Scientometrics
雖然許多研究區分"interdisciplinary"、"multidisciplinary"、"transdisciplinary" 以及 "crossdisciplinary" (Organisation for Economic Co-operation and Development, 2005)，但在實務上可以發現它們之間具有連貫性，很難加以區別(Barry et al., 2008, pp. 27-8)。因此，本研究以interdisciplinary research(跨學科研究)加以統稱。根據美國國家科學院(National Academy of Science of the USA) (2004, p. 2)將跨學科研究(interdisciplinary research)定義為：為了了解或解決解答某些需要超越單一學科或研究實務領域的問題，團體或個人整合來自兩個或以上學科與特殊知識體系的資訊、資料、技術、工具、觀點、概念以及理論的一種方式。在這個定義中，關鍵的概念是知識整合(knowledge integration)。而所謂的學科(discipline)係指科學組織的結果。學科結構可以應用叢集演算法(cluster algorithm)等統計工具來產生，例如Rosvall and Bergstrom (2008) 和 Leydesdorff and Rafols (2009)等研究；也有像是國際十進位分類法(Universal Decimal Classification, UDC)的哲學結果：或是例如Moya-Anego´n et al., 2004 和 Leydesdorff and Rafols (2009)等有關跨學科性的實務研究上經常利用期刊引文報告(Journal Citation Reports, JCR)的期刊主題分類(Subject Categories)。
Rafols and Meyer (2010)提出一個研究跨學科性的分析架構，他們強調跨學科性的關鍵過程是知識整合(knowledge integration)，兩個重要的觀察面向是多樣性(diversity)和凝聚性(coherence)。多樣性所指的是使用類別的廣度，也就是強調整合的知識有多麼不同，Rafols and Meyer (2010)提出使用參考文獻的參考文獻(references-of-references)的JCR分類來測量。Stirling (2007)認為多樣性是描述一個系統的元素如何被分配到的類別的特性，其概念包含三個層次：一為牽涉的類別數量(Variety)，二是以Simpson指標、Shannon熵、Gini指標或是變異量係數(the coefficient of variation)等各種古典多樣性(Classical diversity)來測量均勻度(evenness)，三是同時涵蓋多樣性的variety、balance和disparity等三個面向的最佳測量，能將類別間的距離與差異考慮進來的Rao-Stirling測量
此處的dij是類別 i 和 j之間的差異度， pi 和 pj 分別是所有項目在類別 i 和 j 上的比例。 α 和 β 則是調整重要性的參數，通常設為1。
凝聚性則是在這個研究上元素彼此間透過主題或類別間相互關連的程度，強調研究中不同體系間如何連貫銜接並形成有意義的群體，是由元素所構成網路的特性，Rafols and Meyer (2010)使用在參考文獻網路中的書目耦合(bibliographic coupling)強度來測量，也就是以參考文獻為節點，參考文獻彼此間的書目耦合值的大小決定節點間連結線的存在與否，並且以平均路徑長度(mean path length)測量凝聚性。
Rafols and Meyer (2010)提出一個研究跨學科性的分析架構，他們強調跨學科性的關鍵過程是知識整合(knowledge integration)，兩個重要的觀察面向是多樣性(diversity)和凝聚性(coherence)。多樣性所指的是使用類別的廣度，也就是強調整合的知識有多麼不同，Rafols and Meyer (2010)提出使用參考文獻的參考文獻(references-of-references)的JCR分類來測量。Stirling (2007)認為多樣性是描述一個系統的元素如何被分配到的類別的特性，其概念包含三個層次：一為牽涉的類別數量(Variety)，二是以Simpson指標、Shannon熵、Gini指標或是變異量係數(the coefficient of variation)等各種古典多樣性(Classical diversity)來測量均勻度(evenness)，三是同時涵蓋多樣性的variety、balance和disparity等三個面向的最佳測量，能將類別間的距離與差異考慮進來的Rao-Stirling測量
此處的dij是類別 i 和 j之間的差異度， pi 和 pj 分別是所有項目在類別 i 和 j 上的比例。 α 和 β 則是調整重要性的參數，通常設為1。
凝聚性則是在這個研究上元素彼此間透過主題或類別間相互關連的程度，強調研究中不同體系間如何連貫銜接並形成有意義的群體，是由元素所構成網路的特性，Rafols and Meyer (2010)使用在參考文獻網路中的書目耦合(bibliographic coupling)強度來測量，也就是以參考文獻為節點，參考文獻彼此間的書目耦合值的大小決定節點間連結線的存在與否，並且以平均路徑長度(mean path length)測量凝聚性。
In a recent article, Rafols and Meyer (2010) presented an analytic framework for the study of interdisciplinarity. The two main factors of this framework are diversity and coherence. These authors stress that the key process characterizing interdisciplinarity is knowledge integration (National Academy of Sciences, 2004; Porter et al. 2006).
According to the National Academy of Sciences (2004, p. 2) of the USA, interdisciplinary research is:
[...] a mode of research by teams or individuals that integrates information, data, techniques, tools, perspectives, concepts and/or theories from two or more disciplines or bodies of specialised knowledge to advance fundamental understanding or to solve problems whose solutions are beyond the scope of a single discipline or area of research practice.
In this definition the key concept is knowledge integration.
Although some researchers make a distinction between the terms “interdisciplinary”, “multidisciplinary”, “transdisciplinary“ and “crossdisciplinary“ research (Organisation for Economic Co-operation and Development, 2005) in empirical studies one finds a continuum that makes it difficult to distinguish among these modes (Barry et al., 2008, pp. 27-8). Hence, we just use the term “interdisciplinary” as a general term, comprising all the latter, as was done in Rafols and Meyer (2010).
When studying interdisciplinarity, the notion of “a discipline” comes logically first. A discipline is the result of the organisation of science (Turner, 2000). The disciplinary structure can be captured using statistical tools, for example by applying a cluster algorithm, as in Rosvall and Bergstrom (2008) and Leydesdorff and Rafols (2009), a philosophical result (as the categories used in the Universal Decimal Classification (UDC)) or a practice-based categorisation, supported by statistics, such as the Subject Categories of the Journal Citation Reports (JCR) (Moya-Anego´n et al., 2004; Leydesdorff and Rafols, 2009).
Diversity refers to the breadth in categories used (Stirling, 2007); coherence to the extent that different elements in the research (categories or topics) are interrelated. The notion of diversity puts the emphasis on how different the incorporated knowledge is, while the notion of coherence emphasizes how different bodies of research are consistently articulated and form a meaningful constellation (Rafols and Meyer, 2010).
Diversity refers to the breadth in categories used (Stirling, 2007); coherence to the extent that different elements in the research (categories or topics) are interrelated. The notion of diversity puts the emphasis on how different the incorporated knowledge is, while the notion of coherence emphasizes how different bodies of research are consistently articulated and form a meaningful constellation (Rafols and Meyer, 2010).
In this sense, an increase in diversity reflects the divergence of knowledge integration and diffusion, whereas an increase in coherence reflects their convergence.
In Rafols and Meyer (2010), diversity is measured using the JCR categories of the references-of-references and coherence using the strength of bibliographic coupling in the network of references.
In order to capture diversity and coherence we will consider a framework that consists of three entities:
(1) the source or object of enquiry (often an article or set of articles) used as a representation of an author or group of authors;
(2) an intermediary set (IM) derived from the source; and
(3) a target set, defining the notion we want to study.
These three sets are connected by two mappings: one from the source set to the intermediary set, and one from the intermediary set to the target set.
[...] knowledge integration can be captured as a property of an article (Porter et al., 2007). This leads to the question: how does one describe a relation between an article and the set of all cats?
(1) words used in the article;
(2) words used in the articles in the reference list;
(3) the byline;
(4) the byline of the articles in the reference list;
(5) the reference list;
(6) the reference lists of the articles in the reference list; and
(7) the union of items 5 and 6.
If the cats are disciplines delineated by a set of keywords and IM consists of words then each word is either mapped to itself (if it happens to be a keyword) or to that keyword (or keywords) that are closest to it in meaning (to be determined by a specific algorithm).
If the cats are disciplines and IM consists of journals, then each journal is mapped to the discipline associated with this journal (the case of journals covered by the WoS and the corresponding JCR subject categories is an obvious example).
Contrary to the case of knowledge integration, knowledge diffusion with respect to one article is largely determined by outsiders[1]. ... Instead, we have to determine an intermediary set taking into account the properties of the “audience” or users of the article(s).
This may be (and again no exhaustiveness is claimed):
(1) the set of articles citing the article under consideration, denoted CIT;
(2) the union of CIT and all articles citing an article in CIT (hence including several citation generations, as studied, for example, in Hu et al., 2011);
(3) the set of journals citing the article;
(4) all books citing the article;
(5) the set of persons downloading this article;
(6) the departments where downloading has taken place; and
(7) all web pages linked to the article (if it exists in electronic form).
If the cats are countries or regions and IM consists of citing articles (the case of knowledge diffusion), then each citing article is mapped to those countries appearing in the byline.
For the same set of cats and an IM consisting of books that appear in the reference list, each book is mapped to the country of the publisher.
If IM consists of web pages, each web page is mapped to its country domain name (either removing other domain names; or considering.com,.org, etc. as “regions”).
If the cats are journals and IM consists of citing articles, then each citing article is mapped to the journal in which the citing article has been published.
Diversity is the property of how the elements of a system are apportioned into categories (Stirling, 2007). As one aspect of knowledge integration, diversity is now determined on the image of the cats-mapping. There are three levels on which one may work.
(1) Variety: the number of cats involved, or (maybe better) the relative number of cats (with respect to the total number of cats) involved.
(2) Classical diversity (as the opposite of evenness). This quantity can be measured using a classical evenness measure such as the Simpson index, the Shannon entropy measure, the Gini index or the coefficient of variation (Nijssen et al., 1998).
(3) As explained by Rafols and Meyer (2010) the best approach is to take the three aspects of diversity – i.e. variety, balance and disparity – into account. If a distance or dissimilarity measure exists in cats (and this is assumed in our framework) this suggests using the Rao-Stirling measure, or one of the generalisations that can be derived from Stirling’s (2007) framework [2].
Recall that the Rao-Stirling measure is defined as:
Here, dij denotes the dissimilarity between cat i and cat j, and pi and pj denote the proportions of the total number of items under study in cat i and cat j, respectively. Finally, α and β are parameters that adjust the importance given to small distances (α) and weights (β).
Coherence is the property describing how the elements of a system are related to each other. Hence, coherence is a property of networks.
It is independent from the concept of diversity: diversity reflects the distribution of elements in the IM set into categories; coherence reflects how these elements are related to each other (as measured through cats).
Different network measures may be used to capture coherence, such as the mean path length or the mean dissimilarity between elements (or linkage strength).
Rafols and Meyer (2010), the network nodes consist of the set of references of the original article. These references are the nodes of the network, and the relation studied, determining the existence of links, is bibliographic coupling.
In this way each source can be represented on a two-dimensional graph (coherence versus diversity) as in the Rafols and Meyer (2010) study, where they represented mean-linkage strength versus Stirling measure. In the case where the study of coherence reveals a fragmented structure, the diversity of each of the clusters can then be analysed for each of them.
However, for a group of articles, such as those published by one author, one may calculate an interdisciplinarity value per article and study how this measure changes over time (when new articles are added to the group of articles). Hence the time aspect of the group of articles under study is carried over to a time aspect of the corresponding interdisciplinarity, or more general, knowledge integration measure.
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