Citation numbers are extensively used for assessing the quality of scientific research. The use of raw citation counts is generally misleading, especially when applied to cross-disciplinary comparisons, since the average number of citations received is strongly dependent on the scientific discipline of reference of the paper. Measuring and eliminating biases in citation patterns is crucial for a fair use of citation numbers. Several numerical indicators have been introduced with this aim, but so far a specific statistical test for estimating the fairness of these numerical indicators has not been developed. Here we present a statistical method aimed at estimating the effectiveness of numerical indicators in the suppression of citation biases. The method is simple to implement and can be easily generalized to various scenarios. As a practical example we test, in a controlled case, the fairness of fractional citation count, which has been recently proposed as a tool for cross-discipline comparison. We show that this indicator is not able to remove biases in citation patterns and performs much worse than the rescaling of citation counts with average values.
In this paper, a new field-normalized indicator is introduced, which is rooted in early insights in bibliometrics, and is compared with several established field-normalized indicators (e.g. the mean normalized citation score, MNCS, and indicators based on percentile approaches). Garfield (1979) emphasizes that bare citation counts from different fields cannot be compared for evaluative purposes, because the "citation potential" can vary significantly between the fields. Garfield (1979) suggests that "the most accurate measure of citation potential is the average number of references per paper …
Metrics based on percentile ranks (PRs) for measuring scholarly impact involves complex treatment because of various defects such as overvaluing or devaluing an object caused by percentile ranking schemes, ignoring precise citation variation among those ranked next to each other, and inconsistency caused by additional papers or citations. These defects are especially obvious in a small-sized dataset. To avoid the complicated treatment of PRs based metrics, we propose two new indicators - the citation-based indicator (CBI) and the combined impact indicator (CII). Document types of publications …
A citation-based indicator for interdisciplinarity has been missing hitherto among the set of available journal indicators. In this study, we investigate network indicators (betweenness centrality), journal indicators (Shannon entropy, the Gini coefficient), and more recently proposed Rao-Stirling measures for "interdisciplinarity." The latter index combines the statistics of both citation distributions of journals (vector-based) and distances in citation networks among journals (matrix-based). The effects of various normalizations are specified and measured using the matrix of 8,207 journals …
Can change in citation patterns among journals be used as an indicator of structural change in the organization of the sciences? Aggregated journal-journal citations for 1999 are compared with similar data in the Journal Citation Reports 1998 of the Science Citation Index. In addition to indicating local change, probabilistic entropy measures enable us to analyze changes in distributions at different levels of aggregation. The results of various statistics are discussed and compared by elaborating the journal-journal mappings. The relevance of this indicator for science and technology policies…
Recently, the integrated impact indicator (I3) indicator was introduced where citations are weighted in accordance with the percentile rank class of each publication in a set of publications. I3 can also be used as a field-normalized indicator. Field-normalization is common practice in bibliometrics, especially when institutions and countries are compared. Publication and citation practices are so different among fields that citation impact is normalized for cross-field comparisons. In this study, we test the ability of the indicator to discriminate between quality levels of papers as defined …
The article "Caveats for the journal and field normalizations in the CWTS (`Leiden') evaluations of research performance", published by Tobias Opthof and Loet Leydesdorff (arXiv:1002.2769) deals with a subject as important as the application of so called field normalized indicators of citation impact in the assessment of research performance of individual researchers and research groups. Field normalization aims to account for differences in citation practices across scientific-scholarly subject fields. As the primary author of the papers presenting the "Leiden" indicators and of many reports …
h-index has become the most popular indicator for quantifying a scientist's scientific impact in various scientific fields. h-index is defined as the largest number of papers with citation number larger than or equal to h and it treats each citation equally. However, different citations usually come from different papers with different influence and quality, and a citation from a highly influential paper is a greater recognition of the target paper than a citation from an ordinary paper. Based on this assumption, we proposed a new indicator named x-index to quantify a scientist's scientific im…
A new percentile-based rating scale P100 has recently been proposed to describe the citation impact in terms of the distribution of the unique citation values. Here I investigate P100 for 5 example datasets, two simple fictitious models and three larger empirical samples. Counterintuitive behavior is demonstrated in the model datasets, pointing to difficulties when the evolution with time of the indicator is analyzed or when different fields or publication years are compared. It is shown that similar problems can occur for the three larger datasets of empirical citation values. Further, it is …
We submit newly developed citation impact indicators based not on arithmetic averages of citations but on percentile ranks. Citation distributions are-as a rule-highly skewed and should not be arithmetically averaged. With percentile ranks, the citation of each paper is rated in terms of its percentile in the citation distribution. The percentile ranks approach allows for the formulation of a more abstract indicator scheme that can be used to organize and/or schematize different impact indicators according to three degrees of freedom: the selection of the reference sets, the evaluation criteri…
This paper is a reply to the article "Scopus's Source Normalized Impact per Paper (SNIP) versus a Journal Impact Factor based on Fractional Counting of Citations", published by Loet Leydesdorff and Tobias Opthof (arXiv:1004.3580v2 [cs.DL]). It clarifies the relationship between SNIP and Elsevier's Scopus. Since Leydesdorff and Opthof's description of SNIP is not complete, it indicates four key differences between SNIP and the indicator proposed by the two authors, and argues why the former is more valid than the latter. Nevertheless, the idea of fractional citation counting deserves further ex…
Ageing of publications, percentage of self-citations, and impact vary from journal to journal within fields of science. The assumption that citation and publication practices are homogenous within specialties and fields of science is invalid. Furthermore, the delineation of fields and among specialties is fuzzy. Institutional units of analysis and persons may move between fields or span different specialties. The match between the citation index and institutional profiles varies among institutional units and nations. The respective matches may heavily affect the representation of the units. No…
Many different measures are used to assess academic research excellence and these are subject to ongoing discussion and debate within the scientometric, university-management and policy-making communities internationally. One topic of continued importance is the extent to which citation-based indicators compare with peer-review-based evaluation. Here we analyse the correlations between values of a particular citation-based impact indicator and peer-review scores in several academic disciplines, from natural to social sciences and humanities. We perform the comparison for research groups rather…
Van Raan et al. (2010; arXiv:1003.2113) have proposed a new indicator (MNCS) for field normalization. Since field normalization is also used in the Leiden Rankings of universities, we elaborate our critique of journal normalization in Opthof & Leydesdorff (2010; arXiv:1002.2769) in this rejoinder concerning field normalization. Fractional citation counting thoroughly solves the issue of normalization for differences in citation behavior among fields. This indicator can also be used to obtain a normalized impact factor.
We find evidence for the universality of two relative bibliometric indicators of the quality of individual scientific publications taken from different data sets. One of these is a new index that considers both citation and reference counts. We demonstrate this universality for relatively well cited publications from a single institute, grouped by year of publication and by faculty or by department. We show similar behaviour in publications submitted to the arXiv e-print archive, grouped by year of submission and by sub-archive. We also find that for reasonably well cited papers this distribut…
Van Raan et al. (2010; arXiv:1003.2113) have proposed a new indicator (MNCS) for field normalization. Since field normalization is also used in the Leiden Rankings of universities, we elaborate our critique of journal normalization in Opthof & Leydesdorff (2010; arXiv:1002.2769) in this rejoinder concerning field normalization. Fractional citation counting thoroughly solves the issue of normalization for differences in citation behavior among fields. This indicator can also be used to obtain a normalized impact factor.
The launching of Scopus and Google Scholar, and methodological developments in Social Network Analysis have made many more indicators for evaluating journals available than the traditional Impact Factor, Cited Half-life, and Immediacy Index of the ISI. In this study, these new indicators are compared with one another and with the older ones. Do the various indicators measure new dimensions of the citation networks, or are they highly correlated among them? Are they robust and relatively stable over time? Two main dimensions are distinguished -- size and impact -- which together shape influence…
In bibliometrics, the association of "impact" with central-tendency statistics is mistaken. Impacts add up, and citation curves should therefore be integrated instead of averaged. For example, the journals MIS Quarterly and JASIST differ by a factor of two in terms of their respective impact factors (IF), but the journal with the lower IF has the higher impact. Using percentile ranks (e.g., top-1%, top-10%, etc.), an integrated impact indicator (I3) can be based on integration of the citation curves, but after normalization of the citation curves to the same scale. The results across document …
A percentile-based bibliometric indicator is an indicator that values publications based on their position within the citation distribution of their field. The most straightforward percentile-based indicator is the proportion of frequently cited publications, for instance the proportion of publications that belong to the top 10% most frequently cited of their field. Recently, more complex percentile-based indicators were proposed. A difficulty in the calculation of percentile-based indicators is caused by the discrete nature of citation distributions combined with the presence of many publicat…
Bibliometric indicators can be determined by comparing specific citation records with the percentiles of a reference set. However, there exists an ambiguity in the computation of percentiles because usually a significant number of papers with the same citation count are found at the border between percentile rank classes. The present case study of the citations to the journal Europhysics Letters (EPL) in comparison with all physics papers from the Web of Science shows the deviations which occur due to the different ways of treating the tied papers in the evaluation of the percentage of highly …
The arbitrariness of the h-index becomes evident, when one requires q*h instead of h citations as the threshold for the definition of the index, thus changing the size of the core of the most influential publications of a dataset. I analyze the citation records of 26 physicists in order to determine how much the prefactor q influences the ranking. Likewise, the arbitrariness of the highly-cited-publications indicator is due to the threshold value, given either as an absolute number of citations or as a percentage of highly cited papers. The analysis of the 26 citation records shows that the ch…
In addition to science citation indicators of journals like impact and immediacy, social network analysis provides a set of centrality measures like degree, betweenness, and closeness centrality. These measures are first analyzed for the entire set of 7,379 journals included in the Journal Citation Reports of the Science Citation Index and the Social Sciences Citation Index 2004, and then also in relation to local citation environments which can be considered as proxies of specialties and disciplines. Betweenness centrality is shown to be an indicator of the interdisciplinarity of journals, bu…
We applied a set of standard bibliometric indicators to monitor the scientific state-of-arte of 500 universities worldwide and constructed a ranking on the basis of these indicators (Leiden Ranking 2010). We find a dramatic and hitherto largely underestimated language effect in the bibliometric, citation-based measurement of research performance when comparing the ranking based on all Web of Science (WoS) covered publications and on only English WoS covered publications, particularly for Germany and France.
We test 16 bibliometric indicators with respect to their validity at the level of the individual researcher by estimating their power to predict later successful researchers. We compare the indicators of a sample of astrophysics researchers who later co-authored highly cited papers before their first landmark paper with the distributions of these indicators over a random control group of young authors in astronomy and astrophysics. We find that field and citation-window normalisation substantially improves the predicting power of citation indicators. The two indicators of total influence based…
In reaction to a previous critique(Opthof & Leydesdorff, 2010), the Center for Science and Technology Studies (CWTS) in Leiden proposed to change their old "crown" indicator in citation analysis into a new one. Waltman et al. (2011)argue that this change does not affect rankings at various aggregated levels. However, CWTS data is not publicly available for testing and criticism. In this correspondence, we use previously published data of Van Raan (2006) to address the pivotal issue of how the results of citation analysis correlate with the results of peer review. A quality parameter based on p…
Citation numbers and other quantities derived from bibliographic databases are becoming standard tools for the assessment of productivity and impact of research activities. Though widely used, still their statistical properties have not been well established so far. This is especially true in the case of bibliometric indicators aimed at the evaluation of individual scholars, because large-scale data sets are typically difficult to be retrieved. Here, we take advantage of a recently introduced large bibliographic data set, Google Scholar Citations, which collects the entire publication record o…
We present an empirical comparison between two normalization mechanisms for citation-based indicators of research performance. These mechanisms aim to normalize citation counts for the field and the year in which a publication was published. One mechanism is applied in the current so-called crown indicator of our institute. The other mechanism is applied in the new crown indicator that our institute is planning to adopt. We find that at high aggregation levels, such as at the level of large research institutions or at the level of countries, the differences between the two mechanisms are very …
It is shown that under certain circumstances in particular for small datasets the recently proposed citation impact indicators I3(6PR) and R(6,k) behave inconsistently when additional papers or citations are taken into consideration. Three simple examples are presented, in which the indicators fluctuate strongly and the ranking of scientists in the evaluated group is sometimes completely mixed up by minor changes in the data base. The erratic behavior is traced to the specific way in which weights are attributed to the six percentile rank classes, specifically for the tied papers. For 100 perc…
This paper proposes an indicator of journals' scientific prestige, the SJR indicator, for ranking scholarly journals based on citation weighting schemes and eigenvector centrality to be used in complex and heterogeneous citation networks such Scopus. Its computation methodology is described and the results after implementing the indicator over Scopus 2007 dataset are compared to an ad-hoc Journal Impact Factor both generally and inside specific scientific areas. The results showed that SJR indicator and JIF distributions fitted well to a power law distribution and that both metrics were strong…
How to quantify the impact of a researcher's or an institution's body of work is a matter of increasing importance to scientists, funding agencies, and hiring committees. The use of bibliometric indicators, such as the h-index or the Journal Impact Factor, have become widespread despite their known limitations. We argue that most existing bibliometric indicators are inconsistent, biased, and, worst of all, susceptible to manipulation. Here, we pursue a principled approach to the development of an indicator to quantify the scientific impact of both individual researchers and research institutio…
A theory of citations should not consider cited and/or citing agents as its sole subject of study. One is able to study also the dynamics in the networks of communications. While communicating agents (e.g., authors, laboratories, journals) can be made comparable in terms of their publication and citation counts, one would expect the communication networks not to be homogeneous. The latent structures of the network indicate different codifications that span a space of possible 'translations'. The various subdynamics can be hypothesized from an evolutionary perspective. Using the network of aggr…
The Hirsch index or h-index is widely used to quantify the impact of an individual's scientific research output, determining the highest number h of a scientist's papers that received at least h citations. Several variants of the index have been proposed in order to give more or less preference to highly cited papers. I analyse the citation records of 26 physicists discussing various suggestions, in particular A, e, f, g, h(2), h_w, h_T, \hbar, m, π, R, s, t, w, and maxprod. The total number of all and of all cited publications as well as the highest and the average number of citations are als…
Scientists are embedded in social and information networks that influence and are influenced by the quality of their scientific work, its impact, and the recognition they receive. Here we quantify the systematic relationship between a scientist's position in the network of scientific collaborations and the citations they receive. As expected, we find that authors closer to others in this network are, on average, more highly cited than those further away from others. We construct a novel indicator, the s-index, that explicitly captures performance linked to network position along two compliment…
Using bibliometric data artificially generated through a model of citation dynamics calibrated on empirical data, we compare several indicators for the scientific impact of individual researchers. The use of such a controlled setup has the advantage of avoiding the biases present in real databases, and allows us to assess which aspects of the model dynamics and which traits of individual researchers a particular indicator actually reflects. We find that the simple citation average performs well in capturing the intrinsic scientific ability of researchers, whatever the length of their career. O…
It is widely recognized that citation counts for papers from different fields cannot be directly compared because different scientific fields adopt different citation practices. Citation counts are also strongly biased by paper age since older papers had more time to attract citations. Various procedures aim at suppressing these biases and give rise to new normalized indicators, such as the relative citation count. We use a large citation dataset from Microsoft Academic Graph and a new statistical framework based on the Mahalanobis distance to show that the rankings by well known indicators, i…
Citation distributions are so skewed that using the mean or any other central tendency measure is ill-advised. Unlike G. Prathap's scalar measures (Energy, Exergy, and Entropy or EEE), the Integrated Impact Indicator (I3) is based on non-parametric statistics using the (100) percentiles of the distribution. Observed values can be tested against expected ones; impact can be qualified at the article level and then aggregated.
The large amount of information contained in bibliographic databases has recently boosted the use of citations, and other indicators based on citation numbers, as tools for the quantitative assessment of scientific research. Citations counts are often interpreted as proxies for the scientific influence of papers, journals, scholars, and institutions. However, a rigorous and scientifically grounded methodology for a correct use of citation counts is still missing. In particular, cross-disciplinary comparisons in terms of raw citation counts systematically favors scientific disciplines with high…
A new indicator, a real valued $s$-index, is suggested to characterize a quality and impact of the scientific research output. It is expected to be at least as useful as the notorious $h$-index, at the same time avoiding some its obvious drawbacks. However, surprisingly, the $h$-index is found to be quite a good indicator for majority of real-life citation data with their alleged Zipfian behaviour for which these drawbacks do not show up. The style of the paper was chosen deliberately somewhat frivolous to indicate that any attempt to characterize the scientific output of a researcher by just …
The basic indicators of a researcher's productivity and impact are still the number of publications and their citation counts. These metrics are clear, straightforward, and easy to obtain. When a ranking of scholars is needed, for instance in grant, award, or promotion procedures, their use is the fastest and cheapest way of prioritizing some scientists over others. However, due to their nature, there is a danger of oversimplifying scientific achievements. Therefore, many other indicators have been proposed including the usage of the PageRank algorithm known for the ranking of webpages and its…
The growing importance of citation-based bibliometric indicators in shaping the prospects of academic careers incentivizes scientists to boost the numbers of citations they receive. Whereas the exploitation of self-citations has been extensively documented, the impact of reciprocated citations has not yet been studied. We study reciprocity in a citation network of authors, and compare it with the average reciprocity computed in an ensemble of null network models. We show that obtaining citations through reciprocity correlates negatively with a successful career in the long term. Nevertheless, …
Impact factors (and similar measures such as the Scimago Journal Rankings) suffer from two problems: (i) citation behavior varies among fields of science and therefore leads to systematic differences, and (ii) there are no statistics to inform us whether differences are significant. The recently introduced SNIP indicator of Scopus tries to remedy the first of these two problems, but a number of normalization decisions are involved which makes it impossible to test for significance. Using fractional counting of citations-based on the assumption that impact is proportionate to the number of refe…
The aggregated citation relations among journals included in the Science Citation Index provide us with a huge matrix which can be analyzed in various ways. Using principal component analysis or factor analysis, the factor scores can be used as indicators of the position of the cited journals in the citing dimensions of the database. Unrotated factor scores are exact, and the extraction of principal components can be made stepwise since the principal components are independent. Rotation may be needed for the designation, but in the rotated solution a model is assumed. This assumption can be le…
A desirable goal of scientific management is to introduce, if it exists, a simple and reliable way to measure the scientific excellence of publicly-funded research institutions and universities to serve as a basis for their ranking and financing. While citation-based indicators and metrics are easily accessible, they are far from being universally accepted as way to automate or inform evaluation processes or to replace evaluations based on peer review. Here we consider absolute measurements of research excellence at an amalgamated, institutional level and specific measures of research excellen…
Measures for research activity and impact have become an integral ingredient in the assessment of a wide range of entities (individual researchers, organizations, instruments, regions, disciplines). Traditional bibliometric indicators, like publication and citation based indicators, provide an essential part of this picture, but cannot describe the complete picture. Since reading scholarly publications is an essential part of the research life cycle, it is only natural to introduce measures for this activity in attempts to quantify the efficiency, productivity and impact of an entity. Citation…
