1.4.5 Individual h-index (3 variations)

Hirsch (2005) indicates that there will be large differences in typical h-values in different fields. Academic disciplines differ in the average number of references per paper and the average number of papers published by each academic. As a general rule of thumb h-indices are much higher in the Natural Sciences than in the Social Sciences and Humanities, although there is a large variability even within these fields.

Podlubny (Podlubny, 2005 and Podlubny and Kassayova, 2006) showed that for nine broadly defined disciplines the average ratio of total citations to the number of citations in mathematics varied considerably (Mathematics: 1, Engineering/technology: 5, Biology: 8, Earth/space sciences: 9, Social/behavioral sciences: 13, Chemistry: 15, Physics: 19, Biomedical Research: 78, Clinical Medicine: 78).

Similarly, Iglesias & Pecharroman (2006) calculated the average number of citations/paper in the 21 different ISI fields and used this to design a normalization factor. Unfortunately, the discipline areas used in neither studies map closely enough onto the categories used by Google Scholar to use these normalization factors in Publish or Perish. However, they do show that comparisons of bibliometric data across fields are generally inappropriate.

Part of the differences between disciplines are caused by the fact that academics in the Natural Sciences typically publish more (and often shorter) articles and also publish with a large number of co-authors, while academics in the Social Sciences and Humanities typically published fewer (and longer) articles (or books) and publish with fewer co-authors.

However, differences in the number of co-authors also seem apparent within the same discipline. For instance, North American academics tend to publish articles with a larger number of co-authors than European academics. Since 1990, papers in the North-American Academy of Management Journal on average have 2.24 authors, papers in the British Journal of Management 2.01 authors, and papers in the European Management Journal 1.84 authors.

Three implementations of the individual h-index

Hirsch (2005) suggested that in the case of large differences in the number of co-authors, it might be useful to normalize the h-index by a factor that reflects the average number of co-authors. Here I discuss three different implementations.

• The first version of the Individual h-index was proposed by Batista, Campiteli, Kinouchi & (2006). It divides the standard h-index by the average number of authors in the articles that contribute to the h-index, in order to reduce the effects of co-authorship; the resulting index is called hI.
• PoP also implements an alternative individual h-index, hI,norm, that takes a different approach: instead of dividing the total h-index, it first normalizes the number of citations for each paper by dividing the number of citations by the number of authors for that paper, then calculates hI,norm as the h-index of the normalized citation counts. This approach is much more fine-grained than both Batista et al.'s and Schreibers; we believe that it more accurately accounts for any co-authorship effects that might be present and that it is a better approximation of the per-author impact, which is what the original h-index set out to provide.
• The third variation is due to Michael Schreiber (Schreiber, 2008). Schreiber's method uses fractional paper counts instead of reduced citation counts to account for shared authorship of papers, and then determines the multi-authored hm index based on the resulting effective rank of the papers using undiluted citation counts.

The three different metrics are very similar for authors with a small number of co-authors. However, both Batista and Schreiber penalize authors who publish with a lot of co-authors. Which of the three implementations is preferable depends on the importance one attaches to single authorships.