The distribution of WoS categories in the reference list allowed us to compute variety , balance and disparity as described in section 4: variety as the number of WoS categories n that appeared at least once and balance as the evenness of the distribution of WoS categories. In order to compute the disparity measure, a similarity matrix s ij for the WoS categories must be constructed.
A detailed description and analysis of this s ij SC-similarity matrix is provided elsewhere when describing global maps of science [ 20 ]. See descriptive statistics for all these variables in the Table 4 below. Finally, we have also included in our analysis an indicator of diversity that incorporates the three aspects of diversity variety, balance and disparity in a single measure: i.
Rao-Stirling [ 20 , 21 ]. The Rao-Stirling diversity indicator can be expressed as follows:. See Zhang et al [ 57 ] for a recent re-formulation not used here of the Rao-Stirling diversity that might improve its sensitivity to high values of diversity.
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We explicitly consider this indicator for the purpose of having a benchmark for comparison, with regards to the separate impact of the three aspects of diversity. We have included a number of control variables that the literature has considered as potentially associated with the number of citations received by scientific publications [ 58 — 60 ].
Second, we have controlled for the geographic scope of institutional collaboration by building a set of three dummy variables. These three binary variables are aimed to capture whether publications involving an international collaboration are positively associated with citation impact compared to publications involving either domestic collaboration or no collaboration. Third, we have constructed a dichotomous variable to control for the four WoS categories considered in this analysis i. These discipline-level controls are important to account for field-specific citation patterns that may influence the relationships estimated between our three aspects of IDR and citation impact.
In summary, we control for variables that represent social aspects of the research input number of authors and institutions, national and international collaborations, discipline, country , and that may have an effect both on the citations received and on degree of IDR.
For example, the number of authors may be associated with higher citation impact and higher interdisciplinarity. However, we do not control for variables such as number of references or pages that reflect the characteristics of the research output i.
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For example, a larger number of pages or references in a paper may reflect the need of interdisciplinary in the contents. Nevertheless, for the sake of robustness, we have also controlled for the number of references in papers. This control is reasonable since all our three constructs of IDR variety, balance and disparity are based on the references cited in the papers; but it is also problematic, because the total number of references in a publication is extremely highly correlated with the measure of variety a Pearson correlation of 0.
The first one takes value 1 for all those publications that belong to the bottom quartile in terms of number of references: thus, we control for publications with low number of references i. The second variable takes value 1 for those publications that belong to the top quartile in terms of number of publications i. The estimates of our regression analysis including these controls are shown in the Table A in the Supporting Information File S1 File , and indicate that the sign and statistical significance of results regarding the effects of variety, balance and disparity are largely aligned with the results presented in section 6.
Since our dependent variable log transformed of Normalized Citation Score, ln NCS is a continuous variable with a lower boundary at zero and a upper boundary at infinity, and a significant proportion of the observations in our sample are zeros i. Table 4 provides the descriptive statistics and Table 5 the correlation matrix for all the variables used in the analysis.
Table 5 shows that the correlations between our independent variables are rather low: we find positive correlations between variety and balance i. These results provide a first descriptive evidence that these three measures of diversity reflect different properties of interdisciplinarity, and are worth considering separately rather than brought together in a single index. We will next examine to what extent these three attributes of diversity have a distinct effect on citation impact.
This section reports the results of our analysis about the effects of interdisciplinary research on citation impact. Table 6 reports the results of Tobit estimates for the whole sample i. We present the results in six columns: the first two columns display the results for the relationship between a full indicator of IDR Rao-Stirling diversity , and citation impact. Column 3 shows the linear effects of each of the diversity measures on our normalized measure of citation impact, while the remaining three columns—columns 4 to 6—display results regarding evidence of a curvilinear relationship between diversity measures and citation impact, by introducing the quadratic term for each of the diversity measures in turn.
First, Table 6 shows that there is no evidence of a statistically significant relationship, either positive or negative, between the composite indicator of IDR Rao-Stirling diversity and citation impact. This finding runs apparently contrary to the presumption that IDR has a significant impact on citations. Given the non-significant outcome of Rao-Stirling which is a distance weighted Simpson index , we also investigated the effect of a distance weighted Shannon diversity, with a similar non-significant results.
However, Column 3 in Table 6 shows that the three aspects of diversity have a statistically significant and distinct effect on citation impact. While variety is positively associated with citation impact, balance and disparity are negatively associated with citation impact. Therefore, the number of different WoS categories a publication draws upon has a strong positive effect on the citation impact, but this effect can be outweighed by the effects of too high a distance between the WoS ategories high disparity or too even a distribution across WoS categories high balance.
The second important result from Table 6 is that all the quadratic terms are statistically significant and negative. For all three diversity measures, the results from Table 6 indicate the presence of a curvilinear inverted U-shape between each of the separate diversity measures and the citation impact of publications.
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This curvilinear relationship indicates, in principle, that while variety, balance and disparity have an initial positive effect on the citation impact of publications, a threshold is reached beyond which higher levels of diversity might be detrimental to the citation impact of publications. This curvilinear relationship is illustrated in Fig 2 , showing the inverted U-shape relationship for each of the three aspects of diversity.
Top: Relation between variety a , balance b and disparity c with citation impact as found in the regression analysis. Bottom: Distribution of articles with over variety a , balance b and disparity c. These results are overall consistent with those obtained for the complete sample. In particular, we observe that the three aspects of diversity have all a significant effect on the citation impact of publications, and with a similar sign to that obtained for complete sample with minor exceptions. Moreover, we also observe that the curvilinear inverted U-shape relationship does generally apply for most of the cases in which a quadratic term is introduced in the regression analysis.
These results have not been included in the paper but are available from request to the authors. However, a more careful inspection of Fig 2 reveals that the distributions of articles in the curvilinear relationships in the inverted U curves, fall in the positive side of the slope for variety and the negative side of slopes for balance and disparity. This means that most articles would increase their citations by increasing variety and by decreasing balance and disparity—in agreement with the linear model in column 3.
Regarding other determinants of citation impact included in the analysis, our findings are consistent with results in previous studies. We have found that citation impact is positively and significantly shaped by: the number of authors and the number of institutions involved in a paper. We have also found support for the positive impact of international collaborations on the citations received by a paper, even though this effect is in some cases weakly statistically significant in agreement with the review by Frenken et al.
In this paper we have investigated the relationship between interdisciplinary research and citation impact. A key novel element in our study is the way in which we operationalise the concept of interdisciplinarity by exploring separately the three different attributes of diversity, i. This more comprehensive implementation of interdisciplinarity accounts not only for the dimensions of variety and balance but, unlike previous studies, also encompasses cognitive distance, i. Our results show that the relationship between interdisciplinary research and citation impact is heavily dependent on how IDR is measured and operationalised.
Another difference of our study with previous approaches is the use of multivariate regression analysis. This allows us to disentangle the effect of our three measures of IDR on citation impact, once accounting for the effects of a wide range of control variables. The first contribution of this study is that different aspects of diversity push in distinct and possibly opposite directions when examining their association to citation impact. These distinct effects of the various components of diversity are likely to be the reason for the contrasting findings in the literature, which has pointed out in all possible directions: positive, negative and curvilinear relationships between IDR and citation impact.
These different effects, may also explain why the full indicator of IDR i. Rao-Stirling diversity , which expresses the three aspects of diversity within a single measure, shows no statistically significant association with citation impact. However, in contrast with this result, we find that the three aspects of diversity have a strong significant effect when they are examined as independent explanatory factors: variety is positively associated with citation impact, while balance and disparity are negatively associated with citation impact.
Our results further qualify the separate effect of the three aspects of diversity by pointing out that all three dimensions of IDR i. In other words, there is an inverted U-Shape relationship between citations received and the number of WoS categories cited variety , the distribution of references over WoS categories balance and the cognitive distance of the references disparity.
This means that there is a threshold beyond which more of any of the different aspects of IDR may be detrimental to citation impact.
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The disagreement may have various origins. Moreover this approach does not take into account the proportions of categories referenced within a paper, but only whether two disciplines are co-cited.
A first insight from these results is that publications that accrue the most citations are moderately interdisciplinary neither too much, nor too little , in accordance with suggestions from previous studies [ 48 , 50 ]. The key new insight of this study is that highly cited papers tend to cite various disciplinary categories higher variety , but cite little outside their disciplinary vicinity lower disparity and in small proportions lower balance. We propose the concepts of proximal and distal interdisciplinarity to interpret these results. Distal interdisciplinarity would refer to bold interdisciplinary papers that draw a significant proportion of references from disparate disciplines.
According to various studies this type of work is unlikely to become highly cited. Instead, proximal interdisciplinarity would reflect more cautious research practices that go beyond the immediate sub-discipline, but still mainly draw on related knowledge. The results should be taken with caution given various limitations.
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First, the diversity measures used are just one of various possible and equally legitimate measures of variety, balance and disparity. Second, the inaccuracies in the WoS categories used to define subdisciplinary categories may create biases in the indicators of citation impact since citation impact is highly affected by normalisation [ 24 , 44 ] and may have an important effect as well in diversity measures.
Third, we do not consider potential differences in behaviour between disciplines since the four WoS categories studied show relatively similar results. However, other disciplines might have different dynamics [ 52 ]. Fourth, in this study we use a 5-year window that might be insufficient for IDR research, since IDR may accrue citations later and over longer periods.
For instance, although variety and disparity have a negative effect on diversity with 3-year windows, they have a positive effect with year windows according to Wang et al. Sixth, the inclusion or not of some control variables such as number of co-authors, institutions or article length is open to debate and these may have an effect on results.
The differences in field classification, citation window and control variables across studies may explain the sometimes contradictory results found in different studies.
A systematic, muldimensional approach testing many hypotheses will be needed to find out which factors from those listed above explain the source of disagreement between the different recent publications. For example, the partial disagreement of our results with Wang et al. Another serious limitation for the policy relevance of this study is that the analysis is based on the IDR of single publications, instead of analysing the degree of IDR in a given research group or project, which would be the proper sociological unit of analysis.
We pose the hypothesis that the "optima" of diversity found for papers can be lower than the optima for research groups, since failed and risky interdisciplinary articles may feed fruitful knowledge into future IDR efforts. These findings may portray two distinct social dynamics. On the one hand, they are consistent with the view that high citation impact research is achieved in scientific efforts clearly positioned in a given field with only a small proportion of contributions from related fields proximal IDR. This finding aligns with the notion that researchers have bounded rationality and are only capable of making productive knowledge combinations within their cognitive proximity, as distant explorations are associated with high uncertainty [ 63 ].
Distal IDR might be highly successful in a few cases, but in average it produces more failures with lower citation impact due to coordination costs described in section 2 such as lack of epistemic understanding across partners or bureaucratic hurdles [ 36 , 43 ]. Studies in other areas of knowledge management have found analogous results; for example, innovative performance of firm alliances shows an inverted U-shape dependence on the technological distance between firms [ 64 ]. A second interpretation of the findings is that scientific audiences do not have enough absorptive capacity for reading, valuing and then citing unconventional knowledge combinations.