Measuring a journal's input rhythm based on its publication–reference matrix
Introduction
A recent article (Neuhaus & Daniel, 2009) reveals considerable differences of publication activity and citation habits among fields. Its results also show that citation habits vary extensively not only between fields but also within fields. A new reference standard for citation analysis is suggested. This study draws our attention once more to the old problem of diversity of citation habits over fields and the necessity of normalization or standardization of evaluation indicators (Glänzel, 1996). In fact, to solve this problem scientometricians have put forward indicators such as ISSRU's NMCR indicator (Braun et al., 1985, Schubert and Braun, 1986, Schubert et al., 1983, Schubert et al., 1989) and CWTS's CpP/JCSm and the crown indicator CpP/FCSm (Moed, 2005, Moed et al., 2005, van Raan, 2006). The key methodology is to compare the actor's observed value with a journal's or field's expected value.
Basic research can be considered as an input–output system. The process occurs as follows: research results, codified as articles and acknowledged as references, are inputs for a new article. Outputs consist of the citations that this new article receives over time (Liang & Rousseau, 2008). It is the difference among journal reference characteristics of various fields that causes the difference in their citation counts. Usually the longer the article's reference list, the higher the average citations per paper (Abt, 2000, Uzun, 2006), all other aspects (field, journal, type of document) being the same. We note that there do exist bibliometric indicators related to the reference characteristics, such as the “journal citing half-life” and “aggregate citing half-life”, which have been used in the Journal Citation Reports (Thomson Reuters). For the purpose of improving indicators used in cross-field evaluations it is necessary to continue explorations corresponding to the characteristics of journal references. Such an exploration would offer new clues for solving problems related to cross-field research evaluations.
Since 2005 a series of new indicators called rhythm indicators (and R-sequences) has been proposed. Various R-sequences have been determined for the journals JASIS(T) (Journal of the American Society for Information Science and Technology; formerly Journal of the American Society for Information Science), Nature and Science (Liang, 2005, Liang, 2007, Liang et al., 2006). Egghe, Liang, and Rousseau (2008) further studied the fundamental mathematical properties of these rhythm sequences. An article and the citations it received after its publication form a cited–citing relation. Here, the original article is the cited actor, while through their reference lists other articles are the citing actors. Symmetrically, an article and the references in the article's reference list form another relation, the citing–cited relation. Here, the article is the citing actor and the references are the cited actors. Naturally, one can ask: can R-cluster indicators be used to study the citing–cited relation, i.e. the relation between the journal articles and their references? Does such an R-sequence pattern reflects another rhythm of science, one we could call the input rhythm?
The answer is positive. Theoretically, rhythm indicators can be created and calculated based on any source–item matrix. All the R-cluster indicators are created based on various types of publication–citation (p–c) matrices (Liang & Rousseau, 2007). In a p–c matrix the publications are sources, the citations received by the publications are items. A journal's publications and their references form another source–item relationship: the publications are sources, their references are items. Thus, we may construct the publication–reference matrix for a journal (a field, an institute, etc.), and calculate the R-sequences based on the publication–reference matrix, which reflects the input rhythm of the journal (the field, the institute, etc.).
In this article we create the rhythm indicator for measuring a journal's input rhythm, and illustrate the measure to two journals: JASIS(T) and JDOC.
Section snippets
The p–c matrix and its corresponding R’ indicator
First, let us review the p–c matrix and the creation of the R′ indicator (Liang, 2005) taking a journal as an example. This will help us to understand the new p–r matrix and the definition of the new rR′ indicator.
Table 1 is a p–c matrix of a journal. In this example years are numbered from 1 to 9. The symbol Pi denotes the number of articles published in the year i, i = 1, …, 9. In general we consider n years: i = 1, …, n. The symbol Cij denotes the number of citations received in the year j by
The relative reference factor
Recall that the -year diachronous impact factor of journal J is defined as (Ingwersen, Larsen, Rousseau, & Russell, 2001):Here Y denotes a particular year and PY(J) denotes the number of publications in the year Y.
In a similar way we define a -year relative reference factor for the year Y and journal J, denoted as as:where PY(J) denotes the number of articles published in year Y in journal J, and RY,m(J) denotes the
A characterization of the constant rR’-sequence
Similar to the main result of Egghe et al. (2008) we have the following theorem. Theorem A p–r matrix has a constant rR′ sequence (with window w) if and only if its -year relative reference factor is constant. Proof In order to prove the theorem we first prove the rearrangement equality . By , we have . Summing for k = 1 to , yieldsThe left hand side of this equation is nothing
The p–r matrix of JASIS(T) and its rR′ sequence
By searching the data in the Web of Science (Thomson Reuters) we created the p–r matrix of JASIS(T). Only research articles are included. The publication time span is 1973–2008, a total of 36 years. Table 4 shows a section of the p–r matrix.
Table 5 lists JASIS(T)’s rR′-sequences with citation window , and , respectively. Fig. 1 shows the corresponding curves. It is very clear that all the rR′ curves have increasing trends, though with some fluctuations. The three rR′-curves are
The p–r matrix of JDOC and its rR′ sequences
By searching the data in the Web of Science (Thomson Reuters) we created the p–r matrix of JDOC. Only research articles are included. The publication time span is 1955–2008, a total of 54 years. Table 7 shows a section of the p–r matrix.
Table 8 lists JDOC's rR′-sequences with citation windows , and , respectively. Fig. 2 shows the corresponding curves. Similar to the case of JASIS(T), all the rR′ curves have clear increasing trends, while the fluctuations are even heavier than for
Conclusion and discussion
From the viewpoint of applications the rhythm indicators have another methodological significance: rhythm indicators can be applied to many rhythm studies. They are meaningful if the system is a source–item system with two time dimensions, ensuring the construction of a p–c-like matrix. The application to the study of journal references is an actual example. Apart from the study of a journal's input rhythm, the method explained here can also be used to study the input rhythm of a research group
Acknowledgements
The authors thank reviewers for useful comments on an earlier version. The work presented in this paper is sponsored by the National Natural Science Foundation of China (Project 70673019).
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