The predictability of the Hirsch index evolution

The h-index can be used as a predictor of itself. However, the evolution of the h-index with time is shown in the present investigation to be dominated for several years by citations to previous publications rather than by new scientific achievements. This inert behaviour of the h-index raises questions, whether the h-index can be used profitably in academic appointment processes or for the allocation of research resources. Introduction Due to its simplicity the so-called Hirsch index or h-index has become attractive as a frequently used metric for describing the scientific achievements of a researcher. It was introduced by Hirsch (2005) as the largest number h of publications of a scientist which have received at least h citations each. This means h = max{r | c(r) ≥ r}. Here c(r) denotes the number of citations to the paper at rank r, after the papers have been sorted according to decreasing c(r). In spite of several weaknesses and in spite of doubts how representative this measure is, the hindex has become popular and is often used in academic appointment processes and evaluation procedures of research projects. Hirsch (2007) determined a high correlation comparing the h-index values of researchers after 12 years and after 24 years of their careers. He concluded that “the h-index has the highest abibility to predict future scientific achievement”. Utilizing a complicated fit with 18 parameters, Acuna, Allesina, and Kording (2012) were able to predict the future h-index rather accurately for several years. It is controversial (Rousseau and Hu, 2012) whether such an approach is meaningful. In a validation study Garcia-Perez (2013) showed that the predicted h-index trajectories overestimate the future h indices more and more for later and later target years. I have recently demonstrated (Schreiber, 2013) that the increase of the h-index with time after a given point of time (e.g., the appointment year or the evaluation year) is for several years not related very much to the scientific achievements after that date. Rather the growth of the h-index is nearly the same for several years, irrespective of whether further work had been published or not after that date. In my previous publication I have presented examples for the rather smooth increase of the hindex with time thus confirming that the h-index is a good predictor of itself. However, I have also presented evidence in 4 examples that the growth of the h-index does not depend very much on the factual performance for several years in the future but rather results mostly from previous, often rather old publications. As evidence I had selected the most impressive example years so that the deviations were small for a particularly long time interval and not representative. It is the purpose of the present investigation to analyze quantitatively the duration for which the h-index remains unchanged or only slightly changed. Figure 1: The Hirsch index h = hy(y) for the publication record of the present author (top line). The dependence of hs(y) is shown for s = 1976, 1977, ... (from bottom to top). For the years s = 1980, 1990, and 2000 thick broken lines are utilized. y is the year of evaluation, s is the last year from which publications are taken into consideration. The citation data and the calculation of the h-index I harvested my own citation record from the ISI Web of Science database in March 2013. I determined the citations up to a given year y and counted the publications with high citation frequencies selectively, namely considering only publications up to a certain year s ≤ y. This yields the selective h-index hs(y) for the year y, under the assumption that I had stopped publishing in year s. Of course, if s = y then the usual h-index h = hy(y) is obtained. As h and likewise hs(y) are restricted to integer values, a graphical representation of hs(y) curves is very difficult to survey, because many values coincide. Therefore I had restricted by previous investigation (Schreiber, 2013) to selective values of s and discussed the resulting curves qualitatively. I have repeated the analysis now with the updated data for the interpolated version of the hindex, which is obtained after a piecewise linear interpolation of the citation distribution c(r) between r and r + 1, as suggested and utilized previously by Rousseau (2006), van Eck and Waltman (2008) and myself (Schreiber, 2008, 2009). The interpolated h-index then results from the solution of c(h) = h. By truncating the interpolated index values one obtains the usual integer results. In Fig. 1 the determined hs(y) curves are presented, showing the expected rather smooth behaviour. The original h-index h = hy(y) shows a steady increase with a slope of approximately one index point per year. Selecting a particular year s, one can see that for a duration of several years t = y – s the deviation d = hy(y) – hs(y) remains rather small, 0 5 10 15 20 25 3