The Importance of Being First: Position Dependent Citation Rates on arXiv:astro-ph

The Importance of Being First: Position Dependent Citation Rates on arXiv:astro-ph

J. P. Dietrich ESO, Karl-Schwarzschild-Str. 2, 85748 Garching b. München, Germany

We study the dependence of citation counts of e-prints published on the arXiv:astro-ph server on their position in the daily astro-ph listing. Using the SPIRES literature database we reconstruct the astro-ph listings from July 2002 to December 2005 and determine citation counts for e-prints from their ADS entry. We use Zipf plots to analyze the citation distributions for each astro-ph position. We find that e-prints appearing at or near the top of the astro-ph mailings receive significantly more citations than those further down the list. This difference is significant at the level and on average amounts to two times more citations for papers at the top than those further down the listing. We propose three possible non-exclusive explanations for this positional citation effect and try to test them. We conclude that self-promotion by authors plays a role in the observed effect but cannot exclude that increased visibility at the top of the daily listings contributes to higher citation counts as well. We can rule out that the positional dependence of citations is caused by the coincidence of the submission deadline with the working hours of a geographically constrained set of intrinsically higher cited authors. We discuss several ways of mitigating the observed effect, including splitting astro-ph into several subject classes, randomizing the order of e-prints, and a novel approach to sorting entries by relevance to individual readers.

Subject headings:
sociology of astronomy – astronomical data bases: miscellaneous

1. Introduction

A number of studies looking at the influence of e-printing on citation counts across disciplines (e.g., Lawrence 2001) and in Astronomy and Physics in particular (e.g., Schwarz & Kennicutt 2004; Metcalfe 2005; Henneken et al. 2006) found that papers freely available online, particularly through the arXiv e-print server111, are cited more often than those not. This difference was studied in more detail by Kurtz et al. (2005), who proposed three (non-exclusive) effects potentially responsible for higher citations rates of journal articles also published as astro-ph e-prints. These are defined as (see Kurtz et al. 2005):

  • The Open Access (OA) postulate – Because the access to articles is unrestricted by any payment mechanism authors are able to read them more easily, and thus they cite them more frequently;

  • The Early Access (EA) postulate – Because the article appears sooner it gains both primacy and additional time in press, and is thus cited more;

  • The Self-selection Bias (SB) postulate – Authors preferentially tend to promote (in this case by posting to the internet) the most important, and thus most citable articles.

Kurtz et al. (2005) found that open access to older issues of astronomical journals through the Astrophysics Data System (ADS, Kurtz et al. 2000) did not lead to increased citation counts, plausibly denying a significant effect of the OA postulate. The EA postulate was supported by a significant increase in citation rate for recent papers. Concerning the SB postulate, Kurtz et al. (2005) note that significantly fewer papers not posted to astro-ph are among top 200 cited articles in the year 2003 Astrophysical Journal article than expected from the combined OA+EA effect alone. It is thus established that EA and SB play a significant role in gathering citations.

We observed that on many days the arXiv astro-ph listing is headed by one or more articles submitted a few seconds after the passing of the deadline for submissions for the next astro-ph mailing. One example – among many others – is the astro-ph listing of Sep 24, 2007 headed by three articles received within 20 s after this list was started. Considering that the number of new articles posted to astro-ph on a typical day is about , this temporal clustering close to the submission deadline is conspicuous and suggests a peculiar form of self-promotion. Apparently, a subset of authors expects higher visibility and thus also higher citation rates for articles listed at or close to the top of an astro-ph mailing.

In the following we study the dependence of citation counts on articles’ positions in the astro-ph listings. In Sect. 2 we describe how we reconstructed the daily astro-ph mailings for a span of 2.5 years and count citations to e-prints. We analyze the dependence of citations rates on astro-ph listing position in Sect. 3 and discuss three possible explanations for the effect we find in our dataset. We present our conclusions in Sect. 4.

2. Data

Using the SPIRES High-Energy Physics Literature Database222 we reconstructed the daily astro-ph mailings in the period from July 2002 to December 2005. The starting date of our analysis is fixed by the date from which on astro-ph is automatically added to SPIRES HEP as soon as it is posted. Restricting SPIRES HEP queries by the date a record was added allows us to request astro-ph listings for single days. Older astro-ph articles were added to SPIRES HEP later in 2002. They were easily recognized by their arXiv identifier and discarded from our dataset. Remaining articles added out of order and occasional small gaps were also found based on their arXiv identifiers. These articles were associated with the correct posting date based on the consecutive arXiv identifier if the association to a date was unambiguous. Otherwise the article and the dates in question were flagged as unreliable and excluded from the analysis. Numerous spot checks confirmed that we were in this way able to reliably reproduce daily astro-ph listings.

We chose not to include e-prints appearing on astro-ph after December 2005 so that all articles had at least one year to gather citations before we filled our citation database in December 2006. Our database contains astro-ph listings for 839 days judged as reliable, with a total of 27 109 articles on these days.

We used NASA’s Astrophysics Data System (ADS) Bibliographic Services333 to determine if and where an e-print was published in printed form and to determine the number of citations that an article has. Henneken et al. (2006) estimate that the concordance achieved by the ADS between astro-ph e-prints and journal articles is 98%. The remaining incompleteness should not be a significant source of error, especially considering that ADS also lists citations to arXiv e-prints.

Astronomy is in the fortunate situation that only a few journals dominate the publication of refereed articles. In agreement with Kurtz et al. (2005) we consider these 7 core journals to be The Astrophysical Journal (Letters) and its Supplement Series, Astronomy & Astrophysics, Monthly Notices of the Royal Astronomical Society, The Astronomical Journal, and Publications of the Astronomical Society of the Pacific. We set a flag in our database for those e-prints that are also published in one of the core journals.

3. Analysis

Random and systematical variations cause considerable fluctuations of the length of the astro-ph listings. For our analysis we exclude unusually short listings ( entries), which typically occur in the period between Christmas and New Year, and extremely long postings (), of which we have 5 in our database, from our analysis. This selection leaves 816 days to be considered.

Figure 1.— Zipf plot for different astro-ph positions. The -axis shows the logarithm of the normalized rank of astro-ph postings after sorting them by citations. The -axis shows the logarithm of the number of citations. The different line colors/styles encode the Zipf law for different astro-ph positions as given in the upper right corner of the figure. The solid black line indicates the slope of the power law. The high citation count of the top-ranked paper in the bin of astro-ph positions 21-25 is due to the WMAP first-year paper by Spergel et al. (2003), which has a submission time 1 s before the deadline and appeared as 23rd and last paper on Feb. 12, 2003. With 4118 citations reported by ADS at the time of writing, this is the most cited article in all of astronomy.

Redner (1998) found that the citation distribution is a power law over a large range of citation numbers. The mean and median number of citations that papers of a given sample get are not good estimators as the mean is strongly affected by a few highly cited papers in the tail of the distribution while the median looks only at the large number of very poorly cited papers. A better way to analyze such data is in a Zipf plot. A Zipf plot shows the most cited paper out of an ensemble of size versus its rank . Figure 1 shows the Zipf plot for some positions in the astro-ph listing. We use the normalized rank instead of the rank to account for the different lengths of astro-ph mailings. We bin higher astro-ph positions to beat down the noise that comes from the smaller number of articles at higher positions, i.e., from the smaller number of astro-ph mailings that are longer than average.

The constant slope of the Zipf plots over a wide range of normalized ranks confirms the power law nature of the citation distribution. One clearly sees that the loci of the curves for positions 1 and 3 are higher than those of e-prints further down the astro-ph listing with an apparent continuous progression down for lower astro-ph positions. The different loci of the curves correspond to the different normalizations of the power law, i.e., the different number of citations that e-prints at different positions in the astro-ph listing get. We call this the positional citation effect (PCE) and adopt the following procedure to quantify the magnitude and significance of the PCE.

We make a Zipf plot for the ensemble of all astro-ph e-prints and fit a line to it in the range in which the distribution follows a power law. In agreement with Redner (1998) we find with a very small error of . Keeping fixed at this value we fit to the Zipf plots for each (binned) astro-ph position in the range . The value of is directly related to the normalization of the power law and determines the loci of the citation distributions in Fig. 1.

Figure 2.— Normalization of the citation distribution power law. Blue boxes give the value of the power law normalization for all articles on astro-ph and its error. The widths of the boxes corresponds to the size of the bins. Red boxes show the same quantity but with the analysis restricted to the 7 core journals in Astronomy. The dotted horizontal lines are the normalization factors of the respective samples of all papers on astro-ph positions between and .

Figure 2 shows the results of this analysis for two data sets. The blue boxes give the normalization for the ensemble of all astro-ph e-prints, while the red boxes corresponds to those e-prints that also appeared in one the core journals. Comparing the normalization of the bins to that of the ensemble of e-prints on astro-ph positions , given by the dotted lines in Fig. 2, we find that the PCE is significant for the first six astro-ph positions for both data sets. The difference between the normalization at position and the articles on positions is significant at the level for all e-prints and at the level for core journal articles.

We have now established that the PCE is present and highly significant. Most scientists will, however, wonder how the different normalizations of the Zipf law translate into citation counts. By restricting an analysis of average citations to the range over which the power law holds, we avoid both the tail of exceptionally highly cited papers and the bulk of mostly ignored publications. We determine average citation counts in the range by integrating over the normalized Zipf distribution. We find an average citation count of for core journal articles and of for all e-prints on astro-ph position . Core journal articles appearing at positions are on average cited times, while the mean citation count for all e-prints at these position is . The overall higher number of citations for articles from the core journals is in agreement with the findings of Schwarz & Kennicutt (2004).

We propose three possible explanations for the observed dependence of citation counts on astro-ph position:

  • The Visibility Bias (VB) postulate – Papers appearing at the top of the astro-ph listing are seen by more people and thus cited more often than those further down the list, where the attention of the astro-ph readers might decrease;

  • The Self-promotion Bias (SP) postulate – Authors tend to promote their most important works, and thus most citable articles, by placing them at prominent positions;

  • The Geography Bias (GB) postulate – The submission deadline preferrentially puts those authors at the top of the listing whose working hours coincide with the submission deadline. This group already has higher citation counts for other reasons.

The last postulate merits some further explanation. Habing (2007) noticed that US American authors have a higher fraction of highly cited papers than their European colleagues. The submission deadline for the arXiv e-print server is 16:00 EST/EDT. This is within the normal working time of astronomers in all of the USA, while it is outside working hours for European astronomers.444In this we of course ignore the few individuals who do the traditional night time work of astronomers. Assuming for the moment that GB is not caused by VB, i.e., that US Americans do not get cited more because they are preferentially at the top of the astro-ph listing, the PCE could be explained by the dominance of American authors at the relevant moment in time. This explanation of GB ignores astronomical communities outside Europe and the USA, but they are comparably small.

To test the GB postulate we analyze the author affiliations of e-prints appearing in core journals. We associate articles to one of the following regions according to the country of the first affiliation of the first author, where the number in parentheses indicates the total number of articles from the respective region in our database: Europe (6843), USA (5659), Asia (1693), North America without USA (605), South America (412), Australia/Oceania (397). Russia (166) and Turkey (32) are counted as Asian countries, Iceland (3) as European. We treat the USA separately from the rest of North America because Habing (2007) made their observation only for authors from the USA.

We repeat the analysis of the Zipf plots separately for authors from Europe and from the USA. We find that the global power law indices for both author sets are marginally inconsistent with each other. This could potentially indicate a more fundamental difference between papers written by European and American authors but our data set is too small to draw firm conclusions and a more detailed study is beyond the scope of this work. We settle for using the slopes of the Zipf laws that were found for the respective sample.

The results of this Zipf plot analysis are shown in Fig. 3 and proof that the PCE is also present for the sample of European authors. This rules out the GB postulate as the single explanation for the observed PCE in the whole sample. Note that the higher normalization of European authors does not mean that these are more cited than their US American colleagues. The difference is simply due to the different power law indices.

We emphasize that European authors who appear at the top of an astro-ph listing had – in all likelihood – to submit their manuscript well outside their normal working hours. It is thus reasonable to assume that a conscious effort was made to gain this position and to self-promote the work presented in these e-prints. This is further supported by a comparison with the same statistics made for US American authors. A significant increase of citations at the top of the astro-ph listings is also seen for these authors but the effect is not nearly as prominent as for their European colleagues. A fair fraction of American authors will appear at or near the top of the astro-ph listing just by chance, without any attempt at self-promotion. They dilute any SP signal in this sample.

So far we could rule out GB as a significant contribution to the PCE and found evidence for SP as a source of the PCE. Analyzing the contribution of VB is much more difficult. In principle this would be possible by examining the submission times of e-prints and grouping them into two samples; one that is submitted so shortly after the deadline that it is statistically expected to be self-promoted, and a second one that is submitted long enough after the deadline to exclude self-promotion. Unfortunately, the arXiv stores only the submission time of the last replacement that was made without generating a new version number. It does not keep the initial submission time of an e-print. Without the latter it is not possible to disentangle VB and SP.

Figure 2 seems to show a marginally significant drop of the power law normalization for articles at the bottom of very long astro-ph mailings. This is most likely an artefact caused by the growth of astro-ph over the period under investigation here. Far fewer listings had more than 40 entries in 2002 and 2003 than in 2004 and 2005. These articles had less time to garner citations, an effect which we, as mentioned previously, do not correct for. We find that the decline in citation rates at the bottom vanishes if we restrict the citation analysis to e-prints that appeared in 2004 and 2005.

Figure 3.— Normalization of the citation distribution power-law for European (red) and American (blue) authors of core journal papers. Note that the binning is coarser than in Fig. 2 to account for the smaller number of articles in each sample.

4. Summary and conclusions

We investigated the positional dependence of citation counts of e-prints on their position in daily arXiv:astro-ph mailings. We found that articles at or near the top of these listings receive significantly more citations than articles at positions and higher. This positional citation effect is present at the level for all e-prints and for the set of those e-prints also appearing as articles in one of the core journals in Astronomy and Astrophysics with a significance of . Restricting the analysis to the range over which the citation distribution follows a power law, the difference in normalization factors translates to a factor 2 difference in average citation counts. E-prints at the top of the astro-ph listing are on average cited times while articles between positions and receive only citations. The PCE is significant for the first six positions in the astro-ph mailings.

We proposed three possible explanations for the observed PCE. By analyzing the affiliations of authors we could exclude the hypothesis that the PCE is caused by a geographical bias, namely by preferentially putting US American authors at the top, who already have higher citation rates than their European colleagues. Confirming that the PCE is present and more pronounced for European authors, who usually can gain the top position on astro-ph only by submitting outside their normal working hours, we could conclude that self-promotion plays a role in creating the PCE.

We cannot present firm statistical evidence that the PCE at the top is due to higher visibility. However, the PCE is present down to astro-ph position 6, where the submission times of e-prints suggest that only a very small fraction of manuscripts at this position was submitted with the intention of self-promotion. Of course, this statement has to be made with some care since the submission times reported by arXiv are often not the original submission times as explained above. We, however, observe that less than of e-prints at position 6 have reported submission times within half an hour after the deadline, while this fraction for e-prints at the top position is , suggesting that VB plays some role.

A situation in which the number of citations a publication gets does not solely depend on its merits is unsatisfactory. One may be tempted to suggest to randomize the order of e-prints in an astro-ph mailing, instead of listing them sorted by submission time. This proposal has severe weaknesses. On the one hand, the PCE in a randomized listing would only vanish if the observed effect is completely due to SP bias, since any visibility effects would immediately recur in a randomized listing. On the other hand, if in fact SP bias is the sole cause of the PCE there is no reason to change anything. It is important to understand that SP means that papers at the top are on average intrinsically more citable – or better by some metric – than papers further down the list. A PCE caused only by SP bias is not in contradiction to merit based citation counts. Hence, randomizing the astro-ph listings would not solve the visibility problem and only remedy a non-existing problem.

Any visibility problem is connected to the length of astro-ph listings. Shorter listing would naturally give the same or almost the same visibility to all articles, irrespective of their position. Looking at the arXiv submission history, it is obvious that the number of astro-ph e-prints will not decrease but only increase with time. A possible method leading to shorter listings would be to split astro-ph into several subject-classes, like the other three big archives “hep” (High-Energy Physics), “cond-mat” (Condensed Matter), and “math” (Mathematics) are subdivided into smaller categories. Ideally, most researchers would have to look at only one or two more specific and hence much shorter listings per day. For example, a cosmologist could avoid seeing e-prints on Solar System objects if he/she chooses not to read a possible Solar System subject-class.

A recent approach to tackle the increasing volume of astro-ph is the arxivsorter555 (Magué & Ménard 2007). Arxivsorter aims to sort daily, recent, or monthly astro-ph listings by relevance to an individual reader. The underlying idea is that scientists through co-authorship form an interconnected network of authors. By specifying a few authors relevant to a reader’s fields of interest, the “proximity” of a new e-print in the author network can be calculated. This proximity seems to be a good proxy for relevance to a reader’s interests. Arxivsorter has some problems with non-unique – mostly Chinese – names, and a small percentage of authors not connected to the global cluster of authors. It is worth pointing out that arxivsorter just re-orders the papers without any loss of information, a clear advantage over a possible split into subject-classes.

This research has made use of NASA’s Astrophysics Data System Bibliographic Services. I am very grateful to Maryam Modjaz, who identified a crucial error in a previous version of the analysis presented here. Brice Ménard and the referee Michael Kurtz gave a number of excellent suggestions, which improved this paper. I thank Uta Grothkopf for a careful reading of the manuscript.


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