Statistical regularities in the rank-citation profile of scientists

Recent science of science research shows that scientific impact measures for journals and individual articles have quantifiable regularities across both time and discipline. However, little is known about the scientific impact distribution at the scale of an individual scientist. We analyze the aggregate production and impact using the rank-citation profile ci(r) of 200 distinguished professors and 100 assistant professors. For the entire range of paper rank r, we fit each ci(r) to a common distribution function. Since two scientists with equivalent Hirsch h-index can have significantly different ci(r) profiles, our results demonstrate the utility of the βi scaling parameter in conjunction with hi for quantifying individual publication impact. We show that the total number of citations Ci tallied from a scientist's Ni papers scales as . Such statistical regularities in the input-output patterns of scientists can be used as benchmarks for theoretical models of career progress

The Z-index: A geometric representation of productivity and impact which accounts for information in the entire rank-citation profile

We present a simple generalization of Hirsch's h-index, Z = \sqrt{h^{2}+C}/\sqrt{5}, where C is the total number of citations. Z is aimed at correcting the potentially excessive penalty made by h on a scientist's highly cited papers, because for the majority of scientists analyzed, we find the excess citation fraction (C-h^{2})/C to be distributed closely around the value 0.75, meaning that 75 percent of the author's impact is neglected. Additionally, Z is less sensitive to local changes in a scientist's citation profile, namely perturbations which increase h while only marginally affecting C. Using real career data for 476 physicists careers and 488 biologist careers, we analyze both the distribution of $Z$ and the rank stability of Z with respect to the Hirsch index h and the Egghe index g. We analyze careers distributed across a wide range of total impact, including top-cited physicists and biologists for benchmark comparison. In practice, the Z-index requires the same information needed to calculate h and could be effortlessly incorporated within career profile databases, such as Google Scholar and ResearcherID. Because Z incorporates information from the entire publication profile while being more robust than h and g to local perturbations, we argue that Z is better suited for ranking comparisons in academic decision-making scenarios comprising a large number of scientists.Comment: 9 pages, 5 figure

Reputation and Impact in Academic Careers

Reputation is an important social construct in science, which enables informed quality assessments of both publications and careers of scientists in the absence of complete systemic information. However, the relation between reputation and career growth of an individual remains poorly understood, despite recent proliferation of quantitative research evaluation methods. Here we develop an original framework for measuring how a publication's citation rate $\Delta c$ depends on the reputation of its central author $i$, in addition to its net citation count $c$. To estimate the strength of the reputation effect, we perform a longitudinal analysis on the careers of 450 highly-cited scientists, using the total citations $C_{i}$ of each scientist as his/her reputation measure. We find a citation crossover $c_{\times}$ which distinguishes the strength of the reputation effect. For publications with $c < c_{\times}$, the author's reputation is found to dominate the annual citation rate. Hence, a new publication may gain a significant early advantage corresponding to roughly a 66% increase in the citation rate for each tenfold increase in $C_{i}$. However, the reputation effect becomes negligible for highly cited publications meaning that for $c\geq c_{\times}$ the citation rate measures scientific impact more transparently. In addition we have developed a stochastic reputation model, which is found to reproduce numerous statistical observations for real careers, thus providing insight into the microscopic mechanisms underlying cumulative advantage in science.Comment: Final published version of the main manuscript including additional analysis: 9 pages, 4 figures, 1 table, and full reference list, including those in the Supplementary Information. For the SI Appendix, see http://physics.bu.edu/~amp17/webpage_files/MyPapers/Reputation_SI.pd

Inequality and cumulative advantage in science careers: a case study of high-impact journals

Analyzing a large data set of publications drawn from the most competitive journals in the natural and social sciences we show that research careers exhibit the broad distributions of individual achievement characteristic of systems in which cumulative advantage plays a key role. While most researchers are personally aware of the competition implicit in the publication process, little is known about the levels of inequality at the level of individual researchers. Here we analyzed both productivity and impact measures for a large set of researchers publishing in high-impact journals, accounting for censoring biases in the publication data by using distinct researcher cohorts defined over non-overlapping time periods. For each researcher cohort we calculated Gini inequality coefficients, with average Gini values around 0.48 for total publications and 0.73 for total citations. For perspective, these observed values are well in excess of the inequality levels observed for personal income in developing countries. Investigating possible sources of this inequality, we identify two potential mechanisms that act at the level of the individual that may play defining roles in the emergence of the broad productivity and impact distributions found in science. First, we show that the average time interval between a researcher’s successive publications in top journals decreases with each subsequent publication. Second, after controlling for the time dependent features of citation distributions, we compare the citation impact of subsequent publications within a researcher’s publication record. We find that as researchers continue to publish in top journals, there is more likely to be a decreasing trend in the relative citation impact with each subsequent publication. This pattern highlights the difficulty of repeatedly producing research findings in the highest citation-impact echelon, as well as the role played by finite career and knowledge life-cycles, and the intriguing possibility that confirmation bias plays a role in the evaluation of scientific careers

The Distribution of the Asymptotic Number of Citations to Sets of Publications by a Researcher or From an Academic Department Are Consistent With a Discrete Lognormal Model

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 institutions grounded on the functional form of the distribution of the asymptotic number of citations. We validate our approach using the publication records of 1,283 researchers from seven scientific and engineering disciplines and the chemistry departments at the 106 U.S. research institutions classified as "very high research activity". Our approach has three distinct advantages. First, it accurately captures the overall scientific impact of researchers at all career stages, as measured by asymptotic citation counts. Second, unlike other measures, our indicator is resistant to manipulation and rewards publication quality over quantity. Third, our approach captures the time-evolution of the scientific impact of research institutions.Comment: 20 pages, 11 figures, 3 table