The Scientometric Measurement of Interdisciplinarity and Diversity in the Research Portfolios of Chinese Universities

On July 29, 2020, the Academic Degrees Committee of the State Council—an advisory council of the Chinese government—announced that the category “interdiscipline” had been added to the list of national disciplines accessible for academic degrees. This initiative will not only result in a structural change to China's classification of academic degrees, it was also designed to promote the future development of interdisciplinarity in China. As a case in point, three months after its release in late October 2020, the National Natural Sciences Foundations of China (NSFC) announced the launch of a new department for “interdisciplinary studies”. This will be the ninth department of the NSFC, and will focus on funding interdisciplinary projects. As the first change to the NSFC funding scheme in 11 years, the decision has drawn much attention.

Interdisciplinarity is a hot topic in science and technology policy. However, the concept of interdisciplinarity is both abstract and complex, which makes it difficult to fully represent or measure interdisciplinarity in terms of indicators, which can be compared among them. A variety of measures for diversity, as a proxy of interdisciplinarity, has been proposed in the literature. Further, one can find such indicators to measure the interdisciplinarity of a set of articles, patents, or journals. In this study, we ask: Can one rank institutions in terms of their disciplinary diversity? And, if so, what does this tell us about interdisciplinarity?—noting that diversity is not necessarily a goal universities strive for; some aspire to be the best in a particular discipline.

During the last few years, we, the authors of this paper, have explored the scientometric measurement of interdisciplinarity and diversity in scholarly communications in collaboration with a number of colleagues. Contributions to this program of studies were made (in alphabetic order) by Lutz Bornmann, Wolfgang Glänzel, Inga Ivanova, Ronald Rousseau, Caroline S. Wagner, and Ping Zhou (Leydesdorff & Ivanova, 2020; Leydesdorff, Wagner, & Bornmann, 2018 and 2019; Zhang, Rousseau, & Glänzel, 2016; Zhang, Sun, Chinchilla-Rodríguez, Chen, & Huang, 2018; Zhang, Sun, Jiang, & Huang, 2021). One of our objectives has been to develop a non-commercial, public-domain application that allows researchers and policy analysts to measure the diversity of any document set or network structure using a range of indicators. To our best knowledge, no such tool has ever been developed, at least not for public consumption.

A large number of indicators of “diversity” have been proposed in the literature (e.g. Rao-Stirling diversity; Stirling (2007), the Gini-coefficient, Simpson (1949) indicator, Hirschman-Herfindahl (Herfindahl, 1950; Hirschman, 1945), etc. In this communication, we report on the facilities which we created during the last two years. Particularly, we introduce the freely available program interd_vb.exe (available at http://www.leydesdorff.net/software/interdisc.2020/) for this purpose. We document the various options and provide instructions for practitioners interested in measuring diversity and interdisciplinarity. By elaborating on the measurement of the disciplinary diversity of the research portfolios of the 42 top universities listed as the “Double First-Class” universities (Liu et al., 2018), we are able to show the options and choices to be made given the current state of the art.

Technical instructions are additionally available at http://www.leydesdorff.net/software/interdisc.2020/index.htm. The inputs and outputs are in .csv format. The same output is also stored in interdis.bdf. The subsequent analysis demonstrates the options and choices that can be made as route to a final comparison. As a disclaimer, note that we are in no way professional programmers. We cannot guarantee that our routines are error-free, and we acknowledge that the user interface could be improved. However, as a test, one of us programmed the application in two different computer languages, and the results were virtually the same. Additionally, we do believe the functionality is unique and, therefore, state of the art for what it is.

One of the advantages of the application is its ability to handle large volumes of data. For example, the need to analyze an entire database, such as Web-of-Science (WoS), Scopus, or Google Scholar, is becoming increasingly common. Analyses of this magnitude can generate baselines for evaluating the disciplinary diversity of articles, journals, topics, etc. The Interdisc program can relieve the computational overhead of processing massive amounts of data. That said, although the equations used to calculate diversity indicators are often mathematically transparent, specifying the terms as computer code can help analysts to further precision in decisions that would not otherwise be involved in a manual calculation.

Interdisciplinarity can be operationalized as references to different literatures. Such co-citing is known in scientometrics as bibliographic coupling (Kessler, 1963). When a document, for example, cites both articles in physics journals and in sociology journals, this can be expected to indicate interdisciplinarity more than citing chemical physics and solid-state physics in the same document or in the same set. In other words, one couples literature from different disciplines in the references. This coupling can be at the level of articles, journals, or Web-of-Science Subject Categories (WCs).

Bibliographic coupling is an indicator on the citing side and thus the operation opposite to co-citation: co-citations across disciplinary borders indicate interdisciplinary diffusion, whereas the measurement of interdisciplinarity by bibliographic coupling focuses on aggregated citing behaviour.

Whereas “interdisciplinarity” by citing papers refers to documents, documents are often not the units of analysis in the case of research evaluation at the institutional level. The interdisciplinary operator of bibliographic coupling is defined in terms of disciplines and not in terms of institutions. Does the diversity of a university in terms of departments indicate interdisciplinarity or only comprehensiveness of a research portfolio? Since there is no coupling in terms of different fields, one may measure only comprehensiveness, and not interdisciplinarity.

Institutional units are primarily administratively and not disciplinarily organized. The diversity indicators apply to disciplinary differentiations; social differentiation in terms of departments, etc., may have a different meaning. For example, diversity may also indicate comprehensiveness. How does this work out empirically?

In this section, we first discuss the following indicators of diversity and interdisciplinarity in terms of the basic equations:

The program interd_vb.exe (http://www.leydesdorff.net/software/interdisc.2020/interd_vb.exe) was rewritten based on the routine Mode2Div.exe previously programmed in the so-called xBase language. Unfortunately, computing cosine values for large matrices can be time-consuming with xBase, which imposes a soft limit on the size of the datasets that can be processed. Hence, we rewrote Mode2Div. exe in Visual Basic 6 to become interd_vb.exe, i.e. the online Interdisc application. Visual Basic 6 runs on Win10 (32/64 bits) and does not require the predetermined amount of memory to be allocated to processing. Therefore, the only limitation to the size of the dataset that can be processed is hardware. The two programs, interd_vb.exe and Mode2Div.exe, have similar objectives but a different organization and architecture, and the results they produce are exactly the same. Both programs are documented in Leydesdorff et al. (2018, 2019) and the software is available for download from https://www.leydesdorff.net/software/interdisc.2020/ and Figshare (https://figshare.com/account/articles/12871529).

One key difference between the two versions of the program is their input requirements. In the case of mode2div.exe, the input is stored listwise using the Pajek format, each line describing the row and column of a cell in a matrix of values. Thus, the input can be read as three fields without any system limitations. The data is assumed to be 2-mode so that an asymmetrical (citation) matrix can be processed. The program then computes the diversity measures along the column vectors of a data matrix saved in .csv format. As an example, to measure the interdisciplinarity of a set of documents, one could use jcitnetw.exe⁽¹⁾ to easily generate a co-occurrence matrix of cited journals in the Pajek format, using plain text downloaded from the Web of Science. More details on this can be found at https://www.leydesdorff.net/software/mode2div/.

Stirling (2007) added a new element to diversity measurement: disparity. Disparity indicates the distance between two subjects in the sample(s) under study. For example, if the distances in a subset are small, this space can be considered a niche of related variety (Frenken et al., 2007). However, disparity as a factor in both RS and the DIV requires the choice of a distance metric. Following Salton and McGill (1983), Ahlgren, Jarneving, and Rousseau (2003) proposed cosine as a non-parametric measure of similarity for bibliometrics. From a comparison of a number of similarity/distance measures, Egghe and Leydesdorff (2009) concluded that the cosine fulfills a number of requirements.

Like Pearson correlations, cosine values are defined in a vector space and are therefore positional, whereas the very similar Jaccard index is relational. Unlike the Pearson correlation, however, cosines do not normalize to a mean and, since bibliometric distributions are highly skewed, normalizations using the mean are to be avoided. Our routines use (1 – cosine), which can be considered a distance measure. Pragmatically, the terms of a cosine can be written as co-occurrence in the numerator and the sum of squares along the two column vectors x and y multiplied in the denominator. Note that, here, the matrix rows contain the disciplines and the columns contain the universities, so the cosine values are computed between the row vectors.

One disadvantage of Mode2Div.exe is that data is often not readily available in Pajek format and converting the data into this format may generate other problems (Pfeffer, Mrvar, & Batagelj, 2013). The most generic format for data, however, is a matrix as a comma or tab-separated plain ASCII file. There are no size limitations for this data, although Excel (depending on the Office version) may not allow for more than 255 variables. This data, however, can also be written using a text editor (e.g. the freeware Note++) or any other program. The size of the matrix is only limited by external factors such as free diskspace.

The routine begins with asking for the name of the .csv file containing the variables and the number of vectors to be compared for the purposes of error correction. The file is then rewritten into output which is reported in the files interdis.dbf and equivalently interdis.csv. The specific differences in terms of inputs, outputs, and other related items about these programs are summarized in Appendix Table S1.⁽²⁾

As empirical data, we used the portfolio of research articles from the 42 Chinese universities listed as “Double First-Class universities” between 2017 (when the list was first released) and 2019. The Chinese government offers substantial support to this select group of universities through a series of special programs. Additionally, although this particular list has only been published since 2017, similar initiatives under different names have existed periodically since the 1990s, with the majority of universities considered to be elite remaining much the same this whole time. Thus, these 42 institutions were selected because this group is both clearly delineated and large enough to provide a large-scale sample. In addition, we also included the portfolios of two well-known American universities, Harvard and Stanford, to provide a standard those in the West might find easier to benchmark. In a subsequent article, Leydesdorff, Wagner, and Zhang (2021), we further compare these results with 205 Chinese universities.

Each of the universities in the sample promotes itself as a comprehensive university. However, some note specific missions or strengths; for instance, the agricultural universities. The publications associated with each university were retrieved using the organization's name and/or its variants from the Preferred Organization Index in WoS.

The domains searched include the Science Citation Index Expanded (SCI-E), the Social Sciences Citation Index (SSCI), and the Arts & Humanities Citation Index (A&HCI) in the Web of Science (WoS) Core Collection. We limited the document type to articles and reviews. The number of articles retrieved per university are listed in Table 1 in decreasing order.

We first organized the data into an asymmetrical occurrence matrix of the 44 universities against 254 WoS categories. We then computed the six diversity measures using Interd_vb.exe.

DIV* values were more in line with our intuition about the diversity of these universities than the RS or True RS values. The latter, particularly worsen when the results are based on local disparity matrices. Using this local matrix, however, some field-specific universities like Ocean University of China and the Northwest Agriculture & Forestry University are found to have high diversity values with the True RS (and RS) indicators. These results raise further questions.

The results for RS/True RS are more sensitive than DIV* to the choice of similarity measures (Rafols & Leydesdorff, 2010). As Rousseau (2019) notes: “DIV, taking disparity into account as just a relative (normalized) sum” is not sensitive to scaling. In Eq. (8), disparity is only defined at the level of the sample; the interaction between category i and category j (p_i and p_j, respectively) with d_ij is not taken into account at the cell level, only the total sum of all disparity values is.

Table 2 (above) showed that the Ocean University has the highest True RS diversity of all universities. However, when checking the specific distribution of Web of Science categories, we found that more papers are published within Oceanography (14.01%) than any other category. Yet, Oceanography is a relatively marginal category in our sample, with much lower cosine similarities than other categories. As a result, the disparity (1-cosine) between Oceanography and other categories is much higher than on average, at a value of 0.73 vs 0.47, respectively. The extraordinarily high proportion of publications in Oceanography and the category's high disparity from other categories leads to an unexpectedly high diversity value when measured with RS/True RS. However, when using a global similarity matrix (Table 4), the scores of RS/True RS in most field-specialized universities decreased. As noted, these rankings were not affected by this effect when using DIV*.

The portfolio of papers with a Harvard address covers a wide range of categories and the distribution is relatively balanced. However, the cosine similarities of the categories with most publications are relatively high, i.e. they tend to have low disparity values, which results in a lower valus of RS/True RS when using a local similarity matrix. These empirical results suggest that RS diversity values based on a global disparity matrix provide results that are more in line with expectations. Therefore, insofar as a user has access to a global matrix one is advised to use this instead of the values generated endogenously by our software.

When universities operate in similar markets with the same institutional imperatives, such as tasks specified in national legislation, one might expect them to develop isomorphism (Halffman & Leydesdorff, 2010; Powell & DiMaggio, 1991; Wagner, Bornmann, Cai, & Leydesdorff, in preparation). However, our results indicate that universities do not tend toward isomorphism when it comes to comprehensiveness, as they do with impact. We reason that this is because impact is measured and prioritized in the bureaucratic frameworks of the state, whereas comprehensiveness is influenced by local opportunities, such as emerging technologies in the companies geographically or intellectually nearby. Hence, developing a deeper understanding of institutional comprehensiveness demands consideration of a broader context and more aspects of society, such as missions of specific universities.

Our analysis clarifies further differences between impact and comprehensiveness. Competition for impact pertains to quality, while competition for diversity/specialty pertains to differentiation. For example, shielding intellectual property rights is specific to a university's relations with industry. When it comes to comprehensiveness, the specificity of the knowledge content matters more than the formal criteria of measuring and comparing output and impact. In our opinion, interdisciplinarity, diversity, or comprehensiveness should not be considered another type of impact. While impact can be formalized across units of operation, e.g. faculties, departments, etc., after proper normalization, diversity or comprehensiveness remains content-based.

In other words, the analytical distinction between intellectual and social organization does not mean that the two dimensions can be traded off at the level of a university. On the contrary, one can expect a correlation, whether positive or negative, between the different types of research efforts. However, the differences between the two make it urgent that we develop a set of indicators for measuring diversity comparable to those of impact. By making an application available that allows users to generate the various measures of diversity for any data matrix, we hope to have contributed to this objective of quantifying and measuring diversity.

Finally, we note that although diversity is often used as a proxy for measuring interdisciplinarity, one should not expect any simplistic index to produce an informative outcome on its own (Abramo et al., 2018). The interpretations of the values of indicators should always be addressed according to the context, the purpose, and the specific object under study. The empirical analysis of the 42+ Chinese universities in terms of diversity measures not only relates to interdisciplinarity at the intellectual level, but also reflects comprehensiveness at the institutional level. Although comprehensiveness is not necessarily a goal of universities, it may reflect the status quo of disciplinary diversity within a university (or at least the structural feature of a disciplinary distribution). The measurement results of this study provide a knowledge base for understanding portfolios. A better understanding may provide new windows on potential policies and thus facilitate the development of interdisciplinarity within a university.