Multilevel Citation Analysis And Its Discrete Measure At The Institutional Level

Citation analysis has been widely used in various fields and become an important quantitative measure of scientific research. multilevel citation analysis focused on some researches about cited analysis, it used number of measurable indicators, such as the total number of papers, total citations, h index. The paper will discuss about citing analysis an important extension direction, trying to build a compound panoramic view on multilevel citation analysis. The whole paper will focus on multilevel citation analysis, and observing the discrete distribution pattern of the measure value.Firstly, we selected 100 academic institutions’papers as empirical samples published from SSCI in 2010, to use the total number of citations, h index and other associated indexes in the cited level. In this way, Harvard University research showed that most indicators are the NO.1, the leadership in the field of social sciences is very significant; the total number of papers P and C、h index have a power law, citing number S and the total number of citations C have a strong correlation, the more citing papers add, the more the number of citations includes.Secondly, while the citing levels also occur as the considerable aspect. This work attempts to introduce the empirical relationship of underlying parameters between cited level and citing level. After giving the theoretical power-law model between the total number of citing sources N and the total number of citations C, we select top 100 academic institutions in SSCI as the empirical samples. By applying four citing levels(journals, institutions, countries/territories and subjects), we explore the numerical properties of citing sources and test the power-law relationship between N and C. Results show that:in the meso-level (journals and institutions), N and C fit the approximate power-law relationship; power exponent is larger than 1, which indicates that C has the accelerated growth trend with N; the relation between the citing sources on journal level and on institution level also fit the approximate power law model; however, at the macro level (countries/territories and subjects), the power-law relationship between N and C has not been fully confirmed by present datasets.Finally, we tried the Herfindahl-Hirschman Index (HHI index) and the coefficient of variation of two methods to measure the discrete case of 100 samples institution thesis based on four Citing levels (country/region, discipline direction, journals, institutions), and found the dispersion of the citing sources on macro-level is clearly higher than the dispersion of that on meso-level, the dispersion of the citing sources on country/region level is significantly higher than the dispersion of that on institution level. So these two methods are some rules to follow:when the greater its value, the greater its dispersion; However, because of the differences in the scope or calculation formula, they show different trends on the dispersion of HHI index and coefficient of variation. HHI index shows a slow rise overall, while the dispersion of coefficient of variation overall has a downward trend.In summary, Through the extension of citing level and the application of discrete measurement methods, we can provide a different perspective and approach of citation analysis to find multidimensional indicators easily and show a more intuitive display on the data relevance, and provides a reference for multidimensional citation analysis in the future.