, Volume 115, Issue 1, pp 395–413 | Cite as

Predicting the research output/growth of selected countries: application of Even GM (1, 1) and NDGM models

  • Saad Ahmed JavedEmail author
  • Sifeng Liu


The study aims to forecast the research output of four selected countries (USA, China, India and Pakistan) using two models of Grey System Theory—Even Model GM (1, 1) and Nonhomogeneous Discrete Grey Model (NDGM). The study also conducts publication growth analysis using relative growth rate (RGR) and the doubling time (D t). The linear and exponential regression analyses were also performed for comparison. The study also proposes and successfully tests two novel synthetic models for RGR and D t that facilities the comparison of the countries’ performance when actual data and forecasted data produce different sequences of performance in the given period of time. The data of documents published by the four countries from 2005 to 2016 was collected from SJR/Scopus website. Performance criterion was Mean Absolute Percentage Error. The study confirms that NDGM is a better model for forecasting research output as its accuracy level is higher than that of the Even Model GM (1, 1) and statistical regression models. The results revealed that USA is likely to continue leading in research output at least till 2025 however the research output difference between USA and China is likely to reduce. The study reveals that the less developed countries tend to possess higher relative growth rate in publications whereas the more developed countries tend to possess lower relative growth rate. Further, the more developed countries need more time for publications to double in numbers for a given relative growth rate and less developed countries need less time to do so. The study is original in term of its analysis of the problem using the models involved in the study. The study suggests that the strategies of USA and China to enhance the research output of their respective countries seem productive for the time being however in long run less developed countries have greater competitive advantage over the more developed countries because of their publication growth rate and time required to double the number of publications. The study reported nearly linear trend of growth in research output among the countries. The study is primarily important for the academic policy makers and encourages them to take corrective measures if the growth rate of their academic/publishing sector is not reasonable.


Nonhomogeneous NDGM GM (1, 1) Research output Research growth Regression USA China Pakistan India Synthetic relative growth rate doubling time 



This work was supported by the Marie Curie International Incoming Fellowship under the 7th Framework Programme of the European Union entitled “Grey Systems and Its Application to Data Mining and Decision Support” (Grant No. FP7-PIIF-GA-2013-629051), a project of the Leverhulme Trust International Network entitled “Grey Systems and Its Applications” (IN-2014-020) and the National Natural Science Foundation of China (71671091). The authors want to thank GreySys Analytics, a project of GreySys Foundation and the Academy of Young Researchers and Scholars, Pakistan, for its assistance in data collection, data entry, formatting and proofreading. The corresponding author is the recipient of the Chinese Government Scholarship thus he wants to thank the Chinese Scholarship Council as well. The authors also want to thank the anonymous/blind reviewers of the journal for their constructive feedback on the earlier versions of the paper.


  1. Ayvaz, B., & Kusakci, A. O. (2017). Electricity consumption forecasting for Turkey with nonhomogeneous discrete grey model. Energy Sources, Part B: Economics, Planning and Policy, 12(3), 260–267.CrossRefGoogle Scholar
  2. Bajwa, R. S., Yaldram, K., & Rafique, S. (2013). A scientometric assessment of research output in nanoscience and nanotechnology: Pakistan perspective. Scientometrics, 94(1), 333–342.CrossRefGoogle Scholar
  3. Bornmann, L., & Mutz, R. (2015). Growth rates of modern science: A bibliometric analysis based on the number of publications and cited references. Journal of the Association for Information Science and Technology, 66(11), 2215–2222.CrossRefGoogle Scholar
  4. Ductor, L., Fafchamps, M., Goyal, S., & van der Leij, M. J. (2013). Social networks and research output. Review of Economics and Statistics, 96(5), 936–948. Scholar
  5. Gupta, B. M. (2012). Scientometric analysis of Pakistan’s S&T research output. Annals of Library and Information Studies (ALIS), 59(1), 25–38.Google Scholar
  6. Gupta, B. M., & Bala, A. (2011). A scientometric analysis of Indian research output in medicine during 1999–2008. Journal of Natural Science, Biology, and Medicine, 2(1), 87.CrossRefGoogle Scholar
  7. Gupta, B. M., & Dhawan, S. M. (2009). Status of India in science and technology as reflected in its publication output in the Scopus international database, 1996–2006. Scientometrics, 80(2), 473–490.CrossRefGoogle Scholar
  8. Hatemi-J, A., Ajmi, A. N., El Montasser, G., Inglesi-Lotz, R., & Gupta, R. (2015). Research output and economic growth in G7 countries: New evidence from asymmetric panel causality testing. Applied Economics, 48(24), 2301–2308.CrossRefGoogle Scholar
  9. Huffman, M. D., Baldridge, A., Bloomfield, G. S., Colantonio, L. D., Prabhakaran, P., Ajay, V. S., et al. (2013). Global cardiovascular research output, citations, and collaborations: A time-trend, bibliometric analysis (1999–2008). PLoS ONE, 8(12), e83440.CrossRefGoogle Scholar
  10. Inglesi-Lotz, R., Chang, T., & Gupta, R. (2015). Causality between research output and economic growth in BRICS. Quality & Quantity, 49(1), 167–176.CrossRefGoogle Scholar
  11. Inglesilotz, R., & Pouris, A. (2013). The influence of scientific research output of academics on economic growth in South Africa: An autoregressive distributed lag (ARDL) application. Scientometrics, 95(1), 129–139.CrossRefGoogle Scholar
  12. Javed, S. A., & Liu, S.F. (2017). Evaluation of project management knowledge areas using grey incidence model and AHP. In Paper presented at the 6th IEEE International Conference on Grey Systems and Intelligent Services. Stockholm, Sweden: IEEE.
  13. Kaur, H., & Gupta, B. M. (2010). Mapping of dental science research in India: A scientometric analysis of India’s research output, 1999–2008. Scientometrics, 85(1), 361–376.CrossRefGoogle Scholar
  14. Kostoff, R. N. (2012). China/USA nanotechnology research output comparison—2011 update. Technological Forecasting and Social Change, 79(5), 986–990.CrossRefGoogle Scholar
  15. Larsen, P. O., & Von Ins, M. (2010). The rate of growth in scientific publication and the decline in coverage provided by Science Citation Index. Scientometrics, 84(3), 575–603.CrossRefGoogle Scholar
  16. Liu, S. F., & Lin, Y. (2010). Grey systems: Theory and applications. Berlin: Springer.CrossRefzbMATHGoogle Scholar
  17. Liu, S. F., & Yang, Y. (2017). Explanation of terms of grey forecasting models. Grey Systems: Theory and Application, 7(1), 123–128.CrossRefGoogle Scholar
  18. Liu, S., Yang, Y., & Forrest, J. (2016). Grey data analysis: Methods. Models and Applications: Springer. Scholar
  19. Murray, M. (2014). Predicting scientific research output at the University of KwaZulu-Natal: Research letter. South African Journal of Science, 110(3–4), 1–4.Google Scholar
  20. Nature. (2014). Central & South Asia. Nature, 515, S89–S90. Retrieved from
  21. Nature. (2016a). US tops global research performance.
  22. Nature. (2016b). 2016 tables: Countries.
  23. Nature. (2016c). Ten institutions that dominated science in 2015. Retrieved from
  24. Neuroskeptic. (2012). Science: Growing too fast?. The official blog of the Discover magazine. Retrieved from
  25. NSF. (2016). Science & engineering indicators 2016.
  26. Ntuli, H., Inglesi-Lotz, R., Chang, T., & Pouris, A. (2015). Does research output cause economic growth or vice versa? Evidence from 34 OECD countries. Journal of the Association for Information Science and Technology, 66(8), 1709–1716.CrossRefGoogle Scholar
  27. OECD. (2017). Research and Development Statistics (RDS). Retrieved from
  28. Pautasso, M. (2012). Publication growth in biological sub-fields: Patterns, predictability and sustainability. Sustainability, 4(12), 3234–3247.CrossRefGoogle Scholar
  29. Pirthee, M. (2017). Grey-based model for forecasting Mauritius international tourism from different regions. Grey Systems: Theory and Application, 7(2), 259–271. Scholar
  30. Scopus. (2017). SCImago Journal & Country Rank.
  31. Sihvonen, J., & Vähämaa, S. (2015). Business research in the Nordic countries: An analysis of research output across countries, disciplines, and institutions. Nordic Journal of Business, 64(4), 266–296.Google Scholar
  32. UN. (2007). Gross domestic expenditure on research and development as a percent of gross domestic product. Accessed from
  33. USR. (2015). UNESCO science report: Towards 2030. Accessed from
  34. Wang, X., Liu, D., Ding, K., & Wang, X. (2012). Science funding and research output: A study on 10 countries. Scientometrics, 91(2), 591–599. Scholar
  35. Wu, L. F., Liu, S. F., Cui, W., Liu, D. L., & Yao, T. X. (2014). Non-homogenous discrete grey model with fractional-order accumulation. Neural Computing and Applications, 25(5), 1215–1221.CrossRefGoogle Scholar
  36. Xie, N., & Liu, S. (2015). Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model. Journal of Systems Engineering and Electronics, 26(1), 96–102.CrossRefGoogle Scholar
  37. Xie, N. M., Liu, S. F., Yang, Y. J., & Yuan, C. Q. (2013). On novel grey forecasting model based on non-homogeneous index sequence. Applied Mathematical Modelling, 37(7), 5059–5068.MathSciNetCrossRefGoogle Scholar
  38. Xie, S., Zhang, J., & Ho, Y. S. (2008). Assessment of world aerosol research trends by bibliometric analysis. Scientometrics, 77(1), 113–130.CrossRefGoogle Scholar
  39. Xin, Z., Jin, C., Zhengrong, G., Liehu, C., Weizong, W., Quan, L., et al. (2016). Orthopedics research output from China, USA, UK, Japan, Germany and France: A 10-year survey of the literature. Orthopaedics & Traumatology: Surgery & Research, 102(7), 939–945.Google Scholar
  40. Zhang, L., Ye, X., Sun, Y., Deng, A. M., & Qian, B. H. (2015). Hematology research output from Chinese authors and other countries: A 10-year survey of the literature. Journal of Hematology & Oncology, 8(1), 8.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2017

Authors and Affiliations

  1. 1.College of Economics and ManagementNanjing University of Aeronautics and AstronauticsNanjingPeople’s Republic of China
  2. 2.Institute for Grey Systems StudiesNanjing University of Aeronautics and AstronauticsNanjingPeople’s Republic of China

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