Summary

it's clear from the literature that OA articles are cited more than articles that are only accessible behind a paywall. There are very many studies documenting this. There are very few studies that found OA articles aren't cited more, and none have ever found that they're cited less. There are some theories that other factors cause the OA citation advantage, which includes number of others, authors only making their higher quality papers OA, and early dissemination of preprints.

A Sample of Research that found a Citation Advantage

Lawrence, S. Free online availability substantially increases a paper's impact. Nature, 411(May 2001), 521-521. https://www.nature.com/articles/35079151.pdf. MF

Appears to be the earliest study of open access citation advantage. Lawrence studied 119,924 computer science articles and found a 157% increase (~2.5 times more likely) in the mean number of citations of OA articles over non-OA.

Brody, T. D. Evaluating research impact through open access to scholarly communications [PhD. Thesis, Philosophy]. University of Southampton, School of Electronics and Computer Science. 2006.http://eprints.soton.ac.uk/263313/. MF

Articles self-archived by authors receive between 50-250% more citations. Rapid pre-printing on the Web has dramatically reduced the peak citation rate from over a year to virtually instantaneously. In addition to discussing citation impact, the thesis describes a new web metric, download impact.

Antelman, K. Do open-access articles have a greater research impact? College & Research Libraries, 65 (2004), no. 5, 372-382. https://crl.acrl.org/index.php/crl/article/view/15683. MF

 Web of Science citation rates are enhanced for OA articles over non-OA articles by 91% for mathematics, 51% for electrical and electronic engineering, 86% for political science) and 45% for philosophy.

Norris, M., Oppenheim, C., & Rowland, F. The Citation advantage of open-access articles. Journal of the American Society for Information Science and Technology, 59 (2008), no. 12, 1963-1972. https://onlinelibrary.wiley.com/doi/abs/10.1002/asi.20898. MF

A study of four subject areas (ecology, applied mathematics, sociology, and economics) showed an average of 57% more citations for journal articles that have an open access version vs. those that are exclusively toll access (subscription-based). 

Eysenbach, G. Citation advantage of open access articles. PLoS Biology, 4 (2006), no. 5, 692-698.https://pubmed.ncbi.nlm.nih.gov/16683865/. MF

A study of open access vs. non-open access articles in the same journal, Proceedings of the National Academy of Science. Open access articles twice as likely to be cited and were more heavily cited than non-OA articles.  Research was controlled for confounding variables including: number of authors, authors' lifetime publication count and impact, submission track, country of corresponding author, funding organization, and discipline.

Davis, P. M. Author-choice open-access publishing in the biological and medical literature: a citation analysis. Journal of the American Society for Information Science and Technology, 60 (2009), no. 1, 3-8. https://onlinelibrary-wiley-com.proxy-bc.researchport.umd.edu/doi/epdf/10.1002/asi.20965. MF

A study of 11 biological and medical journals from 2003-2007 that publish both open access and subscription access articles (author-choice model). The study indicates an average citation advantage for open access articles of 17%. Controlled for number of authors, number of references, length in pages, whether the article was a review, and whether the author was located in the U.S.

Evans, J. A., & Reimer, J. Open access and global participation in science. Science, 323 (2009), no. 5917, 1025-1025. https://www.science.org/lookup/doi/10.1126/science.1154562. MF

Although showing a more modest effect for open access advantage (~8% on average), this study clearly demonstrates that open access articles are much more likely to be cited in poorer countries. Demonstrated that a journal receives a modest increase in citations when it comes online freely, but the jump is larger when it first comes online through commercial sources. This number was reached by  determining that many previous studies of the OA advantage weren't of free articles, but of any online article whether free or not--confusion created because at the time of early studies, nearly all publications still appeared exclusively in print, and online articles were almost exclusively free.

Craig, I. D., Plume, A. M., McVeigh, M. E., Pringle, J., & Amin, M.  Do open access articles have greater citation impact? A critical review of the literature. Journal of Informetrics, 1 (2007) no. 3, 239-248. https://www.sciencedirect.com/science/article/pii/S1751157707000466?casa_token=pj2xbq4TLHMAAAAA:rknCgkufcWbv8z_KqSTPHHrB8sN5oqa-ehVaTcyEdHgiBCelNqXaeW34XJI9cKeeykh3irzeUA. MF

This methodological review of 26 papers is highly critical of studies showing any open access vs. toll access citation advantage. The authors conclude that only one study [Moed 2007] properly used a fixed time window and corrected for quality/selection and early view bias effects. When data is adjusted for these biases, the remaining open access citation advantage was reduced to 7%.

. Bernius, S., & Hanauske, M.  Open access to scientific literature: increasing citations as an incentive for authors to make their publications freely accessible. Paper presented at the 42nd Annual Hawaii International Conference on System Sciences, HICSS, January 5, 2009 - January 9, 2009. {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4755635&tag=1} MF

This paper focuses on developing a simulation model of the scientific citation network using vertices. The simulation results support the empirical data regarding the open access citation advantage. They indicate that if two authors produce articles of the same quality, the authors using OA is likely to receive more citations.

A Sample of Research that did not find a Citation Advantage

Davis, Philip M. Open access, readership, citations: a randomized controlled trial of scientific journal publishing. The FASEB Journal 25 (July 2011). pp 2129-34. MF

Articles placed in the open access condition (n712) received significantly more downloads and reached a broader audience within the first year, yet were cited no more frequently, nor earlier, than sub-scription-access control articles (n2533) within 3 yr.

Self-Selection/Quality Bias

Gargouri, Yassine et al. Self-selected or mandated, open access increases citation impact for higher quality research. PLOS ONE, Oct. 18, 2010. https://doi.org/10.1371/journal.pone.0013636. MF

"The OA advantage is greater for the more citable articles, not because of a quality bias from authors self-selecting what to make OA, but because of a quality advantage, from users self-selecting what to use and cite, freed by OA from the constraints of selective accessibility to subscribers only. It is hoped that these findings will help motivate the adoption of OA self-archiving mandates by universities, research institutions and research funders."

Data

Piwowar, H. A., Day, R. S., & Fridsma, D. B. 2007. Sharing detailed research data is associated with increased citation rate. PLoS ONE, 2(3), e308. MF

This is the first study to show a correlation between open access data sets and citation impact for 85 cancer microarray clinical trial publications. Open access data resulted in a 69% increase in citations.