Spline fitting tool for scientometric applications: estimation of citation peaks and publication time-lags

Transcription

1 Spline fitting tool for scientometric applications: estimation of citation peaks and publication time-lags By: Hicham Sabir Presentation to: 21 STI Conference, September 1th, 21

2 Description of the problem Citation analysis is frequently used to compute impact measures and evaluate the performance of various types of entities. One key bibliometric feature is the citation peak? 2

3 Description of the problem Identifying papers published with a given grant is an important challenge for research evaluation. One can use a publication window which includes the peak in the number of papers associated to a grant.? We need a method to automatically extract the system s characteristics. 3

4 Two main approaches for curve fitting Two approaches to extract the system s constants Fitting according to a predictive model Interpolating with a generalized function Number of collaborations y = 1.669x.865 R² = Number of papers (Arbitrary dataset) 4

5 Two main approaches for curve fitting Two approaches to extract the system s constants Fitting according to a predictive model Interpolating with a generalized function? No general analytic model Many different forms to choose from 5

6 Interpolation using generalized functions Arbitrary dataset in the Citation Vs. Time form y x Examples of generalized functions for interpolation: Fourier polynomials, Lagrange polynomials, Greene s function, Dirac s function, A special family: piecewise-defined functions 6

7 Interpolation using generalized functions Most generalized function apply to specific distributions : Lagrange polynomials Greene s function Dirac s function Whittaker-Shannon Nearest neighbor Citation datasets? Distributions in the Lagrange form Inhomogeneous differential equations Dirac peak Continuous-time band-limited signals Slowly varying phenomena Do citation datasets follow one of these trends? If not, need for a more general tool 7

8 Interpolation using generalized functions Observed raw data on citations received by papers, journals institutions etc are very often incomplete. Objective: the interpolation method should be robust against Missing information Non homogeneous data density Quick variations Large variety of general shapes 8

9 Interpolation using generalized functions Most generalized functions can t interpolate such diverse datasets: Interpol Data Set n t kt x( t) xk sinc k 1 T Whittaker-Shannon fails to interpolate datasets with non equally spaced samples Interpolation Data Set

10 Interpolation using generalized functions Most generalized functions can t interpolate such diverse datasets: Interpol Data Set n n x x i L( x) y j j 1 i 1, j i xi x j Lagrange polynomial fails to interpolate datasets with missing information Interpolation Data Set 1

11 Interpolation using generalized functions Piecewise-defined functions can interpolate very diverse datasets: Interpolation Data Set Interpolation Data Set Splines are piecewise-defined functions using polynomials 11

12 Building the interpolating NCS We use in this work natural cubic splines (NCS) to interpolate n+1 given points. 4n unknowns to be solved using 4n equations 12

13 Building the interpolating NCS (Green & Silverman, 1994) 13

14 Building the interpolating NCS M is strictly diagonally dominant by column M is non-singular (Levy Desplanques theorem) 14

15 Building the interpolating NCS Data Set Spline Interpolation 6 y x 15 2 The interpolation is correct The general shape of the dataset is not taken into account 15

16 Soothing natural cubic splines We create a smoothed dataset The penalized sum of squares (Pss) is a compromise between : The sum of squares : The roughness : Smoothing parameter 16

17 Soothing natural cubic splines The penalized sum of squares (Pss) can be written The smoothed dataset 17

18 Soothing natural cubic splines Data Set Spline Interpolation Smooth Correction y x 18

19 Application to citation peaks This method gives a continuous description of the citation curve. Number of citations to 1996 papers p p Peak = 3 years Blood Fit when max point is excluded Year It allows to extract citation peaks and inflexion points from the raw data. 19

20 Application to citation peaks It does not depend on the shape of the curve. Number of citations to 1996 papers Peak = 3 years Peak = 5 years Jrnl of Personality & Social Psychol. British Medical Journal Blood Fit when max point is excluded Peak > 12 years Year 2

21 Application to citation peaks Low computational cost: determination of the citation peak of 12,13 journals. 25 Number of journals Without Splines With Splines Citation peak year of 1996 papers 21

22 Application to publication time-lags Project on the Standard Research Grants (SRG) program of the Social Sciences & Humanities Research Council (SSHRC). Objective: Assessing the effect of research funding on the scientific output of researchers. Problem: The identification of papers that are published with the financial support of specific SRGs is not trivial. Measure the time-lags from first year of financial support to the publication peak. Identify a time window around that peak. 22

23 Application to publication time-lags Example of correction using splines: The case of anthropology 45 Number of publications Time-lag following the first year of funding (Years) 23

24 Application to publication time-lags Example of correction using splines: The case of anthropology 45 Number of publications Time-lag following the first year of funding (Years) 24

25 Application to publication time-lags Subfield Estimated publication peak Research Conference papers Spline Classic Spline Classic Anthropology Economics Education History Literature & Modern Languages Management, Administrative Studies Philosophy Political Science Psychology All humanities

26 Number of publications Application to publication time-lags Identification of the time window Years after first funding 26

27 Conclusion Spline interpolation for citations and publications time-lag : Low computational cost Applies to various data shapes Compensates for the imperfections in the data A robust tool to extract the system s characteristics (Citation peak, Time-lag before publication, Time-windows, ) 27

28 Contact information Hicham Sabir, MSc Research Analyst Thank you for your time! 28