parameter.Computation of the “value” of the whole publicationproduction of institution i in domain k is conditional to thevaluation function v(s).
![Page 111: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/111.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
The scientific output : articles and citations
Then the vector of structured publication outcome ofinstitution i in domain k is computed by summing over allarticles a and filtering out the article scores in the sum on theright side of previous equation. It gives :
f ki (s) =
∑j=1,...,ni
pki ,a × 1 {sj = s} .
Assume the exists some s such that ∀i , f ki (s) = 0 if s ≥ s.
The “value” (for the agent, the consumer, the holder, thesponsor...) of the whole publication production of institution iin domain k is assumed to be symmetric and additiveseparable given by :
V k (Si ) = ωk
∫ s
0v(s)f k
i (s) ds,
with ωk the discipline dependent normalization parameter.Computation of the “value” of the whole publicationproduction of institution i in domain k is conditional to thevaluation function v(s).
![Page 112: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/112.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
The scientific output : articles and citations
Then the vector of structured publication outcome ofinstitution i in domain k is computed by summing over allarticles a and filtering out the article scores in the sum on theright side of previous equation. It gives :
f ki (s) =
∑j=1,...,ni
pki ,a × 1 {sj = s} .
Assume the exists some s such that ∀i , f ki (s) = 0 if s ≥ s.
The “value” (for the agent, the consumer, the holder, thesponsor...) of the whole publication production of institution iin domain k is assumed to be symmetric and additiveseparable given by :
V k (Si ) = ωk
∫ s
0v(s)f k
i (s) ds,
with ωk the discipline dependent normalization parameter.
Computation of the “value” of the whole publicationproduction of institution i in domain k is conditional to thevaluation function v(s).
![Page 113: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/113.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
The scientific output : articles and citations
Then the vector of structured publication outcome ofinstitution i in domain k is computed by summing over allarticles a and filtering out the article scores in the sum on theright side of previous equation. It gives :
f ki (s) =
∑j=1,...,ni
pki ,a × 1 {sj = s} .
Assume the exists some s such that ∀i , f ki (s) = 0 if s ≥ s.
The “value” (for the agent, the consumer, the holder, thesponsor...) of the whole publication production of institution iin domain k is assumed to be symmetric and additiveseparable given by :
V k (Si ) = ωk
∫ s
0v(s)f k
i (s) ds,
with ωk the discipline dependent normalization parameter.Computation of the “value” of the whole publicationproduction of institution i in domain k is conditional to thevaluation function v(s).
![Page 114: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/114.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Implicit valuation : examples
0 1 2 3 4 T s
A
B C D
E F
![Page 115: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/115.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Various assumptions
Assumption 1. v ≥ 0 (A1)
Assumption 2. v ′ ≥ 0 (A2)
Assumption 3. v ′′ ≥ 0 (A3)
Assumption 4. v ′′ ≤ 0 (A4)
According to your goals and/or beliefs, you can rely uponwell defined dominance relations that can be used to producerankings and references classes.
![Page 116: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/116.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Various assumptions
Assumption 1. v ≥ 0 (A1)
Assumption 2. v ′ ≥ 0 (A2)
Assumption 3. v ′′ ≥ 0 (A3)
Assumption 4. v ′′ ≤ 0 (A4)
According to your goals and/or beliefs, you can rely uponwell defined dominance relations that can be used to producerankings and references classes.
![Page 117: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/117.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Various assumptions
Assumption 1. v ≥ 0 (A1)
Assumption 2. v ′ ≥ 0 (A2)
Assumption 3. v ′′ ≥ 0 (A3)
Assumption 4. v ′′ ≤ 0 (A4)
According to your goals and/or beliefs, you can rely uponwell defined dominance relations that can be used to producerankings and references classes.
![Page 118: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/118.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Various assumptions
Assumption 1. v ≥ 0 (A1)
Assumption 2. v ′ ≥ 0 (A2)
Assumption 3. v ′′ ≥ 0 (A3)
Assumption 4. v ′′ ≤ 0 (A4)
According to your goals and/or beliefs, you can rely uponwell defined dominance relations that can be used to producerankings and references classes.
![Page 119: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/119.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Various assumptions
Assumption 1. v ≥ 0 (A1)
Assumption 2. v ′ ≥ 0 (A2)
Assumption 3. v ′′ ≥ 0 (A3)
Assumption 4. v ′′ ≤ 0 (A4)
According to your goals and/or beliefs, you can rely uponwell defined dominance relations that can be used to producerankings and references classes.
![Page 120: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/120.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Various assumptions
Assumption 1. v ≥ 0 (A1)
Assumption 2. v ′ ≥ 0 (A2)
Assumption 3. v ′′ ≥ 0 (A3)
Assumption 4. v ′′ ≤ 0 (A4)
According to your goals and/or beliefs, you can rely uponwell defined dominance relations that can be used to producerankings and references classes.
![Page 121: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/121.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Standard measures using publications and citations
The number of articles published : v(s) = θ > 0
The total number of citations : v(s) = s
The average number of citations per article :vi (s) = s/
∫fi (s)ds
The h-index respects (A1) & (A2) but violates (A3) &(A4).
![Page 122: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/122.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Standard measures using publications and citations
The number of articles published : v(s) = θ > 0
The total number of citations : v(s) = s
The average number of citations per article :vi (s) = s/
∫fi (s)ds
The h-index respects (A1) & (A2) but violates (A3) &(A4).
![Page 123: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/123.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Standard measures using publications and citations
The number of articles published : v(s) = θ > 0
The total number of citations : v(s) = s
The average number of citations per article :vi (s) = s/
∫fi (s)ds
The h-index respects (A1) & (A2) but violates (A3) &(A4).
![Page 124: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/124.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Standard measures using publications and citations
The number of articles published : v(s) = θ > 0
The total number of citations : v(s) = s
The average number of citations per article :vi (s) = s/
∫fi (s)ds
The h-index respects (A1) & (A2) but violates (A3) &(A4).
![Page 125: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/125.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Strong dominance
Definition
The scientific production of institution i in field k stronglydominates the one of institution j , noted i Ik j , if, for anypositive function v (·) (A1),
∫ s0 v(s)f k
i (s) ds ≥∫ s
0 v(s)f kj (s) ds.
Lemma
i Ik j if and only if ∀x ∈ [0,∞[ , f ki (x)− f k
j (x) ≥ 0.
![Page 126: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/126.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Strong dominance
Definition
The scientific production of institution i in field k stronglydominates the one of institution j , noted i Ik j , if, for anypositive function v (·) (A1),
∫ s0 v(s)f k
i (s) ds ≥∫ s
0 v(s)f kj (s) ds.
Lemma
i Ik j if and only if ∀x ∈ [0,∞[ , f ki (x)− f k
j (x) ≥ 0.
![Page 127: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/127.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Implicit valuation of strong dominance : positive functions
0 1 2 3 4 T s
A
B C D
E F
![Page 128: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/128.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Strong dominance
![Page 129: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/129.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
But often :
![Page 130: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/130.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Dominance
Definition
The scientific production of institution i in field k dominates theone of institution j , noted i Bk j , if, for any positive and nondecreasing function v (·) (A1 & A2),∫ s
0 v(s)f ki (s) ds ≥
∫ s0 v(s)f k
j (s) ds.
Lemma
i Bk j , if and only if ∀x ∈ [0, s[ ,∫ sx
[f ki (s)− f k
j (s)]
ds ≥ 0.
![Page 131: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/131.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Dominance
Definition
The scientific production of institution i in field k dominates theone of institution j , noted i Bk j , if, for any positive and nondecreasing function v (·) (A1 & A2),∫ s
0 v(s)f ki (s) ds ≥
∫ s0 v(s)f k
j (s) ds.
Lemma
i Bk j , if and only if ∀x ∈ [0, s[ ,∫ sx
[f ki (s)− f k
j (s)]
ds ≥ 0.
![Page 132: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/132.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Implicit valuation of dominance : positive and increasingfunctions
0 1 2 3 4 T s
B C
E
![Page 133: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/133.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Dominance
![Page 134: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/134.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Dominance
![Page 135: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/135.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Dominance
![Page 136: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/136.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Dominance
![Page 137: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/137.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Dominance
![Page 138: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/138.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Weak dominance
Definition
The scientific production of institution i in field k weaklydominates the one of institution j , noted i Dk j , if, for anypositive, non decreasing function and weakly convex functionv (·) (A1, A2 & A3),
∫ s0 v(s)f k
i (s) ds ≥∫ s
0 v(s)f kj (s) ds.
Lemma
i Dk j , if and only if ∀x ∈ [0, s[ ,∫ sx s[f ki (s)− f k
j (s)]
ds ≥ 0.
![Page 139: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/139.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Weak dominance
Definition
The scientific production of institution i in field k weaklydominates the one of institution j , noted i Dk j , if, for anypositive, non decreasing function and weakly convex functionv (·) (A1, A2 & A3),
∫ s0 v(s)f k
i (s) ds ≥∫ s
0 v(s)f kj (s) ds.
Lemma
i Dk j , if and only if ∀x ∈ [0, s[ ,∫ sx s[f ki (s)− f k
j (s)]
ds ≥ 0.
![Page 140: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/140.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Implicit valuation of weak dominance : positive, increasingand weakly convex functions
0 1 2 3 4 T s
B
F
![Page 141: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/141.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Weak Dominance
fik (s)
fjk (s)
![Page 142: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/142.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Weak Dominance
fik (s)
fjk (s)
![Page 143: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/143.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Weak Dominance
fik (s)
fjk (s)
![Page 144: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/144.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Weak Dominance
![Page 145: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/145.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Weak concave dominance
Definition
The scientific production of institution i in field k weaklyconcavely dominates the one of institution j , noted iBk j , if, forany positive, non decreasing function and weakly concavefunction v (·) (A1, A2 & A4),
∫ s0 v(s)f k
i (s) ds ≥∫ s
0 v(s)f kj (s) ds.
Lemma
iBk j if and only if ∀x ∈ [0, s[ ,∫ x
0 s[f ki (s)− f k
j (s)]
ds ≥ 0.
![Page 146: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/146.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Weak concave dominance
Definition
The scientific production of institution i in field k weaklyconcavely dominates the one of institution j , noted iBk j , if, forany positive, non decreasing function and weakly concavefunction v (·) (A1, A2 & A4),
∫ s0 v(s)f k
i (s) ds ≥∫ s
0 v(s)f kj (s) ds.
Lemma
iBk j if and only if ∀x ∈ [0, s[ ,∫ x
0 s[f ki (s)− f k
j (s)]
ds ≥ 0.
![Page 147: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/147.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Upward dominance
Definition
Let sφk be the smallest visibility a paper may exhibit among the φ%most visible papers in the field k (in the world).
Strong dominance at order φ : i Iφk j .
Dominance at order φ : i Bφk j .
Weak dominance at order φ : i Dφk j .
Upward dominance relations are obviously generalization ofthe dominance relations which are equivalent to upwarddominance relations at order 1.
![Page 148: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/148.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Upward dominance
Definition
Let sφk be the smallest visibility a paper may exhibit among the φ%most visible papers in the field k (in the world).
Strong dominance at order φ : i Iφk j .
Dominance at order φ : i Bφk j .
Weak dominance at order φ : i Dφk j .
Upward dominance relations are obviously generalization ofthe dominance relations which are equivalent to upwarddominance relations at order 1.
![Page 149: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/149.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Upward dominance
Definition
Let sφk be the smallest visibility a paper may exhibit among the φ%most visible papers in the field k (in the world).
Strong dominance at order φ : i Iφk j .
Dominance at order φ : i Bφk j .
Weak dominance at order φ : i Dφk j .
Upward dominance relations are obviously generalization ofthe dominance relations which are equivalent to upwarddominance relations at order 1.
![Page 150: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/150.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Upward dominance
Definition
Let sφk be the smallest visibility a paper may exhibit among the φ%most visible papers in the field k (in the world).
Strong dominance at order φ : i Iφk j .
Dominance at order φ : i Bφk j .
Weak dominance at order φ : i Dφk j .
Upward dominance relations are obviously generalization ofthe dominance relations which are equivalent to upwarddominance relations at order 1.
![Page 151: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/151.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Upward dominance
Definition
Let sφk be the smallest visibility a paper may exhibit among the φ%most visible papers in the field k (in the world).
Strong dominance at order φ : i Iφk j .
Dominance at order φ : i Bφk j .
Weak dominance at order φ : i Dφk j .
Upward dominance relations are obviously generalization ofthe dominance relations which are equivalent to upwarddominance relations at order 1.
![Page 152: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/152.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Upward Dominance
fik (s)
fjk (s)
fik (s)
fjk (s)
sφ
![Page 153: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/153.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Upward Dominance
fik (s)
fjk (s)
fik (s)
fjk (s)
sφ
![Page 154: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/154.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
The Interdisciplinary scientific output
Θi =(Θk
i
)k=1,...|K |, the vector of publication informed by
citations performance in all disciplines/domains k ∈ K
The value of the publication performance of institution i asthe weighted and valued sum of the articles of thatinstitution :
V (Θi ) =∑k
ωk
∫ s
0v(s)f k
i (s) ds.
We propose to set ωk as the inverse of the average number ofcitations made by articles in field k .
The value function is not symmetric anymore.
![Page 155: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/155.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
The Interdisciplinary scientific output
Θi =(Θk
i
)k=1,...|K |, the vector of publication informed by
citations performance in all disciplines/domains k ∈ K
The value of the publication performance of institution i asthe weighted and valued sum of the articles of thatinstitution :
V (Θi ) =∑k
ωk
∫ s
0v(s)f k
i (s) ds.
We propose to set ωk as the inverse of the average number ofcitations made by articles in field k .
The value function is not symmetric anymore.
![Page 156: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/156.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
The Interdisciplinary scientific output
Θi =(Θk
i
)k=1,...|K |, the vector of publication informed by
citations performance in all disciplines/domains k ∈ K
The value of the publication performance of institution i asthe weighted and valued sum of the articles of thatinstitution :
V (Θi ) =∑k
ωk
∫ s
0v(s)f k
i (s) ds.
We propose to set ωk as the inverse of the average number ofcitations made by articles in field k .
The value function is not symmetric anymore.
![Page 157: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/157.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
The Interdisciplinary scientific output
Θi =(Θk
i
)k=1,...|K |, the vector of publication informed by
citations performance in all disciplines/domains k ∈ K
The value of the publication performance of institution i asthe weighted and valued sum of the articles of thatinstitution :
V (Θi ) =∑k
ωk
∫ s
0v(s)f k
i (s) ds.
We propose to set ωk as the inverse of the average number ofcitations made by articles in field k .
The value function is not symmetric anymore.
![Page 158: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/158.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
The scientific output : articles and citations
Definition
The scientific production of institution i inter-disciplinary (a)strongly dominates
(i Iφ j
), (b) dominates
(i Bφ j
)or (c) weakly
dominates(i Dφ j
)at order φ ∈ ]0, 1] the one of institution j , if∫ s
sφk
v(s)f ki (s) ds ≥
∑k
∫ ssφk
v(s)f kj (s) ds for any (a) positive
function (b) positive and non-decreasing (c) positive andnon-decreasing and weakly convex function v (·) .
![Page 159: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/159.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
The scientific output : articles and citations
Lemma
The three following statements hold :i) i Iφ j iff, ∀x = (xk)k=1...|K | st
∀k , xk ∈[sφk , s
[,∑
k ωk
[f ki (xk)− f k
j (xk)]
ds ≥ 0;
ii) i Bφ j iff, ∀x = (xk)k=1...|K | st
∀k, xk ∈[sφk , s
[,∑
k ωk
∫ sxk
[f ki (s)− f k
j (s)]
ds ≥ 0;
iii) i Dφ j iff ∀x = (xk)k=1...|K | st
∀k, xk ∈[sφk , s
[,∑
k ωk
∫ sxk
s[f ki (s)− f k
j (s)]
ds ≥ 0.
![Page 160: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/160.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Properties of dominance relations
Lemma
All the dominance relations introduced (upward strong dominance,upward dominance and upward weak dominance) are transitive : ifi � j and j � h, then i � h, where � potentially accounts forIφ
k ,Bφk or Dφ
k , with ∀φ ∈ ]0, 1].
![Page 161: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/161.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Relations between dominance relations
Definition
A dominance relation � is stronger than dominance relation �′,noted ���′, if, ∀i , j , i � j implies i �′ j .
Theorem
∀φ, φ′ ∈ [0, 1] such that φ ≥ φ′, then
- Iφk�Bφ
k�Dφk ,
- Iφk�Iφ′
k , Bφk�Bφ′
k and Dφk�Dφ′
k ,- Iφ�Bφ�Dφ, and- Iφ�Iφ′ , Bφ�Bφ′ and Dφ�Dφ′ .
Thus the weaker the dominance relation, the more complete,that is the more dominance relations it is possible to establisha given set of institutions.
![Page 162: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/162.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Relations between dominance relations
Definition
A dominance relation � is stronger than dominance relation �′,noted ���′, if, ∀i , j , i � j implies i �′ j .
Theorem
∀φ, φ′ ∈ [0, 1] such that φ ≥ φ′, then
- Iφk�Bφ
k�Dφk ,
- Iφk�Iφ′
k , Bφk�Bφ′
k and Dφk�Dφ′
k ,- Iφ�Bφ�Dφ, and- Iφ�Iφ′ , Bφ�Bφ′ and Dφ�Dφ′ .
Thus the weaker the dominance relation, the more complete,that is the more dominance relations it is possible to establisha given set of institutions.
![Page 163: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/163.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Relations between dominance relations
Definition
A dominance relation � is stronger than dominance relation �′,noted ���′, if, ∀i , j , i � j implies i �′ j .
Theorem
∀φ, φ′ ∈ [0, 1] such that φ ≥ φ′, then
- Iφk�Bφ
k�Dφk ,
- Iφk�Iφ′
k , Bφk�Bφ′
k and Dφk�Dφ′
k ,- Iφ�Bφ�Dφ, and- Iφ�Iφ′ , Bφ�Bφ′ and Dφ�Dφ′ .
Thus the weaker the dominance relation, the more complete,that is the more dominance relations it is possible to establisha given set of institutions.
![Page 164: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/164.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Publication data
OST in-house ISI-WOS database recording of publications andcitations
Large disciplines : 1/ Fund. bio., 2/ Medicine, 3/ Ap.bio/ecol., 4/ Chem., 5/ Physics, 6/ Science univ., 7/ Eng.sciences, 8/ Maths (Humanities and social sciences areexcluded.
Multidisciplinary sciences papers published in PNAS, Science& Nature have been allocated to their reference discipline fordisciplinary comparisons.
3-years citations moving window for all indexes.
Linearization of the distribution.
![Page 165: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/165.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Publication data
OST in-house ISI-WOS database recording of publications andcitations
Large disciplines : 1/ Fund. bio., 2/ Medicine, 3/ Ap.bio/ecol., 4/ Chem., 5/ Physics, 6/ Science univ., 7/ Eng.sciences, 8/ Maths (Humanities and social sciences areexcluded.
Multidisciplinary sciences papers published in PNAS, Science& Nature have been allocated to their reference discipline fordisciplinary comparisons.
3-years citations moving window for all indexes.
Linearization of the distribution.
![Page 166: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/166.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Publication data
OST in-house ISI-WOS database recording of publications andcitations
Large disciplines : 1/ Fund. bio., 2/ Medicine, 3/ Ap.bio/ecol., 4/ Chem., 5/ Physics, 6/ Science univ., 7/ Eng.sciences, 8/ Maths (Humanities and social sciences areexcluded.
Multidisciplinary sciences papers published in PNAS, Science& Nature have been allocated to their reference discipline fordisciplinary comparisons.
3-years citations moving window for all indexes.
Linearization of the distribution.
![Page 167: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/167.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Publication data
OST in-house ISI-WOS database recording of publications andcitations
Large disciplines : 1/ Fund. bio., 2/ Medicine, 3/ Ap.bio/ecol., 4/ Chem., 5/ Physics, 6/ Science univ., 7/ Eng.sciences, 8/ Maths (Humanities and social sciences areexcluded.
Multidisciplinary sciences papers published in PNAS, Science& Nature have been allocated to their reference discipline fordisciplinary comparisons.
3-years citations moving window for all indexes.
Linearization of the distribution.
![Page 168: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/168.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Publication data
OST in-house ISI-WOS database recording of publications andcitations
Large disciplines : 1/ Fund. bio., 2/ Medicine, 3/ Ap.bio/ecol., 4/ Chem., 5/ Physics, 6/ Science univ., 7/ Eng.sciences, 8/ Maths (Humanities and social sciences areexcluded.
Multidisciplinary sciences papers published in PNAS, Science& Nature have been allocated to their reference discipline fordisciplinary comparisons.
3-years citations moving window for all indexes.
Linearization of the distribution.
![Page 169: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/169.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Data set
French universities :
129 institutionsThe institutions checked the validity of signing patterns.
US research universities :
112 best ranked in the ARWU Shanghaı ranking (30% of PhDgranting Univ.)
![Page 170: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/170.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Data set
French universities :
129 institutions
The institutions checked the validity of signing patterns.
US research universities :
112 best ranked in the ARWU Shanghaı ranking (30% of PhDgranting Univ.)
![Page 171: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/171.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Data set
French universities :
129 institutionsThe institutions checked the validity of signing patterns.
US research universities :
112 best ranked in the ARWU Shanghaı ranking (30% of PhDgranting Univ.)
![Page 172: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/172.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Data set
French universities :
129 institutionsThe institutions checked the validity of signing patterns.
US research universities :
112 best ranked in the ARWU Shanghaı ranking (30% of PhDgranting Univ.)
![Page 173: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/173.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Data set
French universities :
129 institutionsThe institutions checked the validity of signing patterns.
US research universities :
112 best ranked in the ARWU Shanghaı ranking (30% of PhDgranting Univ.)
![Page 174: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/174.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Networks of dominance relations
Let us consider �, which could be any one of the dominancerelations examined above (Iφ
k ,Bφk or Dφ
k , with ∀φ ∈ ]0, 1]).
Let’s build the dominance directed network ~g associated todominance relation � and the institutions set I by writing adirect link from institution i to institution j if i � j .
In this network, transitive triplets are uninformative since thetransitivity property holds. Therefore, let’s build the network~g ′ derived from ~g by deleting all such triplets : ∀i , j , k ∈ I , ifij , ik, jk ∈ ~g and kj /∈ ~g then ik /∈ ~g ′.
![Page 175: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/175.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Networks of dominance relations
Let us consider �, which could be any one of the dominancerelations examined above (Iφ
k ,Bφk or Dφ
k , with ∀φ ∈ ]0, 1]).
Let’s build the dominance directed network ~g associated todominance relation � and the institutions set I by writing adirect link from institution i to institution j if i � j .
In this network, transitive triplets are uninformative since thetransitivity property holds. Therefore, let’s build the network~g ′ derived from ~g by deleting all such triplets : ∀i , j , k ∈ I , ifij , ik, jk ∈ ~g and kj /∈ ~g then ik /∈ ~g ′.
![Page 176: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/176.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Networks of dominance relations
Let us consider �, which could be any one of the dominancerelations examined above (Iφ
k ,Bφk or Dφ
k , with ∀φ ∈ ]0, 1]).
Let’s build the dominance directed network ~g associated todominance relation � and the institutions set I by writing adirect link from institution i to institution j if i � j .
In this network, transitive triplets are uninformative since thetransitivity property holds. Therefore, let’s build the network~g ′ derived from ~g by deleting all such triplets : ∀i , j , k ∈ I , ifij , ik , jk ∈ ~g and kj /∈ ~g then ik /∈ ~g ′.
![Page 177: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/177.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Dominance network : an example
![Page 178: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/178.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Reference classes
Definition
∀k ∈ I , j ∈ c�i (⊆ I ) the reference class of institution i associatedto dominance relation � if i � j and j � i or if i � j and j � i
Reading example : j ∈ cBki means it is not always possible to
rank strictly and in a unique manner the scientific productionof i and j in domain k relying on any implicit valuationfunction of articles according to their impact which would beboth positive and increasing with impact.
![Page 179: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/179.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Reference classes
Definition
∀k ∈ I , j ∈ c�i (⊆ I ) the reference class of institution i associatedto dominance relation � if i � j and j � i or if i � j and j � i
Reading example : j ∈ cBki means it is not always possible to
rank strictly and in a unique manner the scientific productionof i and j in domain k relying on any implicit valuationfunction of articles according to their impact which would beboth positive and increasing with impact.
![Page 180: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/180.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Dominance Networks : Top French universities in FundBio, φ = 1 - citations
Paris 6
Paris 11
Strasbourg 1
Paris 5 Montpellier 2
Aix Marseille 2
Paris 7 Lyon 1
Grenoble 1
![Page 181: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/181.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Dominance Networks : Top French universities in FundBio, φ = .1 - citations
Paris 6
Paris 11
Strasbourg 1
Paris 5 Montpelier 2 Aix Marseille 2
Paris 7
Lyon 1 Grenoble 1
![Page 182: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/182.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Dominance Networks : Top French universities in FundBio, φ = .1 - impact factor
Paris 6
Paris 11
Strasbourg 1
Paris 5
Montpellier 2
Aix Marseille 2
Paris 7
Lyon 1
Grenoble 1
![Page 183: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/183.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Complete dominance relations and ranking
Definition
A dominance relation � is said to be I -complete if ∀i , j ∈ I , i � jor j � i .
Definition
A (complete) dominance ranking R�I can be constructed overinstitutions set I on the basis of dominance relation � if and onlyif � is an I -complete dominance relation.
![Page 184: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/184.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Complete dominance relations and ranking
Definition
A dominance relation � is said to be I -complete if ∀i , j ∈ I , i � jor j � i .
Definition
A (complete) dominance ranking R�I can be constructed overinstitutions set I on the basis of dominance relation � if and onlyif � is an I -complete dominance relation.
![Page 185: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/185.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Complete dominance ranking
Definition
For each type of dominance (strong dominance, dominance, weakdominance), the smallest and strictly positive value of φ for whichthe corresponding dominance relations are I -complete are calledmax-I -complete dominance relations.
1 2 3 4 5 6 7 8
I .009 .004 .005 .022 .016 .019 .002 .009
B .009 .004 .008 .024 .016 .026 .002 .009
D .009 .004 .008 .024 .052 .026 .007 .009
The largest φ such that such dominance relation is I -complete overthe set of 129 French higher Education and research institutions
![Page 186: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/186.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Complete dominance ranking
Definition
For each type of dominance (strong dominance, dominance, weakdominance), the smallest and strictly positive value of φ for whichthe corresponding dominance relations are I -complete are calledmax-I -complete dominance relations.
1 2 3 4 5 6 7 8
I .009 .004 .005 .022 .016 .019 .002 .009
B .009 .004 .008 .024 .016 .026 .002 .009
D .009 .004 .008 .024 .052 .026 .007 .009
The largest φ such that such dominance relation is I -complete overthe set of 129 French higher Education and research institutions
![Page 187: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/187.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Complete dominance ranking
Definition
For each type of dominance (strong dominance, dominance, weakdominance), the smallest and strictly positive value of φ for whichthe corresponding dominance relations are I -complete are calledmax-I -complete dominance relations.
1 2 3 4 5 6 7 8
I .009 .004 .005 .022 .016 .019 .002 .009
B .009 .004 .008 .024 .016 .026 .002 .009
D .009 .004 .008 .024 .052 .026 .007 .009
The largest φ such that such dominance relation is I -complete overthe set of 129 French higher Education and research institutions
![Page 188: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/188.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Pseudo dominance ranking
Definition
For any dominance relation and any set of institutions I , a pseudodominance ranking can be established on the basis of the score ofeach institution i , si = # {j |ij ∈ ~g }, the number of dominancerelations which emanate from institution i .
![Page 189: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/189.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Pseudo dominance ranking : : US universities
Fund Biology I1 B1 D1
citations ri si ri si ri si
Harvard 1 111 1 111 1 111
John Hopkins 3 95 2 106 4 108
UCSF 7 91 3 105 3 109
Pennsylvania 3 95 4 103 8 104
UCLA 2 96 4 103 9 103
UCSD 5 92 6 100 6 105
Yale 11 87 6 100 5 107
Stanford 15 81 6 100 2 110
UW Seattle 5 92 9 99 12 99
Columbia 11 87 10 98 6 105
![Page 190: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/190.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Conclusion
Combinations of influence, quality and quality.
Ranking can also be good way of doing economics (and notjust playing a childish game).
![Page 191: Measuring and ranking scienti c productiondimetic.dime-eu.org/dimetic_files/dimetic_ranking.pdf · Measuring scienti c production Ranking Bibliometrics A eld born with the its object](https://reader036.vdocuments.site/reader036/viewer/2022081408/606103e2504dba4cd5314494/html5/thumbnails/191.jpg)
Measuring scientific production Ranking
The extended stochastic dominance approach
Conclusion
Combinations of influence, quality and quality.
Ranking can also be good way of doing economics (and notjust playing a childish game).