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Weighted indices for evaluating the quality of research with multiple authorship

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Abstract

Devising an index to measure the quality of research is a challenging task. In this paper, we propose a set of indices to evaluate the quality of research produced by an author. Our indices utilize a policy that assigns the weights to multiple authors of a paper. We have considered two weight assignment policies: positionally weighted and equally weighted. We propose two classes of weighted indices: weighted h-indices and weighted citation h-cuts. Further, we compare our weighted h-indices with the original h-index for a selected set of authors. As opposed to h-index, our weighted h-indices take into account the weighted contributions of individual authors in multi-authored papers, and may serve as an improvement over h-index. The other class of weighted indices that we call weighted citation h-cuts take into account the number of citations that are in excess of those required to compute the index, and may serve as a supplement to h-index or its variants.

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Notes

  1. The assumption that the position of an author indicates his/her contribution may not be applied to all areas of research as the conventions followed among different areas might be different e.g. in biological domains, sometimes, the last author is considered to be the lead author. A brief discussion about how the order of weights can be made in conformance with the order of authors according to the conventions followed by a research field or a research group is given in Abbas (2011).

  2. Note that k = 1 means that there is only one author, who is the first author as well as the last author. As a result, there is no difference between the weights of the first author and the last author.

  3. We consider this example with relatively a smaller h-index due to space limitations and just to illustrate the ideas. One can create an example with relatively a larger h-index.

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Authors and Affiliations

  1. Department of Computer Engineering, Aligarh Muslim University, Aligarh, 202002, India

    Ash Mohammad Abbas

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Correspondence to Ash Mohammad Abbas.

Appendix 1

Appendix 1

There are a couple of questions: (i) Can there be a positional weight assignment scheme where the decrease in the weights of later authors is more gradual such as 55:45 or 60:40? The answer is yes, we have discussed such a scheme that we called generalized linear weights in Abbas (2010). The other question is: Why should one consider such a scheme, why not geometric weights? We have discussed in Abbas (2010) that the ratio of the weights of the first author and the last author in a geometric weight assignment scheme is

$$ \frac{w_{1}}{w_{k}}={2^{k-1}}. $$

At least a linear decrease in the weights proposed in this paper is far better than an exponential decrease of geometric weights. Coming to the harmonic weights, the ratio of weights [as discussed in Abbas (2010)] of the first and last author is,

$$ \frac{w_{1}}{w_{k}}=k. $$

In other words, the ratio of the first and the last author in the positional weights is comparable to that of the harmonic weights.

Actually, the purpose of this paper is to propose weighted indices: weighted citation h-cut, and the weighted citation aggregate. The indices proposed in this paper are open to any weight assignment scheme which an evaluator (of the quality of research produced by an author) deems fit for a particular research discipline or research group. The assignment of weights is an issue in itself and can be addressed separately.

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Abbas, A.M. Weighted indices for evaluating the quality of research with multiple authorship. Scientometrics 88, 107–131 (2011). https://doi.org/10.1007/s11192-011-0389-7

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