The inconsistency of the h-index

The h-index is a popular bibliometric indicator for assessing individual scientists. We criticize the h-index from a theoretical point of view. We argue that for the purpose of measuring the overall scientific impact of a scientist (or some other unit of analysis) the h-index behaves in a counterintuitive way. In certain cases, the mechanism used by the h-index to aggregate publication and citation statistics into a single number leads to inconsistencies in the way in which scientists are ranked. Our conclusion is that the h-index cannot be considered an appropriate indicator of a scientist's overall scientific impact. Based on recent theoretical insights, we discuss what kind of indicators can be used as an alternative to the h-index. We pay special attention to the highly cited publications indicator. This indicator has a lot in common with the h-index, but unlike the h-index it does not produce inconsistent rankings

A simple alternative to the h-index

The h-index is a popular bibliometric performance indicator. We discuss a fundamental problem of the h-index. We refer to this problem as the problem of inconsistency. There turns out to be a very simple bibliometric indicator that has similar properties as the h-index and that does not suffer from the inconsistency problem. We argue that the use of this indicator is preferable over the use of the h-index

Spectroscopic Observation and Analysis of HII regions in M33 with MMT: Temperatures and Oxygen Abundances

The spectra of 413 star-forming (or HII) regions in M33 (NGC 598) were observed by using the multifiber spectrograph of Hectospec at the 6.5-m Multiple Mirror Telescope (MMT). By using this homogeneous spectra sample, we measured the intensities of emission lines and some physical parameters, such as electron temperatures, electron densities, and metallicities. Oxygen abundances were derived via the direct method (when available) and two empirical strong-line methods, namely, O3N2 and N2. In the high-metallicity end, oxygen abundances derived from O3N2 calibration were higher than those derived from N2 index, indicating an inconsistency between O3N2 and N2 calibrations. We presented a detailed analysis of the spatial distribution of gas-phase oxygen abundances in M33 and confirmed the existence of the axisymmetric global metallicity distribution widely assumed in literature. Local variations were also observed and subsequently associated with spiral structures to provide evidence of radial migration driven by arms. Our O/H gradient fitted out to 1.1 $R_{25}$ resulted in slopes of $-0.17\pm0.03$, $-0.19\pm0.01$, and $-0.16\pm0.17$ dex $R_{25}^{-1}$ utilizing abundances from O3N2, N2 diagnostics, and direct method, respectively.Comment: Accepted for publication in Ap

Inter-field nonlinear transformation of journal impact indicators: The case of the h-index

[EN] Impact indices used for joint evaluation of research items coming from different scientific fields must be comparable. Often a linear transformation -a normalization or another basic operation-is considered to be enough for providing the correct translation to a unified setting in which all the fields are adequately treated. In this paper it is shown that this is not always true. The attention is centered in the case of the h-index. It is proved that it that cannot be translated by means of direct normalization preserving its genuine meaning. According to the universality of citation distribution, it is shown that a slight variant of the h-index is necessary for this notion to produce comparable values when applied to different scientific fields. A complete example concerning a group of top scientists is shown.The first author was supported by Ministerio de Economia, Industria y Competitividad under Research Grant CSO2015-65594-C2-1R Y 2R (MINECO/FEDER, UE). The second author was suported by Ministerio de Economia, Industria y Competitividad and FEDER under Research Grant MTM2016-77054-C2-1-PFerrer Sapena, A.; Sánchez Pérez, EA. (2019). Inter-field nonlinear transformation of journal impact indicators: The case of the h-index. Journal of Interdisciplinary Mathematics. 22(2):177-199. https://doi.org/10.1080/09720502.2019.1616913S177199222Geuna, A., & Piolatto, M. (2016). Research assessment in the UK and Italy: Costly and difficult, but probably worth it (at least for a while). Research Policy, 45(1), 260-271. doi:10.1016/j.respol.2015.09.004Hicks, D. (2012). Performance-based university research funding systems. Research Policy, 41(2), 251-261. doi:10.1016/j.respol.2011.09.007Hirsch, J. E. (2005). An index to quantify an individual’s scientific research output. Proceedings of the National Academy of Sciences, 102(46), 16569-16572. doi:10.1073/pnas.0507655102Egghe, L. (2010). The Hirsch index and related impact measures. Annual Review of Information Science and Technology, 44(1), 65-114. doi:10.1002/aris.2010.1440440109Van Leeuwen, T. (2008). Testing the validity of the Hirsch-index for research assessment purposes. Research Evaluation, 17(2), 157-160. doi:10.3152/095820208x319175Alonso, S., Cabrerizo, F. J., Herrera-Viedma, E., & Herrera, F. (2009). h-Index: A review focused in its variants, computation and standardization for different scientific fields. Journal of Informetrics, 3(4), 273-289. doi:10.1016/j.joi.2009.04.001Imperial, J., & Rodríguez-Navarro, A. (2007). Usefulness of Hirsch’s h-index to evaluate scientific research in Spain. Scientometrics, 71(2), 271-282. doi:10.1007/s11192-007-1665-4Aoun, S. G., Bendok, B. R., Rahme, R. J., Dacey, R. G., & Batjer, H. H. (2013). Standardizing the Evaluation of Scientific and Academic Performance in Neurosurgery—Critical Review of the «h» Index and its Variants. World Neurosurgery, 80(5), e85-e90. doi:10.1016/j.wneu.2012.01.052Waltman, L., & van Eck, N. J. (2011). The inconsistency of the h-index. Journal of the American Society for Information Science and Technology, 63(2), 406-415. doi:10.1002/asi.21678Rousseau, R., García-Zorita, C., & Sanz-Casado, E. (2013). The h-bubble. Journal of Informetrics, 7(2), 294-300. doi:10.1016/j.joi.2012.11.012Burrell, Q. L. (2013). The h-index: A case of the tail wagging the dog? Journal of Informetrics, 7(4), 774-783. doi:10.1016/j.joi.2013.06.004Schreiber, M. (2013). How relevant is the predictive power of the h-index? A case study of the time-dependent Hirsch index. Journal of Informetrics, 7(2), 325-329. doi:10.1016/j.joi.2013.01.001Khan, N. R., Thompson, C. J., Taylor, D. R., Gabrick, K. S., Choudhri, A. F., Boop, F. R., & Klimo, P. (2013). Part II: Should the h-Index Be Modified? An Analysis of the m-Quotient, Contemporary h-Index, Authorship Value, and Impact Factor. World Neurosurgery, 80(6), 766-774. doi:10.1016/j.wneu.2013.07.011Schreiber, M. (2013). A case study of the arbitrariness of the h-index and the highly-cited-publications indicator. Journal of Informetrics, 7(2), 379-387. doi:10.1016/j.joi.2012.12.006Hicks, D., Wouters, P., Waltman, L., de Rijcke, S., & Rafols, I. (2015). Bibliometrics: The Leiden Manifesto for research metrics. Nature, 520(7548), 429-431. doi:10.1038/520429aDienes, K. R. (2015). Completing h. Journal of Informetrics, 9(2), 385-397. doi:10.1016/j.joi.2015.01.003Ayaz, S., & Afzal, M. T. (2016). Identification of conversion factor for completing-h index for the field of mathematics. Scientometrics, 109(3), 1511-1524. doi:10.1007/s11192-016-2122-zWaltman, L. (2016). A review of the literature on citation impact indicators. Journal of Informetrics, 10(2), 365-391. doi:10.1016/j.joi.2016.02.007Van Eck, N. J., & Waltman, L. (2008). Generalizing the h- and g-indices. Journal of Informetrics, 2(4), 263-271. doi:10.1016/j.joi.2008.09.004Egghe, L., & Rousseau, R. (2008). An h-index weighted by citation impact. Information Processing & Management, 44(2), 770-780. doi:10.1016/j.ipm.2007.05.003Egghe, L. (2006). Theory and practise of the g-index. Scientometrics, 69(1), 131-152. doi:10.1007/s11192-006-0144-7Iglesias, J. E., & Pecharromán, C. (2007). Scaling the h-index for different scientific ISI fields. Scientometrics, 73(3), 303-320. doi:10.1007/s11192-007-1805-xEgghe, L. (2008). Examples of simple transformations of the h-index: Qualitative and quantitative conclusions and consequences for other indices. Journal of Informetrics, 2(2), 136-148. doi:10.1016/j.joi.2007.12.003Schreiber, M. (2015). Restricting the h-index to a publication and citation time window: A case study of a timed Hirsch index. Journal of Informetrics, 9(1), 150-155. doi:10.1016/j.joi.2014.12.00

On Saaty's and Koczkodaj's inconsistencies of pairwise comparison matrices

The aim of the paper is to obtain some theoretical and numerical properties of Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices (PRM). In the case of 3 × 3 PRM, a differentiable one-to-one correspondence is given between Saaty’s inconsistency ratio and Koczkodaj’s inconsistency index based on the elements of PRM. In order to make a comparison of Saaty’s and Koczkodaj’s inconsistencies for 4 × 4 pairwise comparison matrices, the average value of the maximal eigenvalues of randomly generated n × n PRM is formulated, the elements aij (i < j) of which were randomly chosen from the ratio scale ... ... with equal probability 1/(2M − 1) and a ji is defined as 1/a ij . By statistical analysis, the empirical distributions of the maximal eigenvalues of the PRM depending on the dimension number are obtained. As the dimension number increases, the shape of distributions gets similar to that of the normal ones. Finally, the inconsistency of asymmetry is dealt with, showing a different type of inconsistency

Real income growth and revealed preference inconsistency

If a smooth demand function violates the strong axiom of revealed preference, the income and prices can follow a cycle and returm to their starting values even though real income is always rising. We show how real income growth along the "worst" revealed preference cycle depends on the range of price variation and on violations of the Slutsky conditions. We relate this result to proposed reforms of the consumer price index and use it to justify a new index of local demand inconsistency. We also use the Slutsky matrix to determine an upper bound on the number of observations required to detect revealed preference inconsistency