Ranking Algorithm Review

\(\varepsilon\) Ranking Algorithm Review:

The \(\varepsilon\)-index uses a researcher's citation data from Google Scholar, requiring key pieces of information: citations of the top-cited paper, the i10-index, the h-index, and the year of the first peer-reviewed publication. The model involves calculating a power-law-like relationship between citation frequencies (\(i_{10}, h\)) and values (\(10, h, \text{ and } cm\)), then applying a linear model (\(y \sim \alpha + \beta x\)) where \(y\) is the citation frequency and \(x\) is the citation value. The \(\varepsilon\)-index is derived as the residual from this model, offering a relative metric of citation performance.

• Ranking algorithm used to establish a relationship between citation frequencies and their corresponding values, which is then indexed, smoothed, and standardized.
• The algorithm works by a simple linear model \(y = \alpha + \beta_x\) where \[ y = \log_e = \left| \begin{array}{c} i_{10} \\ h \\ 1 \end{array} \right| \] and \[ x = \log_e = \left| \begin{array}{c} 10 \\ h \\ c_{m} \end{array} \right| \]
• Where (\(h\) is both a frequency (\(y\)-axis) and a value (\(x\)-axis).
• The data are then standardized to index \(A_{rel}\) - Citation mass which then becomes the dependent variable in the linear model \(A_{rel} = \lambda + \Theta \log_e t \)
• The residual \((\varepsilon)\) \(A_{Rel}\) then gets computed as a measure of citation performance relative to the sample data.
• The residual \((\varepsilon)\) then gets ranked highest to lowest such that positive values of \((\varepsilon)\) are above "expected performance" and negative values are below "expected performance".

Note: Data Pulled from Google Scholar February 2025. Special thanks to Alex Strong for his contribution to gathering this data.
Note: Faculty without Google Scholar profiles associated with the University of Arizona are not included.
Note: Faculty with less than 30% Research Assignments are not included.
Note: Questions, Comments, and Concerns can be directed to ALVSCE Data Solutions.

See Bradshaw CJA, Chalker JM, Crabtree SA, Eijkelkamp BA, Long JA, Smith JR, et al. (2021) A fairer way to compare researchers at any career stage and in any discipline using open-access citation data. PLoS ONE 16(9): e0257141.