Probing Multivariate Indicators for Academic Evaluation
11 Probing Multivariate Indicators for Academic Evaluation
Journal of Library Science in China (in press)
Helen F. Xue , Loet Leydesdorff , Fred Y. Ye Library, Zhejiang University, Hangzhou 310027, CHINA Amsterdam School of Communication Research (ASCoR), University of Amsterdam, PO Box 15793, 1001 NG Amsterdam, The Netherlands School of Information Management, Nanjing University, Nanjing 210023, CHINA
Abstract:
We combine the Integrated Impact Indicator (I3) and the h-index into the I3-type framework and introduce the publication vector X = (X , X , X ) and the citation vector Y = (Y , Y , Y ) , the publication score I3X=X +X +X and the citation score I3Y=Y +Y +Y , and alternative indicators based on percentile classes generated by the h-index. These multivariate indicators can be used for academic evaluation. The empirical studies show that the h-core distribution is suitable to evaluate scholars, the X and Y are applied to measure core impact power of universities, and I3X and I3Y are alternatives of journal impact factor (JIF). The multivariate indicators provide a multidimensional view of academic evaluation with using the advantages of both the h-index and I3. Keywords:
I3; h-index; publication vector; citation vector; publication score; citation score; multivariate indicator; academic evaluation * Corresponding author: Fred Y. Ye, Email: [email protected]
1. Introduction
Academic evaluation has continued to be an issue in the academic world, as it is difficult to select and set universal evaluating principles in various complicated situations. However, publications and citations remain the main focuses of academic evaluation, particularly for fundamental research. Citations cannot directly be compared with publications and thus one needs a model or at least a formula. A model can be improved and thus the measurement be refined. Since all models also generate error, the quality of a model depends on the quality of the arguments used for constructing the model. Since Garfield introduced the journal impact factor (JIF) and set up citation analysis (Garfield, 1955, 1979), these scientometric indicators have been applied to academic evaluations. Hirsch (2005) proposed the h-index, which was rapidly accepted by the scientific community. This promoted the development of quantitative academic indicators. However, both JIF and h-index have their advantages and disadvantages. JIF is basically designed for journals and the h-index for the evaluation of individual scholars. After developing a set of criteria for an indicator in Leydesdorff et al. (2011), these authors proposed the Integrated Impact Indicator I3 (Leydesdorff & Bornmann 2011). I3 is based on ( i ) transformation of the citation distribution into a distribution of quantiles and ( ii ) integration (instead of averaging) of the quantile values. (Quantiles are the continuous equivalent of percentiles.) The use of percentiles was recently recommended in the Leiden Manifesto (“Ten principles to guide research evaluation”; Hicks et al., 2015), because average citation rates are heavily dependent on the few highly cited papers in a publication set and bibliometric distributions are very skewed. I3 combines citation impact and publication output into a single number – similar to the h- index. The quantile values which are conveniently normalized between zero and hundred provide the weights for the papers, as follows: Ci ii
XXfiI )()(3 (1) where X i indicates the percentile ranks and f (X i ) denotes the frequencies of the ranks with i =[1,C] as the percentile rank classes, which means that the measures X i are divided into C classes each with a scoring function f (X i ) or weight (w i ). One can also re-write Eq. (1) as follows: i ii ii wXwiI (2) As an alternative to quantiles, the h value of a document set can be used to provide a rank class structure. This combines the advantages of I3 and h into a single framework (Rousseau & Ye, 2012; Ye & Leydesdorff, 2014), which can be applied to academic evaluations based on publications and citations at both group and individual levels. In this study, we elaborate this methodology which was previously applied to journals (Ye et al., 2017), to universities as well as individual scholars.
2. Methodology
In many cases, single numbers are used as indicators in academic evaluations. However, a single number can only reflect one side of the overall information and can therefore be expected to have limitations and disadvantages. Possible solutions are multivariate indicators which reflect the multidimensional information. The h-based I3-type multivariate indicators provided a framework of such an elaborate methodology (Ye & Leydesdorff, 2014; Ye et al., 2017).
Let us assume that the y-axis denotes citations and the x-axis indicates ranked publications from high citation to low citation, then we obtain a publication-citation distribution as in Figure 1. The h- index allows us to define three rank classes of both publications and citations in Figure 1. The three classes of publications along the x-axis are: (i) publications in the h- core (Ye & Rousseau, 2010; Chen et al ., 2013) P c , (ii) publications in the h- tail P t , (iii) and publications without citations P z . Along the y-axis of the citations one can analogously distinguish among (i) the “excess citations” in the h- core (Zhang, 2009, 2013) C e =e , (ii) citations to publications in the h square of the h- core C c =h , and (iii) citations to publications in the h- tail C t =t . C 0 P t h h-tail h-core C c =h P c P z C t = t P excess C e = e Fig. 1
The rank distribution of citations versus publications. Let x c =P c /(P c +P t +P z ), x t =P t /(P c +P t +P z ), x z =P z /(P c +P t +P z ), y c =C c /(C c +C t +C e ), y t =C t /(C c +C t +C e ) and y e =C e /(C c +C t +C e ), we may define two independent vectors as publication vector and citation vector respectively: X )/,/,/(),,(),,( PPPPPPPxPxPxXXX ztczzttcc (3) Y )/,/,/(),,(),,( CCCCCCCyCyCyYYY etceettcc (4) as well as an I3 -type publication indicator I3X and an I3 -type citation indicator I3Y as follows XXXPxPxPxXI zzttcc (5) YYYCyCyCyYI eettcc (6) The vector X and the score I3X represent the relative frequencies of the publications, while the vector Y and the score I3Y denote the relative frequencies of the citations. For convenient application, citation score in h-core can be merged into Y h =Y +Y =y h C h , where y h =C h /C, C h =C e +C c . Thus, the h-based I3-type multivariate indicators provide multidimensional indicators: X measures publication score in the h-core (X and Y combination may measure core impact power), X measures publication score in h-tail, Y h measures citation score in h-core, Y measures citation score in h-tail, I3X does total publication score, and I3Y does total citation score. Since P=P c +P t +P z , C=C h +C t =C c +C t +C e , C h =C c +C e , P c =h, C c =h , one needs to measure only five independent numbers, P, C, P z , C h , h, for the computation of X and Y, I3X and
I3Y , via P t =P-P c -P z , C c =h , C t =C-C h , and C e =C h -C c . These five values can be obtained easily from bibliometric databases, like by searching Web of Science (WoS) or Scopus. In order to show the general applicability of these measures, we provide three examples at different levels: 1) individual scholars, we choose the profiles of ourselves in order to avoid issues concerning personal privacy, using 10 years of data from WoS 2005-2015; 2) universities: we chose 25 famous universities, including nine in the USA, nine in China, two in the UK and Germany respectively, and single ones from Australia, Canada, and Japan, with five year data from 2011 to 2015 in WoS; 3) journals, we chose journal datasets 2011- 2015, in the field of electrochemistry (EC). The parameters computed from the datasets are listed in the appendix. We also collected 2009-2013 data of 25 famous universities and the journal data 2011-2015 in the field of history of the social sciences (HSS), for comparative applications.
3. Results
The publication vector X = (X , X , X ) and the citation vector Y = (Y , Y , Y ) are represented by distributed numbers, which are listed in the appendix. The distributed numbers reflect multidimensional academic information, so that the multivariate vectors X and Y contribute possible applications as multidimensional indicators. If we want to compare research objects to one another, we can inspect the tabled values of publication vector X and citation vector Y , where (X , X , X ) and/or (Y , Y , Y ) rank accordingly. However, if we merge the same-type numbers into one indicator, I3 -type indicators can be a good choice. I3 X=X +X +X and I3 Y=Y +Y +Y sum the scores of vector X and Y , respectively. All scores can be plotted into figures. The scholars’ data can be searched via definite field and time span in definite database. Individual dataset is small, so that all indicators can be easily calculated, such as h-index, X i , Y i , I3X, I3Y, even h-core and h-tail distributions of publications and citations. Figure 2 shows the h-core distributions of Leydesdorff L and Ye FY. Fig. 2
Leydesdorff’s and Ye’s citation-publication distribution in h-core
The indicators of an individual scholar are derived from his/her publications in his/her respective h-core. The multivariate indicators supply a feasible way for mining the indicators. For younger scholars with a lower h-index, the indicators X and Y can be used to indicate their potential. For any university, there are lots of publications and citations distributed in many fields, so that the multivariate indicators provide useful indicators from different perspectives. When we are concerned with the core impact, the h-index, X and Y provide important h-core information, while ignoring the h-tail. Figure 3 shows the impact of 25 famous universities. hY1X1 X1 Y1 Fig. 3
The core impact power of 25 famous universities (2011-2015) Figure 3 shows that Harvard occupies the top-1 position in terms of impact of citations and MIT the top-1 in impact power of publications, while Stanford, Berkeley, Cambridge, Oxford follow these top performers. Among these top universities, Yale and Michigan have core advantages of publications indicated by obvious peaks.
As all publications and citations are valuable for evaluating in journals, it is recommendable to use I3X and I3Y, which can cover the distribution of publication scores while integrating citation scores of h-core and h-tail. Figure 4 shows this for journals in electro-chemistry (EC). I3XI3Y
Fig. 4
The I3X and I3Y of 25 EC journals (2011-2015) In order to understand the relations among all the indicators, Table 1 shows the Spearman correlations between h and {X i }, {Y i } (i=1,2,3), IX3, I3Y for 25 famous universities and Table 2 provides Spearman correlations between JIF and {X i }, {Y i } (i=1,2,3), IX3, I3Y for 27 EC journals. Table 1
The correlations of multivariate indicators for 25 top-ranked universities (2011-2015)
Correlations Spearman (Sig.(2-tailed)) h Y Y Y I3Y Spearman (Sig.(2-tailed)) h 1 .958(.000)* .838(.000)* .768(.000)* .843(.000)* X .514(.009)* .678(.000)* .074(.726) .824(.000)* .078(.709) X .630(.001)* .440(.028)** .918(.000)* .159(.447) .912(.000)* X .538(.006)* .405(.044)** .775(.000)* .173(.408) .778(.000)* I3X .671(.000)* .486(.014)** .945(.000)* .188(.369) .942(.000)* *correlation is significant at the 0.01 level (2-tailed); **correlation is significant at the 0.05 level (2-tailed) Table 2
The correlations of multivariate indicators for 27 EC journals (2011-2015)
Correlations Spearman (Sig.(2-tailed)) JIF Y Y Y I3Y Spearman (Sig.(2-tailed)) JIF 1 .887 (.000)* .746 (.000)* .777 (.000)* .761(.000)* X .713 (.000)* .609 (.001)* .208 (.297) .593 (.001)* .233(.242) X .730 (.000)* .844(.000)* .995 (.000)* .679 (.000)* .995(.000)* X -.507 (.007)* -.275 (.165) .095(.637) -.217 (.276) .068(.735) I3X .678(.000)* .802(.000)* .988(.000)* .667(.000)* .986(.000)* *correlation is significant at the 0.01 level (2-tailed) Table 1 shows that most multivariate indicators (except a few X , Y and I3X) are positively correlated to the h-index at university level, with Spearman coefficients 0.514, 0.671, 0.843 between h-index and X , I3X, I3Y respectively. Table 2 shows similar results: most multivariate indicators (except X ) are positive correlations to JIF at journal level. Totally, {X i } (i=1,2) and {Y i } (i=1,2,3), I3X and I3Y are suitable to be independent indicators.
4. Discussion and Comparison
The advantages of X and Y are relative robust like h-index, with non-integral changeability, particularly Y can characterize core impact power of citations. In Table 3, we compare the data of 25 famous universities during the periods of 2009-2013 and 2011-2015, in terms of h-index and Y . One can see the quick development of the Chinese universities compared to the world-class universities. Table 3. The Change of Universities’ h-indices and Y UNIV. h Y HARVARD 272 4763.45 HARVARD 299 5794.92 MIT 217 4506.3 MIT 241 5374.34 UC BERKELEY 203 3426.45 STANFORD 231 4335.86 STANFORD 202 3242.72 UC BERKELEY 210 3232.96 CAMBRIDGE 190 2822.44 OXFORD 206 2926.63 OXFORD 192 2782.86 CAMBRIDGE 201 2870.43 CHICAGO 164 2387.89 CHICAGO 178 2754.38 MICHIGAN 181 2166.96 TORONTO 200 2654.09 CALTECH 154 2081.41 YALE 183 2464.35 TORONTO 178 2051.62 CALTECH 161 2111.04 YALE 161 1840.59 MICHIGAN 186 2094.91 PRINCETON 133 1559.91 PRINCETON 146 1885.78 TSINGHUA 111 878.081 SYDNEY 153 1608.35 SYDNEY 120 853.671 TSINGHUA 135 1195.78 PEKING 112 799.809 FUDAN 128 1183.3 FUDAN 102 734.071 USTC 120 1098.46 KYOTO 114 714.517 HONG KONG 136 977.568 HONG KONG 116 700.921 PEKING 130 949.031 HUMBOLDT 81 609.58 KYOTO 126 931.677 HAMBURG 82 574.298 ZHEJIANG 126 851.592 USTC 89 552.153 HAMBURG 97 805.082 NANJING 98 487.427 HUMBOLDT 92 789.657 SHANGHAI JIAO TONG 92 459.206 NATL TAIWAN 116 786.014 ZHEJIANG 95 428.322 NANJING 123 759.485 NATL TAIWAN 85 294.895 SHANGHAI JIAO TONG 116 712.446
There are disciplinary differences, which could affect the applications of the multivariate indicators. For example, comparing the journals of history of the social sciences with the journals of electrochemistry, the relation of I3X and I3Y as well as their correlations to JIF show differences in Figure 5 and Table 4. I3X
I3Y
Fig.5
The I3X and I3Y of 35 HSS journals (2011-2015)
Table 4
The correlations of multivariate indicators for 35 HSS journals (2011-2015)
Correlations Spearman (Sig.(2-tailed)) JIF Y Y Y I3Y Spearman (Sig.(2-tailed)) JIF 1 .690 (.000)* .521 (.001)* .634 (.000)* .527(.001)* X .548 (.001)* .774 (.000)* .343 (.044)** .626 (.001)* .353(.037)** X .470 (.004)* .347(.041)** .880 (.000)* .408 (.015)** .876(.000)* X .006 (.974) -.037 (.832) .084 (.632) -.172(.323) .088(.614) I3X .131(.455) .080(.647) .348(.041)** -.041(.813) .352(.038)** *correlation is significant at the 0.01 level (2-tailed); **correlation is significant at the 0.05 level (2-tailed) Here we see that the correlations in multivariate indicators are much lower in the social sciences. Particularly, I3X is no longer correlated to JIF; it is an independent indicator. Therefore, the multivariate indicators provide richer measurement information than single indicators.
In general, if we want to compare two academic subject or object A and B, we may compare all elements of their academic matrices M A and M B . If all elements in M A are better than M B (recorded as }{}{ BA MM , not always A>B; for X3, smaller value is better), we can say A is better than B. More generally, academic tensor T is suggested to be a generalized 4 measure including matrix. We can compare all elements of their academic tensors T A and T B . If all elements in T A are better than T B (recorded as }{}{ BA TT ), we can say A is better than B.
5. Conclusions
The multivariate indicators, including publication vector X = (X , X , X ) and citation vector Y = (Y , Y , Y ), publication score I3 X=X +X +X and citation score I3 Y=Y +Y +Y , as well as their elements and integrated indices, provide a methodological framework for extensive academic measurement. Most of them are positively correlated to the h-index and JIF, with relative independence (Spearman coefficients 0.5~0.9), so that they can be considered as independent indicators, which provide multidimensional views for academic evaluation. Particularly, the core-tail measurements of X and Y , as well as I3X and
I3Y combine the advantages of the h -index and I3 : (i) the publications and not only the citations are appreciated; (ii) the indicators are non-parametric; (iii) the results are easy to obtain from WoS or Scopus data; (iv) the results can be plotted via X-Y system. We note that these indicators do not require reference sets as when using quantile or percentile values (Bornmann et al., 2013); the distributions are generated from the h-classes as shown in Figure 1 above. We plan to develop further studies with applications and extensions of these multivariate indicators. Acknowledgements
We acknowledge the National Natural Science Foundation of China Grant No 71673131 for partly financial supports.
References
Bensman, S. J. (2007). Garfield and the impact factor.
Annual Review of Information Science and Technology, 41 (1), 93-155. Jin, B., Liang, L., Rousseau, R., & Egghe, L. (2007). The R- and AR-indices: Complementing the h-index.
Chinese Science Bulletin, 2007, 52(6), 855-863, 52 (6), 855-863. Bornmann, L., & Daniel, H.-D. (2007). What do we know about the h index?
Journal of the American Society for Information Science and Technology , 58(9), 1381-1385 Bornmann, L., & Leydesdorff, L. (2014). On the meaningful and non-meaningful use of reference sets in bibliometrics.
Journal of Informetrics, 8 (1), 273-275. Bornmann, L., & Mutz, R. (2011). Further steps towards an ideal method of measuring citation performance: The avoidance of citation (ratio) averages in field-normalization.
Journal of Informetrics, 5 (1), 228-230. Bornmann, L., Leydesdorff, L., & Mutz, R. (2013). The use of percentiles and percentile rank classes in the analysis of bibliometric data: Opportunities and limits.
Journal of Informetrics, 7 (1), 158-165. Chen, D-Z; Huang, M-H and Fred Y. Ye. (2013). A probe into dynamic measures for h-core and h-tail.
Journal of Informetrics , 7(1), 129-137 Egghe, L. (2005). Power laws in the information production process: Lotkaian informetrics. Amsterdam: Elsevier. Egghe, L. (2006). Theory and practise of the g-index.
Scientometrics, 69 (1), 131-152. Egghe, L. (2007). Untangling Herdan’s law and Heaps’ law: Mathematical and informetric arguments.
Journal of American Society for Information Science and Technology , 58(5), 702–709. Egghe, L. and Rousseau, R. (2012). Theory and practice of the shifted Lotka function.
Scientometrics,
Science,
Science, 66 (No. 1713 (Oct. 28, 1927)), 385-389. Hicks, Diana, Wouters, Paul, Waltman, Ludo, de Rijcke, Sarah, & Rafols, Ismael. (2015). Bibliometrics: The Leiden Manifesto for research metrics.
Nature , 520(7548), 429-431 Hirsch, J. E. (2005). An index to quantify an individual's scientific research output.
Proceedings of the National Academy of Sciences of the USA, 102 (46), 16569-16572. 6 Huang, M.-H., Chen, D.-Z.,Shen, D., Wang, M.S. & Ye, F.Y. (2015). Measuring technological performance of assignees using trace metrics in three fields.
Scientometrics , 104, 61–86 Leydesdorff, L. and Bornmann, L. (2011). Integrated impact indicators compared with impact factors: an alternative research design with policy implications.
Journal of the American Society for Information Science and Technology , 62(11), 2133–2146. Leydesdorff, L., Bornmann, L., Mutz, R., & Opthof, T. (2011). Turning the tables in citation analysis one more time: Principles for comparing sets of documents
Journal of the American Society for Information Science and Technology, 62 (7), 1370-1381. Leydesdorff, L., Bornmann, L., Comins, J., & Milojević, S. (2016). Citations: Indicators of Quality? The Impact Fallacy.
Frontiers in Research Metrics and Analytics, 1 (Article 1). doi: 10.3389/frma.2016.00001 Martin, B., & Irvine, J. (1983). Assessing Basic Research: Some Partial Indicators of Scientific Progress in Radio Astronomy.
Research Policy, 12 , 61-90. Mingers, J. (2014). Problems with SNIP.
Journal of Informetrics, 8 (4), 890-894. Moed, H., & Van Leeuwen, T. (1995). Improving the Accuracy of the Institute for Scientific Information's Journal Impact Factors.
Journal of the American Society for Information Science, 46 (6), 461-467. Opthof, T., & Leydesdorff, L. (2010).
Caveats for the journal and field normalizations in the CWTS (“Leiden”) evaluations of research performance.
Journal of Informetrics, 4 (3), 423-430. Price, D. d. S. (1970). Citation Measures of Hard Science, Soft Science, Technology, and Nonscience. In C. E. Nelson & D. K. Pollock (Eds.),
Communication among Scientists and Engineers (pp. 3-22). Lexington, MA: Heath. Quine, W. V. (1951). Main trends in recent philosophy: two dogmas of empiricism.
The Philosophical Review, 60 (1), 20-43. Rousseau, R. (2013). Modelling some structural indicators in an h-index context : A shifted Zipf and a decreasing exponential model. http://eprints.rclis.org/19896/ Rousseau, R. and Ye, F. Y. (2012). A formal relation between the h-index of a set of articles and their I3 score.
Journal of Informetrics , 6(1), 34–35. Seglen, P. O. (1992). The Skewness of Science.
Journal of the American Society for Information Science, 43 (9), 628-638. Waltman, L. and van Eck, N. J. (2012). The inconsistency of the h-index.
Journal of the American Society for Information Science and Technology,
Journal of Informetrics, 7 (2), 272-285. Ye, F. Y. (2011). A unification of three models for the h-index.
Journal of the American Society for Information Science and Technology , 62(2), 205–207. Ye, F. Y. (2014). A Progress on the Shifted Power Function for Modeling Informetric Laws.
Malaysian Journal of Library and Information Science , 19(1):1-15 Ye, F. Y.; Bornmann, L. and Leydesdorff, L. (2017). h-based I3-type multivariate vectors: multidimensional indicators of publication and citation scores.
COLLNET Journal of Scientometrics and Information Management , 11(1): in press. Ye, F. Y. and Leydesdorff, L. (2014). The “Academic Trace” of the Performance Matrix: A Mathematical Synthesis of the h-Index and the Integrated Impact Indicator (I3).
Journal of the Association for Information Science and Technology , 65(4), 742-750 7 Ye, F. Y. and Rousseau, R. (2010). Probing the h-core: An investigation of the tail-core ratio for rank distributions.
Scientometrics , 84(2), 431–439. Ye, F. Y. and Rousseau, R. (2013). Modelling Continuous Percentile Rank Scores and Integrated Impact Indicators (I3).
Canadian Journal of Information and Library Science , 37(3), 201-206 Zhang, C.-T. (2009). The e-index, complementing the h-index for excess citations.
PLoS ONE , 4(5), e5429. Zhang, C.-T. (2013). A novel triangle mapping technique to study the h-index based citation distribution.
Scientific Reports , 3: 1023, 1-5 (Note: This paper is published in
Journal of Library Science in China , 2017, Vol.43, No. 4) 8
Appendix
Table A1.
Scholars’ data
Indicator
P h=P c P z C C h X1 X2 X3 Y1 Y2 Y3
Leydesdorff L
145 35 15 3673 2404 8.44828 62.2414 1.551724 408.5557 438.4321 378.4484
Ye FY
27 8 4 193 138 2.37037 8.33333 0.592593 21.2228 15.67358 28.37306
Table A2. Publication and citation vectors of 25 famous universities ranked by h-index based on WoS data from 2009 to 2013.
University (ISI Abbreviated Name)
Univ h-index
Publication Vector Citation Vector X1 X2 X3 Y1 Y2 Y3
HARVARD UNIV 272 1.079165 20582.44 2591.597 3426.448 334689.3 4480.493 MIT 217 1.392601 11333.85 522.5067 2081.409 175299.2 3082.672 STANFORD UNIV 203 0.830076 19064.02 4838.446 2822.444 320858.5 3592.503 UNIV CALIF BERKELEY 202 0.840999 10397.27 5768.135 2387.891 175558.4 6812.783 UNIV OXFORD 192 0.807298 44786.92 8136.022 4763.454 910285.6 2386.228 UNIV CAMBRIDGE 190 0.715319 4545.997 822.7618 574.2979 48509.93 1322.582 UNIV TORONTO 181 0.766562 4067.064 776.5024 609.5801 45841.01 725.9668 UNIV MICHIGAN 178 0.397346 16171.09 2814.811 714.5166 188539.5 637.3312 YALE UNIV 164 0.605866 22933.74 6451.1 2166.962 355131.9 3756.614 UNIV CHICAGO 161 1.52057 18113.27 1612.713 4506.299 310350.5 5967.65 CALTECH 154 0.787154 19806.28 5592.797 2782.855 317658.6 6796.675 UNIV SYDNEY 133 1.135803 8201.824 1099.995 1559.91 112274.4 5373.22 PRINCETON UNIV 120 0.922583 20599.48 4332.119 3242.723 373369.8 2358.782 UNIV HONG KONG 116 0.418131 14795.44 4006.171 853.6706 178022.5 1739.573 TSINGHUA UNIV 114 0.552641 24793.15 6599.81 2051.624 364049 2585.307 PEKING UNIV 112 0.725977 15521.04 4035.065 1840.585 269402.6 1784.917 FUDAN UNIV 111 0.481684 12800.7 2125.225 878.081 127291.7 863.3201 KYOTO UNIV 102 0.442985 14005.98 2426.956 799.8086 152382.1 620.4136 ZHEJIANG UNIV 98 0.485374 10470.28 1882.337 734.0713 113237.5 416.0963 NANJING UNIV 95 0.342165 18748.04 3696.568 700.9207 210327.2 536.6424 UNIV SCI & TECHNOL CHINA 92 0.300191 15794.25 2771.264 487.4272 154049.6 417.7406 SHANGHAI JIAO TONG UNIV 89 0.302189 13202.65 2694.276 459.2057 120447.5 701.8614 NATL TAIWAN UNIV 85 0.231481 14935.64 2913.472 294.8955 145383.4 495.7767 UNIV HAMBURG 82 0.537929 8464.17 818.6611 552.1529 87193.86 335.2364 HUMBOLDT UNIV 81 0.265184 16452.78 3102.155 428.3223 160340.9 223.6169
Table A2. Publication and citation vectors of 25 famous universities ranked by h-index based on WoS data from 2011 to 2015.
University (ISI Abbreviated Name)
Univ h-index
Publication Vector Citation Vector X1 X2 X3 Y1 Y2 Y3
HARVARD UNIV 299 1.094619 24314.06 1913.433 3232.96 396695.9 7903.913 MIT 241 1.450045 12384.46 449.9271 2111.042 198999.9 5201.47 STANFORD UNIV 231 0.831177 23130.99 4552.135 2870.434 394468.6 5247.233 UNIV CALIF BERKELEY 210 0.892381 12471.7 5746.589 2754.382 214970 7670.005 UNIV OXFORD 206 0.867213 52946.5 8107.924 5794.924 1042924 5936.042 UNIV CAMBRIDGE 201 0.898491 5597.244 705.9741 805.0824 59230.25 3583.228 UNIV TORONTO 200 0.891792 4919.386 693.7473 789.6574 55358.94 1429.996 UNIV MICHIGAN 186 0.47295 18008.83 2335.886 931.6765 212361.4 828.0422 YALE UNIV 183 0.579624 26893.7 6328.984 2094.907 430861 2882.996 UNIV CHICAGO 178 1.684826 21638.54 1389.099 5374.339 384660.6 9750.973 CALTECH 161 0.786624 24606.31 5552.343 2926.635 413946.2 7558.184 UNIV SYDNEY 153 1.26542 9514.728 968.4489 1885.783 141185.6 5139.476 PRINCETON UNIV 146 1.045679 24906.8 4496.608 4335.864 459288.5 4464.867 UNIV HONG KONG 136 0.567175 18669.88 4325.257 1608.351 236197.7 3317.497 TSINGHUA UNIV 135 0.613459 29408.69 6901.935 2654.091 439022.9 3884.249 PEKING UNIV 130 0.831096 18475.52 4083.185 2464.349 319306.9 3587.126 FUDAN UNIV 128 0.557271 18821.43 1840.817 1195.784 206680.1 1431.567 KYOTO UNIV 126 0.478971 19432.44 2279.871 949.0312 227797.6 1640.276 ZHEJIANG UNIV 126 0.599949 14670.63 1879.865 1183.301 168309.7 1000.845 NANJING UNIV 123 0.414086 23361.4 3347.527 977.5684 282767.1 814.6924 UNIV SCI & TECHNOL CHINA 120 0.356455 23518.15 2710.625 759.4846 245094.5 693.9933 SHANGHAI JIAO TONG UNIV 116 0.361216 19821 2664.592 712.4462 195774.3 1222.995 NATL TAIWAN UNIV 116 0.401708 17416.95 2541.646 786.0145 174981.4 1129.731 UNIV HAMBURG 97 0.763764 11735.74 789.8526 1098.462 133663.5 1277.13 HUMBOLDT UNIV 92 0.368909 23381.48 2908.594 851.592 238996.7 674.8668
Table A3. Publication and citation vectors of 27 journals ranked by JIF in the field of electrochemistry based on WoS data from 2011 to 2015. The journals are ranked by their Journal Impact Factors (JIF) 2015.
Journal (JCR Abbreviated Title)
JIF
Publication Vector Citation Vector X1 X2 X3 Y1 Y2 Y3 BIOSENS BIOELECTRON
J POWER SOURCES
ELECTROCHEM COMMUN
ELECTROCHIM ACTA
SENSOR ACTUAT B-CHEM
CHEMELECTROCHEM
BIOELECTROCHEMISTRY
J ELECTROANAL CHEM
J ELECTROCHEM SOC
INT J HYDROGEN ENERG
ELECTROANAL
J APPL ELECTROCHEM
J SOLID STATE ELECTR
ELECTROCATALYSIS-US
ECS ELECTROCHEM LETT
CHEM VAPOR DEPOS
FUEL CELLS
IONICS
SENSORS-BASEL
INT J ELECTROCHEM SC
CORROS REV
ELECTROCHEMISTRY
J FUEL CELL SCI TECH
T I MET FINISH
RUSS J ELECTROCHEM+
J ELECTROCHEM SCI TE
J NEW MAT ELECTR SYS0.4 0.172249 34.56938 66.62201 5.355372 152.3306 0.809917