•  OA : Is the article Open Access (1 if OA and 0 otherwise)?

• M : Does the author's institution Mandate Open Access (1) or Not (0)?

• Age : How old is the article (articles published from 2002 to 2006)?

• Auth_N : How many co-authors does the article have?

• Ref_N : How many references does the article cite?

• IF : What is the Thompson/ISI "Impact Factor" (average citations per article in 2-year window) of the journal in which the article was published (from 0 to 30)?

• Sci : Is the article classified by ISI as Science (1) or Social Science (0)

• Page_N : How many pages in the article?

• USA : What is the country of the first author (USA 1, other 0)?

• Review : Is the article classified by ISI as a "review" article (1) or not (0)?

• CERN : Is the first author from CERN (1/0)?

• South : Is the first author from Southampton  (1/0)?

• Minho : Is the first author from Minho (1/0)?

• Queens : Is the first author from Queensland University of Technology (1/0)?

• Age*OA : The interaction between Age and OA

1. Logistic regression:

We used stepwise logistic regression, for each test selecting the model that maximizes the chi-square likelihood ratio.

To make the interpretation of the coefficients easier, we exponentiated the ß coefficients (Exp(ß)) and interpreted them as odds-ratios. For example, we can say for the first model that for a one unit increase in OA, the odds of receiving 1-5 citations (versus zero citations) increased by a factor of 0.957.

The following table (Tab.1) reports Exp(ß) values for each model having "Cit_a_x-y&y-z" as dependent variables  ((x,y,z) {1, 2, 3, ..., 20}), where Cit_a_x-y&y-z = 1 if citation count (minus self-citations) is between y and z and 0 if between x and y. Models are referred to as "M_r".

The Exp(ß) values of variables turned out to have the same polarity and to be quite similar, with and without self-citations.

The figure (Fig.2) shows that citation count is positively correlated with IF, Age, Ref_N, Auth_N, OA, USA and M. In other words:

- The higher the IF of the journal in which it was published, the higher an article's citation count.

- The longer since an article was published, the higher its citation count.

- The more references an article cites, the higher its citation count.

- The more co-authors an article has, the higher its citation count.

- Articles that are made OA have higher citation counts, and this small but significant independent OA effect is present in every citation range but it is greatest in the highest citation range (1-5 citations vs 20+ citations): The OA advantage is strongest for highly cited articles.

- Articles from authors at institutions that have Mandates have higher citation counts; this effect is present only in the medium-high citation ranges (and is of course confounded with the level of author compliance with the institutional Mandate, discussed further below).

- Review articles have higher citation counts; the effect is greater, the higher the citation range.

- CERN articles have higher citation counts in the lowest and especially the highest citation range. (However, when all CERN articles are excluded from our sample, there is no significant change in the other variables).

Tab.1:  The Exp(ß) values for logistic regressions

* Bold: significance < 0,01

* Italique: significance between 0,01 and 0,05 

Fig.2:  The Exp(ß) values for logistic regressions

There is a significant interaction between Age and OA (Age*OA) for low citation interval (between 1 and 5) as well for high citation interval (20 citations and more). Both the linear main effect of age and OA, and this nonlinear interaction are significant.. The following figure ( Fig.3) shows the citation mean (Cit_a_1-5&20+) for OA and NOA articles corresponding to each Age value. This figure confirms the OA advantage. The difference between the two lines corresponding to OA and NOA is higher for older articles.  

Fig.3: The citation count means of Age and OA

2. Logistic Regression by Impact Factor interval:

In order to compare articles belonging to comparable journals, we divided our sample into 4 quartile ranges by journal impact Factor (IF), each range covering 25% of the articles:

        IF_1 :          0 ≤ IF < 0.633

        IF_2 :   0.633 ≤ IF < 1.053

        IF_3 :   1.035 ≤ IF < 1.782

        IF_4 :   1.782 ≤ IF < 29.957

Only the top quartile contains journals with IFs from 1.782 to 29.957.  As we are also interested in the variability within this quartile, we further subdivided it into two subgroups, each covering 12.5% of all the articles. Subdividing more minutely would generate would make the sample sizes too small to detect effects o interest. Finally, 5 ranges of IF are selected:

        IF_1 :         0 ≤ IF < 0.633

        IF_2 :   0.633 ≤ IF < 1.053

        IF_3 :   1.035 ≤ IF < 1.782

        IF_4 :   1.782 ≤ IF < 2.468

        IF_5 :   2.468 ≤ IF ≤ 29.957

The same regression is done separately for each IF range by controlling all the variables (except IF). The following tables summarizes the values of Exp(ß) corresponding to the controlled variables for each IF range.

Our earlier remark also applies to these regressions: Exp(ß) values of variables have the same polarity and pattern whether or not we exclude self-citations from the citations count.

2.1   IF 1

When articles are published in a low IF journal, article citation counts are positively correlated with Age, Ref_N, Auth_N, OA and M. The OA effect increases for higher citation count intervals. For the low article citation range, the Age*OA interaction is significant, but OA itself is not.

Tab.2:  The Exp(ß) values for logistic regressions (IF 1)

Fig.4:  The Exp(ß) values for logistic regressions (IF 1)