A central question in the topics of “the science of science” is the explanation of driving factors in the diffusion of scientific research related to documents and recorded knowledge (Coccia, 2018, 2021, 2022; Coccia & Bozeman, 2016; Coccia & Roshani, 2024; Coccia & Wang, 2016; Fortunato et al., 2018; Radicchi et al., 2008). Social studies of science and scientometrics analyze manifold factors to explain the drivers of duffusion of scientific results in science and society, such as the role of authorship networks on publication performance (Li et al., 2013), the impact of multiple funding on citation performance of papers (MacLean et al., 1998), etc. Yan et al. (2018) examine the association between research funding and citation impact in different disciplines. Quinlan et al. (2008) analyze the scientific outputs of four US-funded scientific research programs, whereas Pao (1991) shows the relation between funding and publication. Instead, Morillo (2020) investigates how open access publication affects the evolution of research fields. Roshani et al. (2021) analyze the relation between research funding and citation-based performance in three research fields: computer science, medicine and economics. Results suggest that journals in computer science publish more funded papers than unfunded ones. Journals in medicine tend to publish a similar share of funded and unfunded papers, whereas journals in economics, unlike computer science, have a proportion of unfunded publications higher than funded ones. Another finding of this study is that, in these three research fields (computer science, medicine and economics), the Matthew effect (Merton, 1988)-accumulated advantage- is for funded articles greater than unfunded documents. In this context, Mosleh et al. (2022) analyze how research funding affects the citations of scientific output in life sciences (including “agricultural and biological sciences”, “biochemistry, genetics, and molecular biology”, “Immunology and microbiology”, “neuroscience” and “pharmacology, toxicology and pharmaceutics”). Results reveal that, in scientific fields of life sciences, funded publications have higher citations than unfunded papers, though the number of unfunded published papers in journals is higher than published papers supported by research funding. Wang and Shapira (2015) show the role of research sponsorship on performance in nanotechnology papers.
The vast literature in these topics has analyzed many aspects of the relation between funding of research and papers’ citations in specific research fields. However, a generalization of the relationship between research funding and citations of papers between manifold research fields in basic and applied sciences is unknown. The study here reveals, for the first time, general empirical relationships, based on power law model, between citations of articles and their funding status both in basic and applied sciences: the
The collection of articles in research fields under study is done using the search string presented in Table A1 in Appendix. A number of 831,337 documents recorded in the Web of Science (2023) database in 2016 and 16,764,263 citations of these documents over 2016-2021 are examined. The Web of Science database provides access to multiple databases that provide documents and citation data from academic journals, conference proceedings, and other documents and recorded knowledge in various academic disciplines. Web of Science (2023) is one of the most comprehensive and widely used database in the scientific community because it has a coverage of over 211 million records given by journals, books, proceedings, etc. (Clarivate, 2023; Falagas et al., 2008; Singh et al., 2021). This study considers data of all publications in the year 2016 to analyze scientific impact and diffusion in terms of citations in a period of five years (2016-2021). We use the Web of Science Category (WC) for identifying the most relevant articles in each field. The inclusion criteria for creating the large sample are given by: document types: (“Articles”), Publication years: (“2016”), and Language: (“English”).
Understanding the difference of citations and diffusion of recorded knowledge between funded and unfunded research articles is crucial, since funding can play a pivotal role in determining the scientific development, diffusion and dissemination of discoveries, new techniques and concepts in science and society (Coccia, 2021, 2022; Coccia et al., 2021, 2022, 2022a). Science is a complex adaptive system of inter-related research fields and disciplines in continuos evolution; the analysis here considers differences of research fields in a context of basic versus applied sciences as suggested by scientific literature (Coccia & Wang, 2016). In particular, this study endeavors to explain the change of citations in funded and unfunded articles of basic and applied sciences. Some scholars categorize science into basic research and applied research (Davidson Frame & Carpenter, 1979). However, the categorization of science domains in basic and applied sciences is a topic of on-going debate between scholars and a brief background is useful to understand and clarify it to systematize results of the study here. In general, basic fields of research (in short BAS=Basic Sciences) can include: “Astronomy & Astrophysics”, “Chemistry”, “Mathematics & Statistics” and “Physics”. applied research fields (in short, APS=Applied Sciences) can include: “Biology”, “Computer Science”, “Economics”, “Engineering”, “Environmental Sciences”, “Geology”, “Medicine”, “Psychology”, “Sociology”, and “Zoology”.
It is worth noting that these categorizations, while grounded in extensive literature, may not encompass all sub-disciplines or inter-disciplinary research fields. However, the selected fields here are representative of larger scientific domains in science, providing a comprehensive overview for our scientific investigation.
This study analyzes articles published in the year 2016 within the research fields listed in Table A1 (see Appendix). The scientific impact of these articles in 2016 is assessed with citations over a fixed six-year period (2016-2021) providing a robust measure of their influence in the scientific community. The variables under study are: Accumulation of scientific research (explanatory variable, denoted by A) is the number of articles published in academic journals in the year 2016.
These articles, published in journals are categorized based on their funding status into two groups: Funded articles, i.e., articles that present results by receiving funds to conduct scientific research Unfunded articles, i.e., articles that show scientific results and did not receive any funding for research project
Diffusion of scientific research in science and society (dependent variable, denoted as C) is measured by the number of citations received by articles published in 2016, from 2016 to 2021.
The values of these variables are obtained from the “Time Cited” (TC) tag associated with each article, as recorded in the Web of Science (2023).
The overarching hypothesis is that research funding significantly amplifies the impact of scientific publications in science and society.
Our study applies the power law model (1), which has been previously used by Ronda-Pupo and Katz (2016; 2018) in specific research fields to explore the relationship between the number of citations, and the number of articles published in basic and applied sciences. This model is expressed by the following equation (1):
where:
The logarithmic transformation of Equation (1) yields a linear relationship given by a
ε= error term
The parameters of the α > 1: Implies a super linear change, indicating that the number of citations (C) grows at a faster rate than the number of articles (A) published in journals of a field of research. This effect suggests a significant Matthew effect (Merton, 1988) or cumulative advantage (Price, 1976). α=1: Reflects a linear change, i.e. the increase in citations and the increase in the number of articles occur at the same rate (proportional growth). α < 1: Indicates a sub-linear change with the change in citations of articles published in journals that is slower than the change in the number of articles published. This science dynamics generates an inverse Matthew effect or cumulative disadvantage.
The validation of power-law correlation in our data is verified with the approach recommended by Leguendre and Leguendre (2012). Beyond the scaling exponent α_OLS obtained through the Ordinary Least Square (OLS) method of equation (2), just mentioned, we also calculate the Standardized Major Axis exponent (α_SMA). The most prevalent techniques for establishing the optimal line of fit in a two-variable relationship are Ordinary Least Squares (OLS) and Standardized Major Axis (SMA) (Leguendre & Leguendre, 2012). Typically, OLS assumes that the measurement of variable X is error-free, whereas SMA considers the presence of errors in variable X (Ronda-Pupo & Katz, 2017b; Smith, 2009). α_SMA was computed using the relationship:
where
Table 1 shows documents retrieved from the database of Web of Science (2023) per funding status. The arithmetic mean of values between research fields, categorized in basic and applied sciences, suggests that: basic science has an average of 80.77% of papers funded with about 87% of total citations; these percentages are higher than applied sciences (65.71% of funded papers with 72.96% of total citations, cf., Table 1).
Number of documents and citations in research fields according to the funding status, categorized in basic and applied sciences
Field | Sources | Journals In 2016 | Papers in 2016 | % | Citations 2016-2021 | % |
---|---|---|---|---|---|---|
Basic sciences (BAS) | ||||||
Chemistry | Funded | 527 | 155,501 | 84.96 | 3,993,618 | 90.32 |
Unfunded | 526 | 27,526 | 15.04 | 427,631 | 9.68 | |
Physics | Funded | 382 | 104,041 | 81.65 | 2,144,540 | 88.82 |
Unfunded | 382 | 23,368 | 18.35 | 269,907 | 11.18 | |
Astronomy & Astrophysics | Funded | 63 | 17,421 | 87.15 | 414,861 | 93.15 |
Unfunded | 60 | 2,569 | 12.85 | 30,513 | 16.85 | |
Mathematics & Statistics | Funded | 654 | 38,681 | 69.33 | 367,409 | 74.65 |
Unfunded | 653 | 17,117 | 30.67 | 124,795 | 25.35 | |
Total B |
386,224 | 7,773,274 | ||||
Average value in B |
Funded | 80.77 | 86.74 | |||
Unfunded | 19.23 | 15.77 | ||||
A |
Sources | Journals In 2016 | Papers in 2016 | % | Citations 2016-2021 | % |
Engineering | Funded | 431 | 48,805 | 68.36 | 961,499 | 73.74 |
Unfunded | 437 | 22,582 | 31.64 | 342,488 | 26.26 | |
Environmental Sciences | Funded | 464 | 52,262 | 77.51 | 1,273,308 | 82.05 |
Unfunded | 464 | 15,162 | 22.49 | 278,441 | 19.95 | |
Medicine | Funded | 364 | 33,494 | 60.00 | 904,980 | 80.00 |
Unfunded | 373 | 21,925 | 40.00 | 219,956 | 20.00 | |
Biology | Funded | 894 | 105,872 | 85.21 | 2,555,930 | 90.58 |
Unfunded | 866 | 18,373 | 14.79 | 265,972 | 9.42 | |
Psychology | Funded | 572 | 20,202 | 56.46 | 399,767 | 60.80 |
Unfunded | 586 | 15,577 | 43.54 | 257,670 | 39.20 | |
Economics | Funded | 364 | 8,944 | 47.06 | 167,290 | 55.48 |
Unfunded | 372 | 10,059 | 52.94 | 134,287 | 44.52 | |
Sociology | Funded | 131 | 2,035 | 40.54 | 34,158 | 48.68 |
Unfunded | 136 | 2,984 | 59.46 | 36,020 | 51.32 | |
Geology | Funded | 77 | 3,888 | 78.68 | 71,782 | 85.25 |
Unfunded | 77 | 1,054 | 21.32 | 12,425 | 14.75 | |
Zoology | Funded | 176 | 9,380 | 76.50 | 95,128 | 81.86 |
Unfunded | 56 | 2,882 | 23.50 | 21,069 | 18.14 | |
Computer Science | Funded | 518 | 33,157 | 66.80 | 682,237 | 71.15 |
Unfunded | 520 | 16,476 | 33.20 | 276,582 | 28.85 | |
T |
11,125 | 445,113 | 8,990,989 | |||
Average value in A |
Funded | 65.712 | 72.96 | |||
Unfunded | 34.288 | 27.24 | ||||
TOTAL of BASIC AND APPLIED SCIENCES | 831,337 | 16,764,263 |
Table 2 provides information about the scaling exponent from OLS (α) of power law relationship between citations and related number of articles published in journals between fields of basic and applied research. In general, scaling exponent (α) of funded articles is greater than unfunded articles in journals, and this effect suggests a high Matthew effect: a higher change of citations (credit of papers) than the change of funded papers published in journals. Figure 1 shows that the expected increase in citations of papers with an increase of 1% in funded articles published in journals. Citations are higher in the research fields of sociology, geology and economics, whereas citations are lower in some basic sciences, such as physics and mathematics (Figure 1).
Estimated power law relationship between citations and number of articles in journals per funding status between basic and applied sciences
Fields of research | Sources | Pearson Coeff. r | Δ | R2 | N, journals | ||||
---|---|---|---|---|---|---|---|---|---|
Basic sciences (BAS) | |||||||||
Chemistry | Funded | 1.25*** | 0.04 | 1.35 | 0.92 | 3.54*** | 0.84 | 527 | |
Unfunded | 0 94*** | 0.05 | 1.27 | 0.74 | 12.20*** | 0.57 | 526 | ||
Physics | Funded | 1.17*** | 0.05 | 1.28 | 0.90 | 4.60*** | 0.82 | 382 | |
Unfunded | 1.02*** | 0.06 | 1.26 | 0.81 | 7.27*** | 0.66 | 382 | ||
Astronomy & Astrophysics | Funded | 1.22*** | 0.01 | 1.30 | 0.93 | 4.47*** | 0.88 | 63 | |
Unfunded | 0.98*** | 0.05 | 1.30 | 0.75 | 7.90*** | 0.57 | 60 | ||
Mathematics & Statistics | Funded | 1.09*** | 0.04 | 1.30 | 0.84 | 4.66*** | 0.70 | 654 | |
Unfunded | 1.03*** | 0.04 | 1.31 | 0.78 | 4.61*** | 0.61 | 653 | ||
OLS and SMA estimation in all Basic Sciences | Funded | 1.24*** | 0.02 | 1.34 | 0.91 | 0.10 | 1.20*** | 0.84 | 1,628 |
Unfunded | 1.06*** | 0.02 | 1.34 | 0.78 | 0.28 | 1.78*** | 0.62 | 1,622 | |
Sources | ( |
R2 | N | ||||||
Applied sciences (APS) | |||||||||
Engineering | Funded | 1.24*** | 0.04 | 1.36 | 0.91 | 4.17*** | 0.82 | 431 | |
Unfunded | 1.11*** | 0.06 | 1.46 | 0.76 | 6.13*** | 0.58 | 437 | ||
Environmental Sciences | Funded | 1.19*** | 0.03 | 1.28 | 0.92 | 6.42*** | 0.86 | 464 | |
Unfunded | 1.14*** | 0.04 | 1.33 | 0.85 | 7.83*** | 0.72 | 464 | ||
Medicine | Funded | 1.25*** | 0.05 | 1.37 | 0.91 | 5.10*** | 0.83 | 364 | |
Unfunded | 0.71*** | 0.05 | 1.00 | 0.71 | 25.79*** | 0.50 | 373 | ||
Biology | Funded | 1.27*** | 0.03 | 1.27 | 0.90 | 4.24*** | 0.81 | 894 | |
Unfunded | 0.94*** | 0.03 | 1.22 | 0.77 | 12.90*** | 0.59 | 866 | ||
Psychology | Funded | 1.18*** | 0.03 | 1.30 | 0.90 | 8.43*** | 0.81 | 572 | |
Unfunded | 1.11*** | 0.04 | 1.38 | 0.80 | 8.80*** | 0.64 | 586 | ||
Economics | Funded | 1.38*** | 0.05 | 1.57 | 0.87 | 3.48*** | 0.76 | 364 | |
Unfunded | 1.16*** | 0.07 | 1.60 | 0.72 | 5.11*** | 0.52 | 372 | ||
Sociology | Funded | 1.48*** | 0.07 | 1.65 | 0.89 | 3.33*** | 0.80 | 131 | |
Unfunded | 1.13*** | 0.08 | 1.50 | 0.75 | 6.35*** | 0.56 | 136 | ||
Geology | Funded | 1.46*** | 0.06 | 1.51 | 0.96 | 1.99*** | 0.93 | 77 | |
Unfunded | 1.32*** | 0.08 | 1.52 | 0.86 | 3.46*** | 0.75 | 77 | ||
Zoology | Funded | 1.24*** | 0.06 | 1.35 | 0.92 | 3.20*** | 0.85 | 176 | |
Unfunded | 1.07*** | 0.06 | 1.35 | 0.79 | 5.15*** | 0.62 | 56 | ||
Computer Science | Funded | 1.19*** | 0.04 | 1.37 | 0.87 | 5.92*** | 0.75 | 518 | |
Unfunded | 1.17*** | 0.04 | 1.42 | 0.82 | 6.12*** | 0.68 | 520 | ||
OLS and SMA estimation in all Applied Sciences | Funded | 1.23*** | 0.01 | 1.34 | 0.90 | 0.11 | 1.68*** | 0.83 | 3,994 |
Unfunded | 1.04*** | 0.01 | 1.30 | 0.79 | 0.26 | 2.22*** | 0.63 | 4,005 | |
Total | 11,125 |
Note. α_OLS is the scaling factor based on Ordinary Least Squares regression; α_SMA, is the scaling factor derived from the Standardized Major Axis regression. The r is the Pearson correlation coefficient between log-transformed citations (C) and the number of articles (A).
This study can clarify the increase of citations (C) -indicator of diffusion in scientific research– considering the funding of studies that are published in articles of journals (A). In particular, findings reveal the following general relationships of scientific change in citations of funded research that is published in articles categorized per basic and applied sciences:
Results are systematized in Figure 2 both for funded and unfunded papers in basic and applied sciences.
Figures 3–6 show a visualization of plot and estimated relationships for funded and unfunded research in basic and applied sciences.
The empirical results suggest some predictions for scientific diffusion and development and related diffusion: 1st Funded articles in journals receive higher citations than unfunded papers. 2nd Funded articles in journals have a super-linear change of citations. This finding generates a high Matthew effect in funded papers published in journals (given by a higher level of citations and consequential diffusion of scientific research) than unfunded papers. 3rd Invariant property of citations in basic and applied sciences is that: Funding generates both in basic and applied sciences a similar expected change of citations of about 1.23% by increasing 1% funded papers published in journals. Un-funding scientific research generates in basic and applied sciences a similar expected change of citations (lower than funding) of about 1.04% when un-funded articles published in journals grow by 1%.
Moreover, the close alignment between α_OLS and α_SMA values, particularly for funded research in basic and applied sciences (having a difference Δ = α_SMA -α_OLS ≈0.10, see Table 2), seems to validate the overarching hypothesis that research funding significantly amplifies the impact and diffusion of scientific publications, leading to more citations in science and society. For instance, in basic sciences, the sciences of chemistry, physics and astronomy exhibit a noticeable congruence between the α_OLS and α_SMA values for funded research with ΔBasic Sciences ≤0.10, underscoring the pronounced role of funding in higher citation dynamics. Similarly, the same results are for funded articles in applied sciences where the aggregate value shows Δ Applied Sciences = α_SMA -α_OLS ≈0.11. This critical result seems to be a strong confirmation of our general hypothesis that research funding significantly amplifies the impact of publications in science and society. The difference Δ is higher for unfunded papers in basic and applied science in the range of 0.26-0.28 considering all research fields. These findings suggest some main observations. Basic research, when backed by adequate financial support, has the potential to increase the scientific impact by more citations in science domain. In applied sciences funding also remains a critical determinant for scientific diffusion and development, though the change of citations between funded and unfunded research in some research fields is less stark. This aspect could be due to the inherent nature of applied research, which even without direct funding, scientific production can show a consequential diffusion (with citations) of scientific and technological results having a potential commercialization in society.
In general, this main finding here supports the prediction that investments in scientific research have tangible and quantifiable returns in terms of a higher diffusion and impact of recorded knowledge in science and society. In addition, findings here suggest that funding scientific research that is published in journals, it generates a similar (invariant) effect for increasing citations and diffusion of knowledge both in basic and applied sciences. To put it differently, the funding effect for diffusion of scientific research is an invariant factor in basic and applied sciences, suggesting that research fields in science have a common evolutionary nature in scientific and social communities (Smith, 2000; Stephan, 1996).
However, dissimilarities in certain fields, especially for unfunded research, also suggest the complex dynamics of the interaction between publications and citations in research fields. In fact, the lower alignment of α_OLS and α_SMA for unfunded research published in journals of some fields may be due to exogenous and/or endogenous factors, which suggest further investigation is needed.
Findings of this study, suggest general laws of funding for scientific citations that (impact) provide several important observations and science policy implications:
Although this study provides interesting results, it has also some limitations. For Instance, sources of data may only capture certain aspects of the ongoing dynamics of citations, as a consequence other confounding factors should be further investigated, such as networks of international collaborations, role of leading universities, open science, etc. (Adams, 2017; Coccia & Bozeman, 2016; Coccia & Wang, 2016; Newman, 2004; OECD, 2023). A significant concern that needs to be addressed is the potential bias related to funding acknowledgments in the Web of Science database. The database, though it has a vast coverage in natural science engineering and social science, may not always comprehensively or accurately capture funding sources for all articles. These technical issues may be due to the lack of standardization in funding information across different scientific fields and countries that can also lead to inaccuracies in data about funding indicated in publications (Pranckutė, 2021). In addition, the limited reporting of funding data in certain domains, such as in some social sciences, because of their lower reliance on grant funding compared to natural sciences, may result in incomplete data (Grassano, et al., 2017). In fact, some research may receive partial funding from multiple sources, or there might be instances where the funding acknowledgments are inadvertently omitted or inaccurately represented. Furthermore, smaller funding bodies might not be acknowledged or tracked accurately within database of articles and other scientific outputs. All these issues can be improved in the next study by also using data from other platforms of several literature search databases.
To conclude, findings here clearly illustrate a general prediction in scientific diffusion and related development: the driving role of research funding for increasing, with the same effect, the citations of articles and recorded knowledge in basic and applied sciences. Hence, these results here provide main information to policymakers and R&D managers that have to design effective research and science policies directed to allocate funding in research fields having a high potential of growth for increasing the diffusion of research for competitive advantage of nations and overall progress of human society (Coccia, 2018, 2019, 2019a, 2020; Hicks & Isett, 2020; Pagliaro & Coccia, 2021).