27th International Conference on Science, Technology and Innovation Indicators (STI 2023)

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20/04/2023| By

Henrique Pinheiro,

+ 1 David Campbell

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Abstract

The citation uptake of research papers in the non-scientific literature is often sparse. It is thus frequently reported as a proportion of cited papers instead of as an average of the papers’ citation counts. Citation-based indicators are commonly normalized by dividing a paper’s citation count (or binary score; 0 = not cited, 1 = cited) by the world average (or proportion) in the corresponding year, field and document type. Such ratio-based method can generate outliers when dealing with the binary scores. At low aggregation levels, these outliers can produce unreliable results. Here, a ratio-based method is compared to one in which the world’s proportion is subtracted from the papers’ scores using a set of universities as units of analysis. This difference-based method has two main advantages: interpretation of results is more transparent/straightforward, and outliers are less problematic, leading to narrower confidence intervals.

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Henrique Pinheiro*, Etienne Vignola-Gagné** and David Campbell***

0000-0002-2175-7518

Science-Metrix and Analytical and Data Services, Elsevier, Montréal, Canada and Amsterdam, the Netherlands

*** e.vignola-gagne@elsevier.com*

0000-0002-4948-4363

Science-Metrix and Analytical and Data Services, Elsevier, Montréal, Canada and Amsterdam, the Netherlands

0000-0003-3806-3237

Science-Metrix and Analytical and Data Services, Elsevier, Montréal, Canada and Amsterdam, the Netherlands

The citation uptake of research papers in the non-scientific literature is often sparse. It is thus frequently reported as a proportion of cited papers instead of as an average of the papers’ citation counts. Citation-based indicators are commonly normalized by dividing a paper’s citation count (or binary score; 0 = not cited, 1 = cited) by the world average (or proportion) in the corresponding year, field and document type. Such ratio-based method can generate outliers when dealing with the binary scores. At low aggregation levels, these outliers can produce unreliable results. Here, a ratio-based method is compared to one in which the world’s proportion is subtracted from the papers’ scores using a set of universities as units of analysis. This difference-based method has two main advantages: interpretation of results is more transparent/straightforward, and outliers are less problematic, leading to narrower confidence intervals.

Citations of research publications within the peer-reviewed literature are widely used as markers of an entity’s (e.g., a country, institution, researcher) scientific influence/impact. To enable proper comparisons across entities, the common practice is to divide each paper’s citation counts by the world average in the corresponding year, field and document type prior to averaging the normalized scores of an entity’s papers. This ratio-based method is commonly referred to as field normalization and aims to control for confounding factors that can influence the extent to which an entity’s publications get cited beyond the paper’s own performance (Waltman & van Eck, 2018).

With the advent of several alternative sources tracing the uptake of research publications beyond academia, a new range of citation-based indicators emerged. These indicators commonly quantify uptake as the proportion of cited papers, instead of as an average of their citation counts, to cope with the scarcity of several types of altmetric citations. Two such indicators making use of ratio-based normalization include the Equalized Mean-based Normalized Proportion Cited (EMNPC) and the Mean-based Normalized Proportion Cited (MNPC) (Thelwall, 2017). The EMNPC applies equal weights to all normalization strata, regardless of how its papers are distributed across them. As noted by Thelwall, issues associated with this strategy would require the exclusion of small groups, with no clear guideline for such a procedure. Therefore, the EMNPC is not considered further in this paper. The MNPC weights each paper equally in the same manner as the well-known Mean-Normalized Citation Score (MNCS).

After several rounds of experimentation with MNPC in an applied evaluation context, the authors concluded that ratio-based normalization of binary citation counts can generate outliers due to the rarity of citation events for some altmetrics. For example, if an entity has papers in 2 normalization strata (A and B) with different world’s proportions (0.5% for stratum A and 10% for stratum B), the ratio-normalized score of cited papers will be 200 (1/0.005) in stratum A and 10 in stratum B. In such an example, even 1 cited paper in stratum A could drastically influence the score of this entity.

More recently, new ratio-based alternatives to MNPC have been proposed, such as the Mantel-Haenszel Row Risk Ratio (MHRR) (Smolinsky, Klingenberg, & Marx, 2022), an improved version of the Mantel-Haenszel quotient (MHq) (Bornmann & Haunschild, 2018). Whereas MNPC weights each stratum in proportion to its appearance in the output of a given entity, the MHRR/MHq gives more weight to strata in which the citation event is more common, which effectively reduces the impact of outliers. MHRR effectively converts to MNPC by applying the weights of the latter to the former. MHRR’s weighting scheme adds further complexity for interpretation by decision makers. Plus, due to their respective normalization procedures, neither MNPC nor MHRR can be directly connected to an entity’s raw proportion of cited papers calculated over the pooled normalization strata.

In this paper, a difference-based approach is introduced that effectively deals with the problem of outliers while enabling an intuitive interpretation of the data that directly connects an entity’s actual (not normalized) proportion of cited papers and the normalized score. This is achieved by subtracting the world proportion in the corresponding stratum of a paper from its binary citation score. The paper discusses the relative strengths of this approach by comparing it with MNPC, relying, as an example, on the uptake in the policy-relevant literature (UPRL) data for a selected group of British and Indian academic institutions. The authors intend to subsequently add MHRR to the comparison.

**2. Methods**

Scopus was used to extract the peer-reviewed publications (articles,
conference papers, reviews) of a set of entities between 2016 and 2020.
Overton was matched to Scopus using DOIs to uncover which of the
retrieved papers were cited in the policy-relevant literature. The
average of the binary UPRL variable for an entity *e*’s papers
gives its (not normalized, or raw) share of cited papers in the policy
literature (\(p_{e}\)).

For this analysis, all British (187) and Indian (581) universities
with more than 30 papers and at least one paper cited in Overton were
selected to explore the reliability of the proposed approach across
institutions of differing sizes. The Overton coverage of British and
Indian policy documents differs drastically (Szomszor & Adie, 2022)
resulting in a diverse set of institutions in terms of their share of
papers cited.^{1}

Two methods were applied to normalize the binary UPRL data by year,
subfield (using Science‑Metrix
journal-based classification whereby multidisciplinary journals were
reclassified at paper level) and document type. The first (ratio-based)
method leads to MNPC_{R} (MNPC as in Thelwall, 2017, the
subcript R is added in reference to the ratio-based method). First, the
paper-level ratio of paper *i* (*r _{i}*) is
calculated as follows:

\[r_{i} = \left\{ \begin{array}{r} 0\ if\ c_{i} = 0 \\ \frac{1}{p_{f_{i}}^{w}}if\ c_{i} > 0,\ where\ paper\ i\ is\ from\ year,\ subfield \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ and\ document\ combination\ f \\ \end{array} \right.\ \]

Where,

*c*is the number of UPRL (or any other altmetric) citations of paper_{i}*i*\(p_{f_{i}}^{w}\) is the proportion of world’s papers cited in the same year, subfield and document combination

*f*as paper*i*.

It follows that *MNPC _{R}* for a given entity

\[{MNPC}_{R}^{e} = \frac{\sum_{i = 1}^{n}r_{i}}{n}\]

Where,

*n*is the number of papers of that entity.

The second (difference-based) is introduced and defined as follows.
First, the paper-level difference of paper *i*
(*d _{i}*) is calculated as follows:

\[d_{i} = \left\{ \begin{array}{r} 0 - p_{f_{i}}^{w}\ if\ c_{i} = 0 \\ 1 - p_{f_{i}}^{w}\ if\ c_{i} > 0,\ where\ paper\ i\ is\ from\ year,\ subfield \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ and\ document\ combination\ f \\ \end{array} \right.\ \]

It follows that *MNPC _{D}* (expressed in percentage
points) for a given entity equals:

\[{MNPC}_{D}^{e} = \frac{\sum_{i = 1}^{n}d_{i}}{n}\]

The world’s share of papers cited is weighted to reflect the distribution of entity e’s papers across normalization strata (also called synthetic world levels here) as follows:

\[p_{w}^{e} = \frac{\sum_{i = 1}^{n}p_{f_{i}}^{w}}{n}\]

Note that \({MNPC}_{D}^{e}\)
corresponds to the difference between the (not normalized, or raw) share
of cited papers of entity *e* (\(p_{e}\)) and \(p_{w}^{e}\). This property of the
difference-based method makes for a simple and intuitive
presentation/interpretation of results that directly connects an
entity’s raw share with the normalized difference to the world level.
The above indicators were computed using full counting.

**3. Results and Discussion**

Table 1 and Table 2 respectively present the distribution of paper-level scores normalized using the ratio-based and difference-based method for all papers in Scopus. For a small portion of papers (~2%), the ratio-based method led to scores that are much higher than the world level of 1 (> 10). For entities with few papers, just a few high scores could drastically change their average score. This is not the case using the difference-based method in which scores are bounded between -1 and +1. With the ratio-based method, all non-cited papers receive the same score (0), regardless of their corresponding world-level share (\(p_{f}^{w}\)). With the difference-based method, the scores of non-cited papers are lower if they belong to normalization strata with higher world-level shares (\(p_{f}^{w}\)).

Table 3 presents, for each of the top 10 institutions by number of
papers (among those selected), the raw \((p_{e})\) and normalized (using the ratio-
(*MNPC _{R}*) and difference-based
(

This table illustrates a key strength of difference-based
normalization over the ratio‑based method as pertains to the
interpretation of results. Based on *MNPC _{R}*,
University College London scores 145% above the world average. Using the
corresponding score with the difference-based method
(

Table 4 presents the share of institutions with convergent
*MNPC _{R}* and

Note: Both methods were compared based on columns MNCP_{R}
and \({\mathbf{p}_{\mathbf{e}}\mathbf{/p}}_{\mathbf{w}}^{\mathbf{e}}\)
as displayed in Table 3. \({\mathbf{p}_{\mathbf{e}}\mathbf{/p}}_{\mathbf{w}}^{\mathbf{e}}\)
was used as it provides a direct way to express the MNCP_{D} as
a ratio to the world level and, therefore, a viable approach to compare
MNCP_{D} and MNCP_{R}.

Share of convergent results + Share of divergent results = 100%.

The following two columns on divergent cases show that scores normalized using the ratio-based method considerably exceeded those based on the difference-based method more commonly than vice versa. This uneven distribution in the direction of divergent scores is linked to outliers generated by the ratio-based method, which are only located on the right tail of the distribution (Table 1). For smaller institutions, due to their limited number of papers, outliers will not always materialize. In such cases, the ratio-normalized scores will be more influenced by non-cited papers compared to difference-normalized scores. This happens because in the ratio-based method, a score of zero is assigned to all non-cited papers, the minimum possible score in this method, while the difference-based method allows for more nuanced scores of non-cited papers. As the number of papers increases, outliers are more likely to materialize, skewing the scores of these institutions. The last column shows the share of cases in which an observed change of signal (i.e. one of the indicators is above the world level while the other falls below it) was considered relevant according to the margins displayed in the table. Relevant changes in signal are more common in smaller institutions. For institutions with more than 1,000 papers, these discrepancies occur for less than 7% of institutions.

Table 5 presents 10 institutions with divergent
*MNPC _{R}* and

The potential effect of outliers is well illustrated by RK
University. In that case, the exclusion of 1 cited paper (out of 4)
moved its *MNPC _{R}* from 2.14 to 0.87. This paper is
from a normalization stratum (i.e. a conference paper in Networking
& Telecommunications from 2017) whose world’s share of cited papers
(\(p_{f}^{w}\)) is 0.35%. The
ratio-normalized score of this paper (

Note: To remove outliers, all papers from normalization strata
containing the highest ratio-normalized scores (*r _{i}*)
of each institution were excluded. For each institution having 10,000+
papers, the strata containing any of its top 5 papers based on

Simulations were also used to assess the sample size needed to
accurately estimate an entity’s *true* position, relative to the
world, using *MNPC _{R}* versus

Table 6 shows that the difference-based normalization produces
findings that are more likely to align with the *true* population
parameter for most of sample sizes. The exceptions concern those
institutions with *true* population parameters below the world
level for sample sizes ranging from 30 to 100, where
*MNPC _{R}* has a higher degree of agreement with the
population parameters than

*MNPC*discriminates non-cited papers across normalization strata with differing world shares of cited papers whereas_{D}*MNPC*cannot discriminate them._{R}*MNPC*, compared to_{D}*MNPC*, permits juxtaposing an entity’s raw share with its world equivalent in support a of a more nuanced interpretation of observed differences._{R}Cases of divergence between

*MNPC*and_{D}*MNPC*were shown to be due to outliers in the ratio-based paper level scores (_{R}*r*) used to compute_{i}*MNPC*. Accordingly, the difference-based method appears more reliable, especially for smaller institutions._{R}

*4.2 Limitations of the study*

Our conclusions are relevant for institutions of any size, but pending further validation we believe continued caution is warranted in the use of any normalization method when dealing with smaller institutions, especially when a relevant fraction of their papers are from subfields where shares at world level are low. Computing confidence intervals for difference-normalizations could help mitigate this limitation.

Regional coverage biases are documented in many altmetrics sources and should be taken into account within any comparative analysis.

The authors intend to incorporate MHRR in a subsequent version of this paper for a more inclusive assessment of the performance of the proposed difference-based method.

Bornmann, L., & Haunschild, R. (2018). Normalization of
zero-inflated data: An empirical analysis of a new indicator family and
its use with altmetrics data. *Journal of Informetrics*,
*12*(3), 998–1011. https://doi.org/10.1016/J.JOI.2018.01.010

Smolinsky, L., Klingenberg, B., & Marx, B. D. (2022).
Interpretation and inference for altmetric indicators arising from
sparse data statistics. *Journal of Informetrics*,
*16*(1), 101250. https://doi.org/10.1016/J.JOI.2022.101250

Szomszor, M., & Adie, E. (2022). Overton -- A bibliometric
database of policy document citations. *ArXiv*.
https://doi.org/10.48550/arxiv.2201.07643

Thelwall, M. (2017). Three practical field normalised alternative
indicator formulae for research evaluation. *Journal of
Informetrics*, *11*(1), 128–151.
https://doi.org/10.1016/J.JOI.2016.12.002

Waltman, L., & van Eck, N. J. (2018). Field normalization of
scientometric indicators. In W. Glänzel, H. F. Moed, S. U., & M.
Thelwall (Eds.), *Springer Handbook of Science and Technology
Indicators* (pp. 281–300). Springer. Retrieved from
http://arxiv.org/abs/1801.09985

**Open science practices**

The Science-Metrix team at Elsevier uses proprietary implementations of the Scopus and Overton databases in its work. Access to Scopus data for research purposes can be requested by the academic community at ICSR Lab: https://www.elsevier.com/icsr/icsrlab.

**Acknowledgments**

The authors thank Fei Shu for input on an earlier draft of this manuscript.

**Author contributions**

Henrique Pinheiro: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Supervision, Validation, Writing—original draft, Writing—review & editing. Etienne Vignola-Gagné: Conceptualization, Investigation, Methodology, Writing—original draft, Writing—review & editing. David Campbell: Conceptualization, Formal analysis, Investigation, Methodology, Project administration, Supervision, Writing—original draft, Writing—review & editing.

**Competing interests**

The authors are employees of Elsevier B.V.

**Funding information**

Not applicable.

Although not the study’s focus, it also helped to highlight that coverage issues should be considered in selecting an appropriate reference for normalization. Using the difference-based approach (see below) for UPRL, the average rank, among selected entities, is 177 for British universities and 551 for Indian universities. In the case of India and UPRL, normalization against the national level might make more sense with comparisons to other countries relying on within-country ranks.↩︎

Submitted by20 Apr 2023

Henrique Naves Pinheiro

Elsevier

- License: CC BY
- Review type: Open Review
- Publication type: Conference Paper
- Submission date: 20 April 2023
- Conference: 27th International Conference on Science, Technology and Innovation Indicators (STI 2023)
- Publisher: International Conference on Science, Technology and Innovation Indicators

Pinheiro, H., Vignola-Gagné, E. & Campbell, D. (2023). Normalization of rare citation events in the context of uptake of research in the non-scientific literature [preprint]. 27th International Conference on Science, Technology and Innovation Indicators (STI 2023).

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