Open Access: Self-Selected, Mandated & Random
Answers & Questions

Stevan Harnad

What follows below is what we hope will be found to be a conscientious and attentive series of responses to questions raised by Phil Davis about our paper (Gargouri et al, currently under refereeing) -- responses for which we did further analyses of our data (not included in the draft under refereeing).

Gargouri, Y., Hajjem, C., Lariviere, V., Gingras, Y., Brody, T., Carr, L. and Harnad, S. (2010) Self-Selected or Mandated, Open Access Increases Citation Impact for Higher Quality Research.(Submitted)

We are happy to have performed these further analyses, and we are very much in favor of this sort of open discussion and feedback on pre-refereeing preprints of papers that have been submitted and are undergoing peer review. They can only improve the quality of the eventual published version of articles.

However, having carefully responded to Phil's welcome questions, below, we will, at the end of this posting, ask Phil to respond in kind to a question that we have repeatedly raised about his own paper (Davis et al 2008), published a year and a half ago... 

RESPONSES TO DAVIS'S QUESTIONS ABOUT OUR PAPER:

PD: 
"Stevan, Granted, you may be more interested in what the referees of the paper have to say than my comments; I'm interested in whether this paper is good science, whether the methodology is sound and whether you interpret your results properly."

We are very appreciative of your concern and hope you will agree that we have not been interested only in what the referees might have to say. (We also hope you will now in turn be equally responsive to a longstanding question we have raised about your own paper on this same topic.)

PD: 
"For instance, it is not clear whether your Odds Ratios are interpreted correctly. Based on Figure 4, OA article are MORE LIKELY to receive zero citations than 1-5 citations (or conversely, LESS LIKELY to receive 1-5 citations than zero citations). You write: "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 [re: Figure 4 (p.9)]"... I find your odds ratio methodology unnecessarily complex and unintuitive..."

Our article supports its conclusions with several different, convergent analyses. The logistical analysis with the odds ratio is one of them, and its results are fully corroborated by the other, simpler analyses we also reported, as well as the supplementary analyses we append here now.

[Yassine has since added that your confusion was our fault because by way of an illustration we had used the first model (0 citations vs. 1-5 citations), with its odds ratio of 0.957 ("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 "). In the first model the value 0.957 is below and too close to 1 to serve as a good illustration of the meaning of the odds ratio. We should have chosen a better example. one in which (Exp(ß) is clearly greater than 1. We should have said: "For example, we can say for the second model that for a one unit increase in OA, the odds of receiving 5-10 citations (versus 1-5 citations) increased by a factor of 1.323." This clearer example will be used in the revised text of the paper. (See Figure 4S with a translation to display the deviations relative to an odds ratio of one rather than zero {although Excel here insists on labelling the baseline "0" instead of "1"! This too will be fixed in the revised text}.]

PD: 
"Similarly in Figure 4 (if I understand the axes correctly), CERN articles are more than twice as likely to be in the 20+ citation category than in the 1-5 citation category, a fact that may distort further interpretation of your data as it may be that institutional effects may explain your Mandated OA effect. See comments by Patrick Gaule and Ludo Waltman on the review"

Here is the analysis underlying Figure 4, re-done without CERN, and then again re-done without either CERN or Southampton. As will be seen, the outcome pattern, as well as its statistical significance, are the same whether or not we exclude these institutions. (Moreover, I remind you that those are multiple regression analyses in which the Beta values reflect the independent contributions of each of the variables: That means the significant OA advantage, whether or not we exclude CERN, is the contribution of OA independent of the contribution of each institution.)

SUPPLEMENTARY FIGURE S1

PD: 
"Changing how you report your citation ratios, from the ratio of log citations to the log of citation ratios is a very substantial change to your paper and I am surprised that you point out this reporting error at this point."

As noted in Yassine's reply to Phil, that formula was incorrectly stated in our text, once; in all the actual computations, results, figures and tables, however, the correct formula was used.

PD: 
"While it normalizes the distribution of the ratios, it is not without problems, such as: 1. Small citation differences have very large leverage in your calculations. Example, A=2 and B=1, log (A/B)=0.3"

The log of the citation ratio was used only in displaying the means (Figure 2), presented for visual inspection. The paired-sample t-tests of significance (Table 2) were based on the raw citation counts, not on log ratios, hence had no leverage in our calculations or their interpretations. (The paired-sample t-tests were also based only on 2004-2006, because for 2002-2003 not all the institutional mandates were yet in effect.)

Moreover, both the paired-sample t-test results (2004-2006) and the pattern of means (2002-2006) converged with the results of the (more complicated) logistical regression analyses and subdivisions into citation ranges.

PD: 
"2. Similarly, any ratio with zero in the denominator must be thrown out of your dataset. The paper does not inform the reader on how much data was ignored in your ratio analysis and we have no information on the potential bias this may have on your results."

As noted, the log ratios were only used in presenting the means, not in the significance testing, nor in the logistic regressions. 

However, we are happy to provide the additional information Phil requests, in order to help readers eyeball the means. Here are the means from Figure 2, recalculated by adding 1 to all citation counts. This restores all log ratios with zeroes in the numerator (sic); the probability of a zero in the denominator is vanishingly small, as it would require that all 10 same-issue control articles have no citations! 

The pattern is again much the same. (And, as noted, the significance tests are based on the raw citation counts, which were not affected by the log transformations that exclude numerator citation counts of zero.)

SUPPLEMENTARY FIGURE S2

This exercise suggested a further heuristic analysis that we had not thought of doing in the paper, even though the results had clearly suggested that the OA advantage is not evenly distributed across the full range of article quality and citeability: The higher quality, more citeable articles gain more of the citation advantage from OA. 

In the following supplementary figure (S3), for exploratory and illustrative purposes only, we re-calculate the means in the paper's Figure 2 separately for OA articles in the citation range 0-4 and for OA articles in the citation range 5+.

SUPPLEMENTARY FIGURE S3:

The overall OA advantage is clearly concentrated on articles in the higher citation range. There is even what looks like an OA DISadvantage for articles in the lower citation range. This may be mostly an artifact (from restricting the OA articles to 0-4 citations and not restricting the non-OA articles), although it may also be partly due to the fact that when unciteable articles are made OA, only one direction of outcome is possible, in the comparison with citation means for non-OA articles in the same journal and year: OA/non-OA citation ratios will always be unflattering for zero-citation OA articles. (This can be statistically controlled for, if we go on to investigate the distribution of the OA effect across citation brackets directly.)

PD: 
"Have you attempted to analyze your citation data as continuous variables rather than ratios or categories?"

We will be doing this in our next study, which extends the time base to 2002-2008. Meanwhile, a preview is possible from plotting the mean number of OA and non-OA articles for each citation count. Note that zero citations is the biggest category for both OA and non-OA articles, and that the proportion of articles at each citation level decreases faster for non-OA articles than for OA articles; this is another way of visualizing the OA advantage. At citation counts of 30 or more, the difference is quite striking, although of course there are few articles with so many citations:

SUPPLEMENTARY FIGURE 4

REQUEST FOR RESPONSE TO QUESTION ABOUT DAVIS ET AL'S (2008) PAPER:

Davis, PN, Lewenstein, BV, Simon, DH, Booth, JG, & Connolly, MJL (2008) Open access publishing, article downloads, and citations: randomised controlled trial British Medical Journal 337 

Critique of Davis et al's paper: "Davis et al's 1-year Study of Self-Selection Bias: No Self-Archiving Control, No OA Effect, No Conclusion" BMJ Responses.

Davis et al had taken a 1-year sample of biological journal articles and randomly made a subset of them OA, to control for author self-selection. (This is comparable to our mandated control for author self-selection.) They reported that after a year, they found no significant OA Advantage for the randomized OA for citations (although they did find an OA Advantage for downloads) and concluded that this showed that the OA citation Advantage is just an artifact of author self-selection, now eliminated by the randomization.

What Davis et al failed to do, however, was to demonstrate that -- in the same sample and time-span -- author self-selection does generate the OA citation Advantage. Without doing that, all they have shown is that in their sample and time-span, they found no significant OA citation Advantage. This is no great surprise, because their sample was small and their time-span was short, whereas the many of the other studies that have reported finding an OA Advantage were based on much larger samples and much longer time spans.

The question raised was about controlling for self-selected OA. If one tests for the OA Advantage, whether self-selected or randomized, there is a great deal of variability, across articles and disciplines, especially for the first year or so after publication. In order to have a statistically reliable measure of OA effects, the sample has to be big enough, both in number of articles and in the time allowed for any citation advantage to build up to become detectable and statistically reliable.

Davis et al need to do with their randomization methodology what we have done with our mandating methodology, namely, to demonstrate the presence of a self-selected OA Advantage in the same journals and years. Then they can compare that with randomized OA in those same journals and years, and if there is a significant OA Advantage for self-selected OA and no OA Advantage for randomized OA then they will have evidence that -- contrary to our findings -- some or all of the OA Advantage is indeed just a side-effect of self-selection. Otherwise, all they have shown is that with their journals, sample size and time-span, there is no detectable OA Advantage at all. 

What Davis et al replied in their BMJ Authors' Response was instead this:

PD: 
"Professor Harnad comments that we should have implemented a self-selection control in our study. Although this is an excellent idea, it was not possible for us to do so because, at the time of our randomization, the publisher did not permit author-sponsored open access publishing in our experimental journals. Nonetheless, self-archiving, the type of open access Prof. Harnad often refers to, is accounted for in our regression model (see Tables 2 and 3)... Table 2 Linear regression output reporting independent variable effects on PDF downloads for six months after publication Self-archived: 6% of variance p = .361 (i.e., not statistically significant)... Table 3 Negative binomial regression output reporting independent variable effects on citations to articles aged 9 to 12 months Self-archived: Incidence Rate 0.9 p = .716 (i.e., not statistically significant)..."

This is not an adequate response. If a control condition was needed in order to make an outcome meaningful, it is not sufficient to reply that "the publisher and sample allowed us to do the experimental condition but not the control condition." 

Nor is it an adequate response to reiterate that there was no significant self-selected self-archiving effect in the sample (as the regression analysis showed). That is in fact bad news for the hypothesis being tested.

Nor is it an adequate response to say, as Phil did in a later posting, that even after another half year or more had gone by, there was still no significant OA Advantage. (That is just the sound of one hand clapping again, this time louder.)

The only way to draw meaningful conclusions from Davis et al's methodology is to demonstrate the self-selected self-archiving citation advantage, for the same journals and time-span, and then to show that randomization wipes it out.

Until then, our own results, which do demonstrate the self-selected self-archiving citation advantage for the same journals and time-span, show that mandating the self-archiving does not wipe it out.

Meanwhile, Davis et al's finding that although their randomized OA did not generate a citation increase, it did generate a download increase, suggests that with a larger sample and time-span there may well be scope for a citation advantage as well: Our own prior work and that of others has shown that higher early download counts tend to lead to higher later citation counts.

Bollen, J., Van de Sompel, H., Hagberg, A. and Chute, R. (2009) A principal component analysis of 39 scientific impact measures in PLoS ONE 4(6): e6022, 

Brody, T., Harnad, S. and Carr, L. (2006) Earlier Web Usage Statistics as Predictors of Later Citation Impact. Journal of the American Association for Information Science and Technology (JASIST) 57(8) 1060-1072. 

Lokker, C., McKibbon, K. A., McKinlay, R.J., Wilczynski, N. L. and Haynes, R. B. (2008) Prediction of citation counts for clinical articles at two years using data available within three weeks of publication: retrospective cohort study BMJ, 2008;336:655-657 

Moed, H. F. (2005) Statistical Relationships Between Downloads and Citations at the Level of Individual Documents Within a Single Journal. Journal of the American Society for Information Science and Technology 56(10): 1088- 1097 

O'Leary, D. E. (2008) The relationship between citations and number of downloads Decision Support Systems 45(4): 972-980 

Watson, A. B. (2009) Comparing citations and downloads for individual articles Journal of Vision 9(4): 1-4