Skip to main content
SpringerLink
Log in

Statistics for the dynamic analysis of scientometric data: the evolution of the sciences in terms of trajectories and regimes

  • Published:
Scientometrics Aims and scope Submit manuscript

Abstract

The gap in statistics between multi-variate and time-series analysis can be bridged by using entropy statistics and recent developments in multi-dimensional scaling. For explaining the evolution of the sciences as non-linear dynamics, the configurations among variables can be important in addition to the statistics of individual variables and trend lines. Animations enable us to combine multiple perspectives (based on configurations of variables) and to visualize path-dependencies in terms of trajectories and regimes. Path-dependent transitions and systems formation can be tested using entropy statistics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

Notes

  1. More recently, vector autoregression models are developed that capture linear interdependencies among a limited number of time series (Abdulnasser 2004).

  2. Probabilistic entropy (H) is coupled to thermodynamic entropy (S) by Gibbs entropy formula: S = k B  × H. In this formula, k B is the Boltzmann constant with dimensionality Joule/Kelvin. H is dimensionless and, for example, expressed in bits of information. Because of the second law both S and H necessarily increase or, in other words, the change in information (uncertainty) is always positive.

  3. The stand-alone program VOSViewer uses the approach of MDS, but the current version does not provide stress values (Van Eck and Waltman 2010).

  4. The dynamic version of Visone is freely available at http://www.leydesdorff.net/visone.

  5. A different class of models is provided by actor-based models for network dynamics (e.g., Snijders et al. 2010).

References

  • Abdulnasser, H.-J. (2004). Multivariate tests for autocorrelation in the stable and unstable VAR models. Economic Modelling, 21(4), 661–683.

    Article  Google Scholar 

  • Agarwal, P., & Searls, D. B. (2008). Literature mining in support of drug discovery. Briefings in bioinformatics, 9(6), 479–492.

    Article  Google Scholar 

  • Agarwal, P., & Searls, D. B. (2009). Can literature analysis identify innovation drivers in drug discovery? Nature Reviews Drug Discovery, 8(11), 865–878.

    Article  Google Scholar 

  • Arthur, W. B. (1989). Competing technologies, increasing returns, and lock-in by historical events. Economic Journal, 99, 116–131.

    Article  Google Scholar 

  • Bak, P., & Chen, K. (1991). Self-organized criticality. Scientific American, 264(1), 46–53.

    Google Scholar 

  • Bak, P., Tang, C., & Wiesenfeld, K. (1987). Self-organized criticality: an explanation of the 1/f noise. Physical Review Letters, 59(4), 381–384.

    Article  MathSciNet  Google Scholar 

  • Barabási, A. L., & Albert, R. (1999). Emergence of scaling in random networks. Science, 286(5439), 509–512.

    Article  MathSciNet  Google Scholar 

  • Bar-Hillel, Y. (1955). An examination of information theory. Philosophy of Science, 22, 86–105.

    Article  MathSciNet  Google Scholar 

  • Baur, M., Benkert, M., Brandes, U., Cornelsen, S., Gaertler, M., Köpf, B., et al. (2002). Visone software for visual social network analysis. Proceedings of the 9th international symposium graph srawing (GD’01). Lecture Notes of Computer Science, 2265, 554–557.

    Google Scholar 

  • Baur, M. & Schank, T. (2008). Dynamic graph drawing in visone. Technical University Karlsruhe, Karlsruhe. Available at http://i11www.iti.uni-karlsruhe.de/extra/publications/bs-dgdv-08.pdf (retrieved on 2 May 2012).

  • Börner, K. (2010). Atlas of science: visualizing what we know. Cambridge: MIT Press.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Brandes, U. & Wagner, D. (2004). Visone—analysis and visualization of social networks. In: M. Jünger & P. Mtuzel (Eds.), Graph drawing software (pp. 321–340), Berlin: Springer.

  • Callon, M., Courtial, J. P., & Laville, F. (1991). Co-word analysis as a tool for describing the network of interactions between basic and technological research: the case of polymer chemistry. Scientometrics, 22(1), 155–205.

    Article  Google Scholar 

  • Callon, M., Law, J., & Rip, A. (Eds.). (1986). Mapping the dynamics of science and technology. London: Macmillan.

    Google Scholar 

  • Chen, C. (2004). Information visualization: beyond the horizon. New York: Springer.

  • Chen, C. (2006). CiteSpace II: detecting and visualizing emerging trends and transient patterns in scientific literature. Journal of the American Society for Information Science and Technology, 57(3), 359–377.

    Article  Google Scholar 

  • Cook, T., & Campbell, D. (1979). Quasi-experimentations: design and analysis issues for field-settings. Boston: Houghton Mifflin Company.

    Google Scholar 

  • David, P. A. (1985). Clio and the economics of QWERTY. American Economic Review, 75, 332–337.

    Google Scholar 

  • Dolfsma, W., & Leydesdorff, L. (2009). Lock-in and break-out from technological trajectories: modeling and policy implications. Technological Forecasting and Social Change, 76(7), 932–941.

    Article  Google Scholar 

  • Erten, C., Harding, Ph.J., Kobourov, S.G., Wampler, K., & Yee, G.V. (2004). GraphAEL: graph animations with evolving layouts (pp. 98–110). In: Liotta, G. (Ed.), Graph drawing, Perugia, Italy, 21–24 Sept 2003; Berlin: Springer.

  • Fagerberg, J., Mowery, D. C., & Nelson, R. R. (2005). The oxford handbook of innovation. Oxford: Oxford University Press.

    Google Scholar 

  • Gansner, E. R., Koren, Y., & North, S. (2005). Graph drawing by stress majorization. In J. Pach (Ed.), Graph drawing, lecture notes in computer science (Vol. 3383, pp. 239–250). Berlin/Heidelberg: Springer.

    Google Scholar 

  • Griliches, Z. (1994). Productivity, R&D and the data constraint. American Economic Review, 84(1), 1–23.

    Google Scholar 

  • Helbing, D., & Balietti, S. (2011). How to create an innovation accelerator. The European Physical Journal-Special Topics, 195(1), 101–136.

    Article  Google Scholar 

  • Hodgson, G., & Knudsen, T. (2011). Darwin’s conjecture: the search for general principles of social and economic evolution. Chicago/London: University of Chicago Press.

    Google Scholar 

  • Kamada, T., & Kawai, S. (1989). An algorithm for drawing general undirected graphs. Information Processing Letters, 31(1), 7–15.

    Article  MathSciNet  MATH  Google Scholar 

  • Kauffman, S. A. (1993). The origins of order: self-organization and selection in evolution. New York: Oxford University Press.

    Google Scholar 

  • Klavans, R., & Boyack, K. W. (2011). Using global mapping to create more accurate document-level maps of research fields. Journal of the American Society for Information Science and Technology, 62(1), 1–18.

    Article  Google Scholar 

  • Krippendorff, K. (1986). Information theory. Structural models for qualitative data. Beverly Hills: Sage).

  • Krippendorff, K. (2009). Information of interactions in complex systems. International Journal of General Systems, 38(6), 669–680.

    Article  MathSciNet  MATH  Google Scholar 

  • Kruskal, J. B. (1964). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29(1), 1–27.

    Article  MathSciNet  MATH  Google Scholar 

  • Kruskal, J. B., & Wish, M. (1978). Multidimensional scaling. Beverly Hills: Sage Publications.

    Google Scholar 

  • Kullback, S., & Leibler, R. A. (1951). On Information and sufficiency. The Annals of Mathematical Statistics, 22(1), 79–86.

    Article  MathSciNet  MATH  Google Scholar 

  • Lengyel, B., & Leydesdorff, L. (2011). Regional innovation systems in Hungary: the failing synergy at the national level. Regional Studies, 45(5), 677–693. doi:10.1080/00343401003614274.

    Article  Google Scholar 

  • Leydesdorff, L. (1991). The static and dynamic analysis of network data using information theory. Social Networks, 13, 301–345.

    Article  Google Scholar 

  • Leydesdorff, L. (1995). The challenge of scientometrics: the development, measurement, and self-organization of scientific communications. Leiden: DSWO Press, Leiden University; at http://www.universal-publishers.com/book.php?method=ISBN&book=1581126816.

  • Leydesdorff, L. (1997). Why words and co-words cannot map the development of the sciences. Journal of the American Society for Information Science, 48(5), 418–427.

    Article  Google Scholar 

  • Leydesdorff, L. (2000). Is the European Union becoming a single publication system? Scientometrics, 47(2), 265–280.

    Article  Google Scholar 

  • Leydesdorff, L. (2002). The complex dynamics of technological innovation: a comparison of models using cellular automata. Systems Research and Behavioural Science, 19(6), 563–575.

    Article  Google Scholar 

  • Leydesdorff, L. (2003). The mutual information of university–industry–government relations: an indicator of the triple helix dynamics. Scientometrics, 58(2), 445–467.

    Article  Google Scholar 

  • Leydesdorff, L. (2010). The communication of meaning and the structuration of expectations: giddens’ “structuration theory” and Luhmann’s “self-organization”. Journal of the American Society for Information Science and Technology, 61(10), 2138–2150.

    Article  Google Scholar 

  • Leydesdorff, L. (2011). “Structuration” by intellectual organization: the configuration of knowledge in relations among scientific texts. Scientometrics, 88(2), 499–520.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Leydesdorff, L., Cozzens, S. E., & van den Besselaar, P. (1994). Tracking areas of strategic importance using scientometric journal mappings. Research Policy, 23, 217–229.

    Article  Google Scholar 

  • Leydesdorff, L., & Oomes, N. A. (1999). Is the European monetary system converging to integration? Social Science Information, 38(1), 57–86.

    Article  Google Scholar 

  • Leydesdorff, L., & Rafols, I. (2012). Interactive overlays: a new method for generating global journal maps from web-of-science data. Journal of Informetrics, 6(3), 318–332.

    Article  Google Scholar 

  • Leydesdorff, L., Rotolo, D., & de Nooy, W. (in press). Innovation as a nonlinear process, the scientometric perspective, and the specification of an “innovation opportunities explorer”, Technology Analysis and Strategic Management.

  • Leydesdorff, L., Rotolo, D., & Rafols, I. (2012b). Bibliometric perspectives on medical innovation using the medical subject headings (MeSH) of PubMed. Journal of the American Society for Information Science and Technology, 63(11), 2239–2253.

    Article  Google Scholar 

  • Leydesdorff, L., & Schank, T. (2008). Dynamic animations of journal maps: indicators of structural change and interdisciplinary developments. Journal of the American Society for Information Science and Technology, 59(11), 1810–1818.

    Article  Google Scholar 

  • Leydesdorff, L., Schank, T., Scharnhorst, A., & De Nooy, W. (2008). Animating the development of social networks over time using a dynamic extension of multidimensional scaling. El Profesional de la Información, 17(6), 611–626.

    Article  Google Scholar 

  • Leydesdorff, L., & Zawdie, G. (2010). The triple helix perspective of innovation systems. Technology Analysis and Strategic Management, 22(7), 789–804.

    Article  Google Scholar 

  • Liu, Z., & Stasko, J. T. (2010). Mental models, visual reasoning and interaction in information visualization: a top-down perspective. Visualization and Computer Graphics, IEEE Transactions on, 16(6), 999–1008.

    Article  Google Scholar 

  • Luhmann, N. (1990). The cognitive program of constructivism and a reality that remains unknown. In: W. Krohn, G. Küppers & H. Nowotny (Eds.), Selforganization. Portrait of a scientific revolution (pp. 64–85). Dordrecht: Reidel.

  • Luhmann, N. (1995). Social systems. Stanford: Stanford University Press.

    Google Scholar 

  • Malerba, F., Nelson, R., Orsenigo, L., & Winter, S. (1999). ‘History-firendly’ models of industry evolution: the computer industry. Industrial and Corporate Change, 8(1), 3–35.

    Article  Google Scholar 

  • McLuhan, M. (1964). Understanding media: the extension of man. New York: McGraw-Hill.

    Google Scholar 

  • Misue, K., Eades, P., Lai, W., & Sugiyama, K. (1995). Layout adjustment and the mental map. Journal of Visual Languages and Computing, 6(2), 183–210.

    Article  Google Scholar 

  • Nagin, D. S. (2005). Group-based modeling of development. Cambridge: Harvard University Press.

    Google Scholar 

  • Noyons, E. C. M., & van Raan, A. F. J. (1998). Monitoring scientific developments from a dynamic perspective: self-organized structuring to map neural network research. Journal of the American Society for Information Science, 49(1), 68–81.

    Google Scholar 

  • Park, H. W., & Leydesdorff, L. (2010). Longitudinal trends in networks of university-industry-government relations in South Korea: the role of programmatic incentives. Research Policy, 39(5), 640–649.

    Article  Google Scholar 

  • Price, D. S. (1976). A general theory of bibliometric and other cumulative advantage processes. Journal of the American Society for Information Science, 27(5), 292–306.

    Article  Google Scholar 

  • Price, D.de Solla. (1984). The science/technology relationship, the craft of experimental science, and policy for the improvement of high technology innovation. Research Policy, 13, 3–20.

    Article  Google Scholar 

  • Prigogine, I., & Stengers, I. (1984). Order out of Chaos: man’s new dialogue with nature. New York: Bantam.

    Google Scholar 

  • Pyka, A., & Scharnhorst, A. (Eds.). (2009). Innovation networks: new approaches in modelling and analyzing. Berlin/Heidelberg: Springer.

    MATH  Google Scholar 

  • Scharnhorst, A., Börner, K., & Van den Besselaar, P. (Eds.). (2012). Models of science dynamics: encounters between complexity theory and information sciences. Heidelberg: Springer.

  • Seglen, P. O. (1992). The skewness of science. Journal of the American Society for Information Science, 43(9), 628–638.

    Article  Google Scholar 

  • Shannon, C.E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 379–423 and 623–356.

  • Sheskin, D. J. (2011). Handbook of parametric and nonparametric statistical procedures (5th ed.). Boca Raton: Chapman and Hall/CRC.

    Google Scholar 

  • Shinn, T. (2005). New sources of radical innovation: research-technologies, transversality and distributed learning in a post-industrial order. Social Science Information, 44(4), 731–764.

    Article  Google Scholar 

  • Snijders, T. A. B., Van de Bunt, G. G., & Steglich, C. E. G. (2010). Introduction to stochastic actor-based models for network dynamics. Social Networks, 32(1), 44–60.

    Article  Google Scholar 

  • Strand, O., & Leydesdorff, L. (in press). Where is synergy in the Norwegian innovation system indicated? Triple helix relations among technology, organization, and geography. Technological Forecasting and Social Change.

  • Theil, H. (1972). Statistical decomposition analysis. Amsterdam/London: North-Holland.

    MATH  Google Scholar 

  • Van Eck, N. J., & Waltman, L. (2010). Software survey: vOSviewer, a computer program for bibliometric mapping. Scientometrics, 84(2), 523–538.

    Article  Google Scholar 

  • Von Hippel, E. (1976). The dominant role of users in the scientific instrument innovation process. Research Policy, 5(3), 212–239.

    Article  Google Scholar 

  • Von Hippel, E. (1988). The sources of innovation. New York/Oxford: Oxford University Press.

    Google Scholar 

  • Yeung, R. W. (2008). Information theory and network coding. New York: Springer.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Amsterdam, Amsterdam School of Communication Research (ASCoR), Kloveniersburgwal 48, 1012 CX, Amsterdam, The Netherlands

    Loet Leydesdorff

Authors
  1. Loet Leydesdorff
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Loet Leydesdorff.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Leydesdorff, L. Statistics for the dynamic analysis of scientometric data: the evolution of the sciences in terms of trajectories and regimes. Scientometrics 96, 731–741 (2013). https://doi.org/10.1007/s11192-012-0917-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11192-012-0917-0

Keywords

Search

Navigation