Metrics: More h-indices

Note: This tutorial was originally written for Publish or Perish version 4 and all screenshots come from this version. However, the information as such is also applicable for the latest Publish or Perish versions 5 and 6.

There are far more metrics available in Publish or Perish that might interest you if you are a bibliometric researcher or just fascinated by metrics. You can find them by scrolling down in this box.

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Advanced metrics for advanced users

The advanced metrics have been hidden from the standard view, as they are irrelevant for most PoP users that tend to be interested in total citations and the h-index only. Formal definitions of all metrics are provided here: http://www.harzing.com/pophelp/metrics.htm

That said, there are two additional h-index variants that have attracted considerable attention, the Hc-index and the hI index. Hence I discuss them here.

Hc-index (contemporary h-index)

The Contemporary h-index was proposed by Antonis Sidiropoulos, Dimitrios Katsaros, and Yannis Manolopoulos in their paper Generalized h-index for disclosing latent facts in citation networks, arXiv:cs.DL/0607066 v1 13 Jul 2006.

It adds an age-related weighting to each cited article, giving (by default; this depends on the parametrization) less weight to older articles. The weighting is parametrized; the Publish or Perish implementation uses gamma=4 and delta=1, like the authors did for their experiments. This means that for an article published during the current year, its citations count four times. For an article published 4 years ago, its citations count only once (4/4). For an article published 6 years ago, its citations count 4/6 times, and so on.

Difference between h-index and hc-index larger for older academics

The difference between the h-index and the hc-index will typically be larger for older academics than for younger academics. However, mid-career academics who have done most of their significant work immediately post-PhD will also have a relatively low hc-index.Going back to our example for the hI,annual, produces the following comparison. For the younger academics the hc-index is fairly similar to their regular h-index, whereas for the older academics it is substantially lower.

Years active h-index hc-index hc/h
9
24
26
1.08
20
45
41
0.91
29
69
53
0.77
40
82
55
0.67

The hc-index even exceeds the h-index for the early career academic, who has done some of his most impactful work in the last 4 years. This also points to a limitation of the h-index: it doesn’t work very well if you limit the search to for instance the last 5 years as nearly always becomes higher than the h-index.

hI index (Individual h-index)

The best-known alternative to the hI,norm is the hI index. It was proposed by Pablo D. Batista, Monica G. Campiteli, Osame Kinouchi, and Alexandre S. Martinez (2006) in their paper Is it possible to compare researchers with different scientific interests?, Scientometrics, 68(1): 179-189.

hI index punishes co-authorship severely

The hI simply divides the h-index by the average number of authors in the articles contributing to the h-index. However, this can easily lead to anomalies as the hI-index could be brought down by one modestly cited article with a large number of co-authors. This is true even if most of the academic’s citations come from single-authored articles. In general, it includes a vey strong “punishment” for co-authorship.

hI, norm favours a more differentiated co-authorship correction

The hI,norm only reduces the number of citations for each paper by accounting for the number of co-authors. This means that papers with a large number of citations can still be included in the h-index if their number of citations after co-author correction is high enough. Reviewing our example for the hI,norm, produces the following comparison. As we can see the “punishment” for co-authorship for the hI index is very significant and can completely reverse disciplinary comparisons.

Discipline h-index hI,norm hI,norm/h hI hI/h
Social Sciences 45 37 0.82 25.63 0.57
Physics 44 20 0.46 9.05 0.21
Social Sciences 23 20 0.87 9.12 0.46
Humanities 18 18 1.00 18.00 1.00

The Physics Professor’s h-index is 2.5 times as high as that of the Humanities Professor. His hI,norm is similar, but his hI is only half of that of the Humanities Professor.

Conclusion: which individual h-index to use?

Someone’s preference for this individual h-index over the hI,norm depends on the importance one places on single-authored papers. I would argue that the hI,norm is closest to the initial philosophy of the h-index by focusing on citations, rather than on papers. However, in disciplines where single-authorship is very highly valued, the hI might be a valid alternative.

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