A citation index for principal investigators

Abstract

A new citation index $h_{\mathrm{PI}}$ for principal investigators (PIs) is defined in analogy to Hirsch’s index h, but based on renormalized citations of a PI’s papers. To this end, the authors of a paper are divided into two groups: PIs and non-PIs. A PI is defined as an assistant, associate or full professor at a university who supervises an individual research program. The citations for each paper of a certain PI are then divided by the number of PIs among the authors of that paper. Data are presented for a sample of 48 PIs of physics and physics-related engineering departments from a private research-oriented U.S. university using the ISI Web of Science citations database. The main result is that individual rankings based on h and $h_{\mathrm{PI}}$ differ substantially. Also, to a good approximation across the sample of 48 PIs, one finds that $h_{\mathrm{PI}} = h \,/ \sqrt{<}N_{\mathrm{PI}}{>}$ where ${<}N_{\mathrm{PI}}{>}$ is the average number of principal investigators for the papers of the PI in question. Similarly, $h_{\mathrm{PI}} = \frac{1}{2} \sqrt{C_{\mathrm{tot}}\,/<N_{\mathrm{PI}}>}$, where $C_{\mathrm{tot}}$ is the total number of the PI’s citations. Approaches to broadending the scope of h or $h_{\mathrm{PI}}$ with regard to highly cited papers are compared, and a new metric called $h_x$ is introduced for such papers which represents the average number of citations exceeding the minimum of $h^2$ in the h-core. A recent proposal to determine an optimum h-index is also discussed in relationship to actual citation data.