Abstract
This paper proposes a simple graphical mechanism for facilitating the comparison between an author’s citation count, as measured by the Euclidean Index (Perry and Perry in Am Econ Rev 106:2722–2741, 2016), and the visibility of the journals within which an author’s articles were published, as measured by the Weighted Euclidean Index (Haley in PLoS ONE, 2019a. https://doi.org/10.1371/journal.pone.0212760). The goal is to help research review bodies easily grasp the distinction between these two forms of scholarly accomplishment and to also provide them a transparent way to articulate to scholars how the evaluation committee intends to balance these two modes of scholarly accomplishment. The robustness of the proposed composite index is also assessed.
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Notes
Other functional forms are, of course, possible, but the focus here is to keep the combination function simple to facilitate the exposition of the graphical depiction that follows. It is worth noting that scaling \(\hbox{AIp}_i\) by a scalar \(t \in [0,1]\) may not preserve the ranking of the composite function. It is also worth noting that the composite function values can be mirrored using another type of Weighted Euclidean Index:
$$\begin{aligned} \iota _z(\mathbf{x})\equiv \sqrt{\sum ^{n}_{i=1}z_ix^{2}_{i}}, \end{aligned}$$where \(z_i \in [0,1]~ \forall ~ i\). However, this set of weights is not unique, and, more importantly, the alternative weights \(\{z_i\}_{i=1}^n\) are complicated functions of \(\beta ,x_i,\) and \(\hbox{AIp}_i\). This casts aspersions on the usefulness of \(\iota _z(\mathbf{x})\) as an alternative representation for \(\tilde{\iota }(\mathbf{x};\beta )\).
They can also be interpreted as level curves of the bivariate \(\tilde{\iota }(\mathbf{x};\beta )\) function.
See also, Glänzel and Moed (2013).
A radius of 0.03 would induce perturbed \(\beta\) values in the [0.47, 0.53] interval.
Note that \(\iota _W(\mathbf{x})\) includes journal-based weights and all the citations. In contrast, the other extreme, \(\beta = 1\), entirely dismisses journal visibility. In this sense the generalization is inherently tipped in favor of citation-based measurement, though less so than the unweighted Euclidean Index.
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The author is very grateful to David Fuller and M. Kevin McGee for helpful conversations, comments, mathematical insights, and suggestions.
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Haley, M.R. Combining the weighted and unweighted Euclidean indices: a graphical approach. Scientometrics 123, 103–111 (2020). https://doi.org/10.1007/s11192-020-03368-x
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DOI: https://doi.org/10.1007/s11192-020-03368-x