Diagonal Values in ACA

Diagonal Values in ACA

Sean Eom (Southeast Missouri State University, USA)
DOI: 10.4018/978-1-59904-738-6.ch004
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Abstract

Diagonal values in the cocitation frequency counts matrix are a fundamental issue in ACA study. Diagonal values are the co-citation frequency counts between the author himself/herself excluding self-citation. Retrieving exact values of diagonal values in the co-citation matrix requires a manual and time consuming procedure. For that reasons, ACA researchers suggested many different approaches to create, not retrieving the real values, the diagonal cells in the cocitation matrix. They include the mean cocitation count, missing values, zeroes, highest off-diagonal counts, adjusted off-diagonal values, and the number of times cocited with himself/herself. The majority of ACA researchers seem to prefer to use either the adjusted value approach by adding three highest off-diagonal values and divided by two or the missing value approach. This chapter empirically examines the impact of these different approaches on the ACA outcomes. Based on the results of this study, if the pure cocitation counts are not used, the next best alternatives are as follows. They are the missing value approaches, mean cocitation value approach, and the highest off-diagonal value approaches in the order of the highest total variance explained.
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Number Of Times Cocited With Himself/Herself

A possible solution for the diagonal value problem is suggested by Ahlgren, Jarneving, and Rousseau (2003, p.551.) and White (Howard D. White, 2003). The diagonal values should be the number of articles in the bibliographic database that cite at least two (different) works authored or coauthored by the person. Ahlgren, Jarneving, and Rousseau suggest excluding self-citations. This number is very difficult to get when using ISI databases. The custom database and cocitation matrix generation system we have developed allowed us to retrieve the numbers so we can yield a co-citation frequency matrix, which Ahlgren, Jarneving, and Rousseau describe as “a mathematically complete matrix.” One solution for the diagonal value problem is suggested by Ahlgren, Jarneving, and Rousseau (2003, p.551.)

We think that perhaps the best solution for the “diagonal” problem (if such solution is deemed necessary) is to use the number of times for an author, say AU, has been cocited with himself (excluding self-citations). This is the number of articles in the pool under study that cite at least two (different) works (co)authored by AU. Such a method would yield a mathematically complete matrix, which is always easier to study (statistically) than an incomplete one (Fienberg, 1980). Our suggestion is inspired by Eom and Faris (Eom & Farris, 1996), who, however, use the number of times an author is cocited with him/herself as a way to determine the author set to be analyzed.

White (2003, p.1253) also discussed the issue of diagonal values in the cocitation matrix (Howard D. White, 2003). He believes that “the most meaningful entry would be a count of the publications in which two or more of the author’s works are jointly cited.”

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