$h_{PI}$: The Citation Index for Principal Investigators

TL;DR

This paper introduces a new citation index, $h_{PI}$, for principal investigators that adjusts for co-authorship, providing a different ranking metric than the traditional $h$-index, and explores its properties and implications.

Contribution

The paper defines and analyzes the $h_{PI}$ index, a novel metric for PIs based on renormalized citations, and derives relationships between $h_{PI}$, $h$, and total citations.

Findings

$h_{PI}$ differs significantly from $h$-index rankings.

$h_{PI}$ approximately equals $h / \, ext{sqrt}(<N_{PI}>)$.

$h_{PI}$ relates to total citations as $h_{PI} = rac{1}{2} ext{sqrt}(C_{tot} / <N_{PI}>)$.

Abstract

A new citation index $h_{PI}$ 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 who are senior faculty members of physics and physics-related engineering departments at 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 $h_{PI}$ differ substantially. Also, to a good approximation across the sample of 48 PIs, one finds that $h_{PI} = h \,/ \sqrt{<N_{PI}>}$ where <$N_{PI}$> is the average number of principal investigators on the papers of a particular PI. In addition, $h_{PI} = \frac{1}{2} \sqrt{C_{tot}\,/<N_{PI}>}$, where $C_{tot}$ is the total number of citations. Approaches to broadening the scope of $h$ or $h_{PI}$ are discussed briefly, and a new metric for highly cited papers called $h_x$ is introduced which represents the average number of citations exceeding the minimum of $h^2$ in the $h$-core.