Growth rates of modern science: a latent piecewise growth curve approach to model publication numbers from established and new literature databases

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Abstract

Growth of science is a prevalent issue in science of science studies. In recent years, two new bibliographic databases have been introduced, which can be used to study growth processes in science from centuries back: Dimensions from Digital Science and Microsoft Academic. In this study, we used publication data from these new databases and added publication data from two established databases (Web of Science from Clarivate Analytics and Scopus from Elsevier) to investigate scientific growth processes from the beginning of the modern science system until today. We estimated regression models that included simultaneously the publication counts from the four databases. The results of the unrestricted growth of science calculations show that the overall growth rate amounts to 4.10% with a doubling time of 17.3 years. As the comparison of various segmented regression models in the current study revealed, models with four or five segments fit the publication data best. We demonstrated that these segments with different growth rates can be interpreted very well, since they are related to either phases of economic (e.g., industrialization) and/or political developments (e.g., Second World War). In this study, we additionally analyzed scientific growth in two broad fields (Physical and Technical Sciences as well as Life Sciences) and the relationship of scientific and economic growth in UK. The comparison between the two fields revealed only slight differences. The comparison of the British economic and scientific growth rates showed that the economic growth rate is slightly lower than the scientific growth rate.

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How many imputations are really needed? Some practical clarifications of multiple imputation theory.

John W Graham, Allison E Olchowski, Tamika D Gilreath (2007)

Multiple imputation (MI) and full information maximum likelihood (FIML) are the two most common approaches to missing data analysis. In theory, MI and FIML are equivalent when identical models are tested using the same variables, and when m, the number of imputations performed with MI, approaches infinity. However, it is important to know how many imputations are necessary before MI and FIML are sufficiently equivalent in ways that are important to prevention scientists. MI theory suggests that small values of m, even on the order of three to five imputations, yield excellent results. Previous guidelines for sufficient m are based on relative efficiency, which involves the fraction of missing information (gamma) for the parameter being estimated, and m. In the present study, we used a Monte Carlo simulation to test MI models across several scenarios in which gamma and m were varied. Standard errors and p-values for the regression coefficient of interest varied as a function of m, but not at the same rate as relative efficiency. Most importantly, statistical power for small effect sizes diminished as m became smaller, and the rate of this power falloff was much greater than predicted by changes in relative efficiency. Based our findings, we recommend that researchers using MI should perform many more imputations than previously considered sufficient. These recommendations are based on gamma, and take into consideration one's tolerance for a preventable power falloff (compared to FIML) due to using too few imputations.