Gender gaps in international research collaboration: a bibliometric approach

This paper addresses gender differences in international research collaboration measured through international co-authorship. The study is based on a dataset consisting of 5600 Norwegian researchers and their publication output during a 3-year period (44,000 publications). Two different indicators are calculated. First, the share of researchers that have been involved in international collaboration as measured by co-authorship, and second, the share of their publications with international co-authorship. The study shows that the field of research is by far the most important factor influencing the propensity to collaborate internationally. There are large differences from humanities on the one hand, where international collaboration in terms of co-authorship is less common, to the natural sciences on the other, where such collaboration is very frequent. On an overall level, we find distinct gender differences in international research collaboration in Norway in the favour of men. However, men and women are not equally distributed across fields and there are relatively more female researchers in fields where the international collaboration rates generally are lower. When the data are analysed by scientific field, academic position, and publication productivity of the researchers, the gender differences in the propensity to collaborate with colleagues in other countries are minor only, and not statistically significant. Concerning gender inequality in science, the main challenge seems to be the lower productivity level of female researchers, which obviously hinders their academic career development. Differences in international collaboration are unlikely to be an important factor in this respect, at least not in the Norwegian research context analysed in this study.


Introduction
Men and women have been shown in numerous studies to perform differently according to various indicators related to the process of scientific publishing. In particular, female researchers on average are less productive and publish fewer publications than male researchers. This has been demonstrated in numerous studies (for example, Kyvik and Teigen 1996;Piro et al. 2013;Larivière et al. 2013;Mayer and Rathmann 2018). The pattern seems to be universal across fields and nations, although the differences vary. As an example, Rørstad and Aksnes (2015) showed that after adjusting for position and age, female researchers in Norway on average publish 10-20% less than men. The question of whether women are less cited than men has also been analysed in several studies. Here, the results are less clear, and the findings vary. As an example, a previous Norwegian study found only small gender differences (Aksnes et al. 2011), while a global analysis based on articles with first and last authors showed lower citation rates for female authors (Larivière et al. 2013). Lagging behind in terms of scientific production and impact represent a major problem because these two factors are decisive, for example, for academic promotion and in the evaluation of research proposals by funding agencies (European Commission 2015).
In this study, another dimension is analysed, namely gender differences in international collaboration. Studies of scientific collaboration are commonly based on co-authorship data. Here, a publication is considered to be co-authored if it has more than one author and internationally co-authored if it has authors affiliated with institutions located in different countries. International co-authorship is then applied as a proxy or indicator of international collaboration. Compared with other methodologies, bibliometric data can provide unique and systematic insight into the extent and structure of scientific collaboration. One advantage is that large datasets can be easily analysed, for example, entire countries, and the results will be empirically robust. Moreover, the indicator captures both formal and informal types of collaboration. At the same time there are also limitations attached to using such data as a measure of collaboration (Katz and Martin 1997). The biggest issue is that research collaboration does not always result in joint co-authored publications. Another problem relates to the limited coverage of the bibliographic databases typically applied in such studies (e.g. Web of Science (WoS) or Scopus), where books, books chapters, and articles in national journals are not indexed by the databases to the same extent as articles in international journals (Aksnes and Sivertsen 2019). This problem affects the humanities and the social sciences in particular.
In general there has been a large increase in the extent of international collaboration in recent decades, and this is documented in a number of previous studies (e.g. Leydesdorff and Wagner 2008;Adams 2012;Wagner et al. 2017). In many countries, the majority of scientific publications are now internationally co-authored. Another important issue is that there are large differences in the collaboration rates across countries, as was shown in a paper by Luukkonen et al. (1992) and in numerous later studies (e.g. National Science Board 2018). Generally, countries with smaller science systems tend to have higher proportions of internationally co-authored articles than larger nations, although size only explains a minor part of the variances in co-authorship rate at the country level. Finally, previous research has shown that there are large differences in the collaboration rates at the level of fields and disciplines (Aksnes et al. 2008;National Science Board 2018). For example, the proportion of publications involving international co-authorship is much higher in the natural sciences than in the social sciences and humanities. There seems to be an almost universal hierarchy among the disciplines with regard to international collaboration. These differences in turn relate to the nature of the study objects and the role of teamwork in the research process and co-authorship practices. In the humanities, the majority of the publications have only one author, and therefore this field will by default have low collaboration rates (Aksnes et al. 2008).
Gender differences in collaboration have become ever more important to study due to the steady global increase in research collaboration in groups and networks (Leydesdorff and Wagner 2008) and in interdisciplinary research (Lee and Bozeman 2005). Based on a review of former networking studies, Fell and Köning (2016) examined reasons for why gender differences in collaboration might be expected and factors that particularly affect female researchers. Women have generally been found to be more agreeable than men, and this personality trait might lead to more networking. Moreover, women outperform men in tests of emotional intelligence, and this ability might be beneficial for collaborating. On the other hand, there are also issues that pull in the other direction, for example, that women traditionally have more responsibility for child care (which is time-consuming and would limit their time for activities such as building networks). Also, there are findings suggesting that women receive less optimal mentoring than men, which means that their socialisation into the scientific communities is not as good as for men (Fell and Köning 2016).
Several studies have been carried out over the years to investigate whether there are gender differences in collaboration. These studies address collaboration more generally or international collaboration (collaboration with colleagues in other countries) more specifically. Concerning the first issue, empirical evidence has been provided that women generally are less engaged in collaborative projects than men and that they publish more singleauthored works (Boschini and Sjögren 2007;Fox 2001;Jadidi et al. 2018;Nielsen 2016;Zettler et al. 2017). Women have also been shown to be less inclined to participate in longstanding research collaborations, which are associated with high scientific impact (Jadidi et al. 2018;Zheng et al. 2016). Nevertheless, there are also studies reporting deviating findings. Fell and Köning (2016) in a study of industrial-organisational psychologists found that female researchers were more engaged in scientific collaborations than men. Similarly, Abramo et al. (2013) showed that female researchers in Italy had higher overall collaboration rates than men.
When it comes to international research collaboration, the knowledge on gender differences seems inconclusive (Poole and Bornholt 1998;Larivière et al. 2011;Vabø 2012). Some studies have reported that women on average have lower rates of international collaboration then men. For example, Frehill and Zippel (2010) found that among holders of doctoral degrees in the US, men were more often than women engaged in international collaboration. Similarly, a bibliometric analysis by Elsevier (2017) showed that women are less likely than men to collaborate internationally. The She Figures report by the European Commission (2015), however, reported only marginal differences, where the propensity of women to publish articles with international co-authors was almost equal to men. This issue is important to analyse further because international research collaboration has been shown to be advantageous to researchers' productivity and scientific impact (e.g. Abramo et al. 2009Abramo et al. , 2011Adams 2012;Fox 2018;Kyvik and Reymert 2017;Larivière et al. 2013).

Filling the knowledge gaps on gender gaps
In this study, we draw upon the methodological approach of three previous studiespresented below-but using a Norwegian dataset and including additional variables that 1 3 were lacking in these studies. In this way, we are able to provide a better understanding of gender differences in international research collaboration. Larivière et al. (2013) used WoS data from the period 2008-2012 to study differences in international co-authorship on 5.5 million papers with more than 27 million authorships. The dataset included information on the gender of the authors. Women were shown to be less frequently listed as first authors (roughly 2/3 of the papers had male first-authors) and less inclined to participate in international collaborations. In sum, these factors contributed to lower citation rates among women. Needless to say, such a large-scale study did not include individual data for the authors, such as academic position. The authors state (p. 213) that "it is likely that many of the trends we observed can be explained by the under-representation of women among the elders of science. After all, seniority, authorship position, collaboration and citation are all highly interlinked variables." A second study is Abramo et al. (2013) analysis of international co-authorship among Italian professors based on WoS publications from 2006 to 2010. In this study, academic discipline and institutional affiliation were taken into account, documenting gender differences in international collaboration across scientific fields (all hard sciences and economics). Interestingly, female researchers were shown to have a greater capacity to collaborate in all other collaboration forms that were analysed except for the international dimension. The study only included researchers in tenured academic positions.
A third relevant study is Uhly et al. (2017) investigation of gender differences in international research collaborations in academia. This study, unlike the former two, included individual data on age (as well as academic discipline), but not on academic position. This study applied a different methodological approach and was based on answers from a survey (ten countries analysed with 13,000 respondents in total), where the informants answered yes or no to the question "Do you collaborate with international colleagues?" This makes the results difficult to compare with the two former studies. As the authors state, the measurement of international collaborations is highly dependent on the survey respondents' interpretations of the question, as contrasted by use of publication data where such bias does not exist (Melin and Persson 1996). At the same time, most studies on gender differences in research collaboration have been conducted based on surveys (Abramo et al. 2013).
The main result of Uhly et al. (2017) study is that women engage less in international collaboration than men and that the degree of female international collaboration is dependent on a complex set of individual factors (such as partner employment status and having children). The results led the authors to conclude that "glass fences" are apparent in "in the access to international research collaboration, as women are significantly less likely than men to participate in this elite activity" (p. 761).
In our present study, we aim at filling the knowledge gap in the understanding of gender differences in international research collaboration by comparing international paper co-authorship among men and women at Norwegian universities. This study has several important dimensions.
First, we use a database that, in contrast to WoS, has complete coverage of all peerreviewed scientific and scholarly publication output, including books, edited volumes, and conference series. This means that we are able to provide a better coverage of the social sciences and humanities in particular.
Second, we analyse the issue at the level of fields and disciplines. The importance of comparing by fields has been documented by, for example, Kyvik and Reymert (2017) and Abramo et al. (2013), with the latter study arguing that gender differences in international 1 3 cooperation "could be due to certain factors that characterize each discipline, beginning from the percentage of women in the total research staff" (p. 819).
Third, we take the academic position of the researchers into account, which is important because two previous Norwegian studies have found that older academic staff are less inclined than their younger colleagues to participate in international research networks (Kyvik and Reymert 2017;Kyvik and Olsen 2008).
In sum, these factors enable us to first test whether there are gender differences in international collaboration and second whether the differences vary by academic position (which is strongly correlated with age) and research field. In addition to this, we add a third main explanatory variable-scientific productivity-because we believe that international collaboration might be more manifest among established researchers with high scientific productivity. Such a decomposed analysis based on these factors might add important knowledge to the understanding of gender differences because while there might be gender differences at the overall level, or by one factor alone, it is not unlikely that the gender differences show covariation with other factors. Here, we try to isolate such factors in a multivariate analysis.

Data and methods
This study is based on the bibliographic Cristin database (the Norwegian Science Index) that has been developed as part of a current research information system for all public research institutions in Norway. The database has complete coverage of all peer-reviewed scientific and scholarly publication output, including books, edited volumes, and conference series (see Piro et al. 2013 for further details). The system ensures complete, verifiable, and structured data for bibliometric analysis. Of particular importance for the study of scientific collaboration is that all authors and addresses are indexed, including country as a controlled term. In this study, we have analysed publications from the three-year period 2015-2017.
A publication is considered to be internationally co-authored if it has authors affiliated with institutions located in different countries (in our case Norway and one or more other countries). This is the common principle applied in bibliometric studies of scientific collaboration based on co-authorship data (Katz and Martin 1997). A special case is authors having both a domestic and international affiliation. In this study, publications are counted as internationally co-authored if they have at least one foreign institution on the address list, regardless of whether the analysed set of authors or other co-authors are affiliated with this/these institution(s). Thus, we have not excluded cases where the authors have both a domestic and international affiliation. We think this is reasonable because publications authored by the latter type of researchers have an institutional international collaborative dimension. The alternative would be not to consider these publications as internationally co-authored. In order to assess to what extent this alternative would yield different results, we carried out a test and found that the issue is of marginal importance and is not likely to have an influence on the main findings of the study. 1 As a source of information on the individual characteristics of the persons (gender, age, position, and institution), the data in the bibliographic database were coupled with another database, the Norwegian Research Personnel Register. This database contains individual data for all researchers in the Higher Education Sector and Institute Sector in Norway.
The data material consists of 5554 researchers from the four largest universities in Norway (University of Oslo, University of Bergen, The Arctic University of Norway, and The Norwegian University of Science and Technology). The study is limited to professors, associate professors, postdocs, and PhD students with at least one publication during the time period analysed. Their publication output during the period 2015-2017 in total accounts for 43,641 publications ( Table 1). The researchers were assigned to research fields based on the field distribution of their publication output. In the Cristin database, all journals are classified into five broad areas (social sciences, humanities, natural sciences, technology, and medical and health sciences) and 85 subfields/disciplines, and a similar classification system is used for the book publications. Based on this system, the researchers were assigned to the broad areas and sub-areas/disciplines in which they had the highest number of publications. In cases where they had an equal number of publications in two or more categories, they were randomly distributed to one of these categories. It should be noted that some journals have a multi-disciplinary profile and address issues covering several disciplines (e.g. Plos One and Science). These journals are classified in general categories (e.g. multidisciplinary natural sciences and technology). A small minority of the researchers had the highest number of publications in these general categories and were therefore not assigned to specific disciplines.
Female researchers constitute 42% of the study population, while they only account for 32% of the publications. The female share of the researchers varies greatly by field, and it is highest in the medical and health sciences (53%), social sciences (50%), and humanities (46%) and considerably lower in the natural sciences (31%) and technology (22%). The female shares of the publication output, however, do not coincide with the distribution of researchers. Women publish less than men in all fields. In technology, the difference is smallest-22% of the researchers are women and they account for 19% of the output, i.e. a publication output 3 percentage points lower than expected based on the distribution of researchers. This female under-representation of the publications is moderate in the social sciences (4 percentage points difference) and humanities (4 percentage points difference) and high in the natural sciences (9 percentage points difference) and medical and health sciences (12 percentage points difference).
Scientific productivity is very skewed at the level of individuals. A large part of the researchers have very few publications, while a minority are highly prolific. This issue is essential to take into account when studying gender differences in international collaboration. Without a stratification of the study population into different productivity intervals, important nuances are lost. We have classified the individuals into three groups based on their publication output-one consisting of researchers with low productivity, one consisting of prolific researchers, and one consisting of researchers with intermediate productivity above or below the average (7.9) and median (4). The first group consists of researchers with 1 or 2 scientific or scholarly publications during the three-year period (32% of the study population), the second group is the researchers with 3-9 publications during Footnote 1 (continued) co-authored anyway. In fact, only 161 publications have no other co-authors from foreign institutions. These publications account for only 0.36% of the total publication set.

Table 1
Distribution of researchers and publications by research fields and gender the period (46% of the population), and the third group consists of the highly productive researchers with 10 + publications (22% of the population). However, at the level of gender, these proportions differ significantly. For example, 38% of the female population have 1-2 publications compared with 27% for men. On the other hand, men are a higher proportion than women in the group consisting of prolific researchers. These findings hold across all fields analysed (Table 2). Although the specific criteria used for the classification might appear somewhat arbitrary, it nevertheless allows us to add further insight into how international collaboration relates to productivity. However, as an alternative we have calculated a field-normalised productivity indicator where the number of publications from each researcher has been compared with the average for their subfield (85 categories).
In the analyses, we also include the academic position of the researchers. Thus, the analyses are carried out by field of research, academic position, and scientific production. A complete overview of the distribution of researchers across these variables can be found in Appendix Table 12.
The unit for the analysis is the individual researcher. For each person, we calculate whether they have published at least one publication involving international co-authorship (i.e. having co-authors affiliated with institutions in other countries) during the study period. Second, we calculate the proportion of each individual's publication output involving international co-authorship. Based on these measures, we calculate averages for the different categories the individuals are affiliated with in our cross-sectional analysis (see below). In other words, all individuals count equally as one unit in the analysis regardless of how many publications they have published. This way we avoid the analysis being biased towards highly productive researchers.
We believe both measures are important to consider. The first is a measure of whether the individuals have collaborated internationally, while the second is a measure of the degree of international collaboration. Based on the first dichotomous measure, we are able to analyse the shares of men and women that are involved in international collaboration, but this measure lacks information about the degrees of internationalisation among the individuals. As an example, in two groups we might find that 54% of the men have collaborated with colleagues in other countries, while 57% of the women have such collaboration. If, on the other hand, the measure is the proportion of internationally co-authored publications, we might find that in the female group the individuals on average have 35% of their publications with international co-authors, while the average for men is 39%. We now have two results that pull in different directions, and the two factors provide complementary information on gender differences in international collaboration. What is needed is a measure that takes both factors simultaneously into account. We therefore suggest a simple indicator combining both the presence and scope of international collaboration among men and women, which we call the Gender Difference Collaboration Index (GDCI), which is calculated as: where m/w is the total number of men/women in the study sample, m int/w int is the number of men/women with international collaboration, pub tot is the total number of publications, and pub int is the number of publications with international collaboration. The GDCI varies between − 1 (complete gender difference in favour of women) to 1 (complete gender difference in favour of men). Table 2 Distribution of researchers by gender, field, and publication productivity In addition to GDCI values, we report size-adjusted GDCIs, i.e. GDCIs multiplied by the number of individuals (GDCI * Group n). Size-adjusted GDCIs are reported as percentages of the sum of total GDCIs (% of ∑GDCI * Group N). The rationale for adjusting the GDCIs by sample size (n) is that GDCI is only a measure of the size and direction of gender inequality and does not include information on the relative or weighted importance of the difference to the overall gender inequality. For example, we might find that men in one particular group are much more internationally collaborative than women. However, this group might consist of few individuals. Hence, even a large gender difference in international cooperation will make only a small contribution to the overall gender differences. In other groups we might find minor gender differences, but if the sample size is very large this might still have a large influence on the overall gender inequalities.
Below, we present analyses using the different indicators described above. First, the two basic indicators are presented separately, i.e. the proportions of individuals who have collaborated internationally and the degree of international collaboration, and then GDCIindicators are presented in multivariate analyses.

Results
Overall, 56% of the female researchers are involved in international collaboration as measured by co-authorship. The corresponding figure for men is 66%. Thus, our study shows that overall male researchers are more often involved in international collaboration than their female colleagues. However, as expected there are large differences across fields (Fig. 1). International collaboration is much more frequent in the natural sciences, medical and health sciences, and technology compared with humanities and social sciences, and this holds for both genders. In the humanities, fewer than onethird of the researchers have publications involving international collaboration. There are gender differences in all fields. The gap is largest in the social sciences where the proportion for men is 44% and for women is 36% for women. The gap is smallest in the humanities (the difference is 3 percentage point).
Interestingly, in all domains the gaps are smaller than 10 percentage points, which is the difference for the total/all fields. This is due to the fact that male and female researchers are unevenly distributed across fields (see Table 2), and there are relatively more women in fields where the collaboration rates are lower. Correspondingly, in the natural sciences, which have the highest collaboration rates, there are relatively more men than women, and 28% of male researchers are in this category compared with 18% of female researchers. Figure 2 shows the corresponding figures using the proportions of publications involving international collaboration as the indicator. Overall, male researchers have 37% of their publications in collaboration with researchers in other countries, while the corresponding figure for female researchers is 32%. Gender differences are observed across all fields, but now the differences are reduced. The most evident reduction in gender gaps is observed in natural sciences, where a 7-percentage point higher share of men are involved in international collaboration (Fig. 1), while the share of the publications that involve international collaboration is just 2 percentage points higher for men (Fig. 2). The reduction can be explained by differences in the underlying collaboration patterns. Among the researchers who have collaborated internationally (i.e. have published at least one internationally coauthored paper), women on average have higher collaboration rates than men.
The analysed dataset also includes data at the level of disciplines. An overview of both measures for the largest disciplines can be found in Appendix Table 13. This table shows that there are notable variations in the proportions of international collaboration also within the various fields. For example, in the humanities these proportions are much higher in archaeology and conservation than in literature. In medical and health sciences, international collaboration is much less frequent in nursing than in most of the other disciplines. In the social sciences, anthropology and law have the lowest proportions and geography  International collaboration is only one kind of collaboration. Collaboration more generally involves co-operation among two or more researchers, regardless of whether they are located at the same institution, at external national institutions, or at institutions in other countries. One might assume that the international collaboration dimension partly is influenced by the other dimensions. If male researchers tend to have more co-authors generally than female researchers have, then they might have access to a larger collaborative network and would thus have an increased likelihood of also having more international coauthors. In order to assess this question, we have analysed the average number of authors per publication for each individual (Tables 3 and 4). As expected, researchers involved in international collaboration (i.e. those who have published at least one internationally coauthored paper), tend to have a much higher number of co-authors per publication on average (7.2 authors, including the researcher in question) than those who have not collaborated internationally (2.7 authors, including the researcher) (Table 3). Interestingly, there are hardly any gender differences. For researchers who have not collaborated internationally, women have marginally higher numbers of co-authors on average than men, while the opposite is the case for researchers with international collaboration. Similarly, the issue was analysed according to the intensity of the international collaboration (Table 4). The analysis shows that there is a strong correlation between this intensity and number of coauthors. For example, researchers who have 0-10% of their publications in collaboration with colleagues in other countries have 2.7 authors per publication on average, while the corresponding figure for those with an international collaboration rate of 90-100% is 12.4 authors. This correlation holds for both genders, and overall there are small gender differences and no systematic patterns. In some categories, women have slightly higher numbers of authors than men, while the pattern is the opposite in other categories. In conclusion, this analysis does not support the assumption that men and women are different when it comes to co-authorship practices more generally. The analysis so far has shown that gender differences in international collaboration are observed for the two different measures, albeit to various extents. These crude figures might, however, be contingent upon the gender composition by academic position and publication output. In order to assess this question, in Tables 5 and 6 we present the results split by field, gender, academic position, and publication volume simultaneously. Here figures are shown only for categories with more than 20 researchers. In Table 5 we report the percentage of men/women who have collaborated internationally (yes or no), while in Table 6 we report the average shares of publications with international co-authors.
Comparing academic fields, researchers in the humanities (32%) and social sciences (40%) have the lowest shares of international co-publications, while those in technology (65%), medical and health sciences (73%), and natural sciences (81%) are far more international (Table 5, right column). The same rank order is also found when comparing shares of publications that involve international co-authorship (Table 6). Here, the lowest share is found in the humanities (12%) and the highest in natural sciences (56%).
In both tables, there is a clear association between the publication volume and international collaboration. At the overall level, 37% of men with 1-2 publications have collaborated internationally, while the corresponding figure for women is 33% (Table 5). For the group with 3-9 publications, the figures are 66% and 63%, respectively, and for the group with 10 + publications the figures are 95% and 93%, respectively. Thus, a higher publication volume increases the probability for international collaboration. This is not surprising because this indicator requires only one publication with international co-authorship. For the other indicator there is a similar but weaker association (Table 6). Across the three productivity groups, the proportions increase from 31 to 50% for men and from 27 to 45% for women.
In most fields and productivity groups, shares of international collaboration are highest among men. There are (at the overall level, i.e. by fields not taking academic position into account) only three categories where women rank higher than men on both measures (Tables 5 and 6), namely researchers with 1-2 publications in the medical and health sciences, researchers with 3-9 publications in technology, and researchers with 10 + publications in the social sciences. There are also a few categories where the two indicators show deviating patterns and one gender has the highest proportion on one indicator and the lowest on the other.
The findings above have important implications for the interpretation of the aggregated figures presented in Figs. 1 and 2. As shown in Table 2, a larger part of the female researchers are found in the category of researchers with low productivity (1-2 publications) compared with men (overall 38% and 27%, receptively). At the same time, this group has the lowest proportions of international collaboration. Thus, some of the inequalities at aggregated levels can be explained by the different representations of genders across productivity groups. As an example, in the natural sciences overall, 76% of the female researchers have collaborated with researchers in other countries compared with 83% for male researchers (Fig. 1). In other words, there is a difference of 7 percentage points. However, when the issue is analysed at the level of productivity groups, men in the natural sciences overall have 1, 4, and 2 percentage points higher proportions than women in the three productivity groups (1-2, 3-9, and 10 + publications, respectively) ( Table 5). This means that in all groups the difference is significantly smaller than the difference at the overall level.
When also taking academic position into account, the pattern becomes less clear. In Table 5, men have higher collaboration proportions than women in 20 of 31 categories based on combinations of fields, academic positions, and productivity intervals, while the opposite is the case in 10 categories. In Table 6, there are 15 categories where men rank above women, 14 categories where women rank above men, and 2 categories with no difference. There are also a few cases where the two indicators provide contradictory results (i.e. categories where one gender has the highest proportion on one indicator and the lowest on the other). In addition, the number of observations in each category varies significantly (Appendix Table 12). Accordingly, it might be difficult to interpret and draw conclusion based on these findings. In order to analyse these findings further, a bivariate correlation analysis was carried out of the dependent and independent variables. Spearman's rank-correlation coefficients (rho) were calculated because the data were not normally distributed (Table 7). As can be seen, there is a very weak correlation between gender and the two core indicatorsengaging in international collaboration (yes/no) (Spearman's rho = 0.10, significant at the 0.01 level) and the proportion of publications with international co-authorship (Spearman's rho = 0.08, significant at the 0.01 level). In contrast, the two other variables of productivity interval and field show a stronger correlation with the indicators of international collaboration. Here the Spearman's rho ranges from 0.27 to 0.44. Thus, these results indicate that international collaboration is more strongly associated with publication productivity and field rather than gender. There is no correlation between gender and average number of authors per publication (Spearman's rho = 0.01). As expected there is a very strong correlation between productivity and the normalised number of publications. As a next step, a regression analysis for each field was carried out. When we take academic position, productivity intervals, and average number of authors per publication into account and conduct regression analysis on each major field, we are able to determine whether men collaborate more internationally than their female colleagues do. Table 8 summarises the regression results of the indicator of researchers involved in international collaboration (i.e. if a researcher has or has not collaborated internationally, see Table 5). The table includes the numbers of observations, the adjusted regression coefficients, and the standardised coefficients for each of the variables-gender (men = 1, women = 0), position (professors, associated professors, and postdocs relative to PhD students), productivity intervals (relative to the less productive group of researchers), and average number of authors per publication. Because the dependent output variable is binominal (1 or 0 if the researcher has collaborated internationally or not), logistic regression analyses were conducted. Due to the large differences in the propensity to collaborate internationally across fields, we have not carried out this analysis on the overall level (all fields).
The analysis shows that the selected variables-gender, academic position, productivity, and average number of authors per publication-in total explain 25-35% of the variance. The figure is lowest for the social sciences (0.25) and highest for the natural sciences (0.35). International collaboration can therefore partly be explained by these variables.
The regression summary reveals that productivity is the most important variable in terms of international collaboration, while gender is the least important variable. For all fields, researchers who have published 3-9 articles collaborate more internationally than the less productive researchers, and the highly productive researchers have even higher figures. These results correspond with the findings in Table 5. As for academic position, the results are not completely consistent across fields. However, we find that the international collaboration rates of professors are statistically significant and higher than for PhD students in all fields except the humanities. Interestingly, the results show that gender is a statistically significant variable only in the natural sciences.
A similar regression analysis was also carried out for the indicator measuring the degree of collaboration, i.e. the share of publications with international co-authorship (see Table 6). Because the dependent variable in this case is continuous and not categorical, we used linear regression. Moreover, the variable was not normally distributed and thus was log-transformed. As a result of the log-transformation, the researchers without international collaboration (values of 0) were left out of the analysis. Thus, this analysis has important limitations but nevertheless provides interesting complementary results. The regression results are presented in Table 9 below. This analysis concerning gender shows results in line with those presented above. For none of the fields was gender a statistically significant variable.
In Table 10 we present GDCI values in all categories so that we can identify one unified expression of the gender inequality. In addition to GDCI values, we report size-adjusted GDCIs (summed to 100, where GDCIs are adjusted for sample size). This enables us to identify in which categories the origins of the gender equality can be found and the relative contribution of each category to the total inequality.
The first observation in Table 10 is that it is in the group of less productive researchers (1-2 publications) that we find the greatest source of gender inequality. In the two publication output groups that we consider the most important ones, the gender inequality is much higher among the most productive researchers (36% of the total size-adjusted Table 8 Logistic regression analysis, researchers involved in international collaboration (yes or no), and selected variables by fields Unstandardised regression coefficients, standard errors in brackets. Statistically significant relationships shown with *signs (95% confidence interval) and **signs (99% confi-

Table 9
Linear regression analysis, average proportion of international co-authorship, and selected variables by fields Unstandardised regression coefficients, standard errors in brackets. Statistically significant relationships shown with *signs (95% confidence interval) and **signs (99% confi-

Table 10
Gender Difference Collaboration Index (GDCI) by field and publication productivity  GDCIs) compared to the middle group (3-9 publications, 23%). Second, gender differences are almost non-existent in the humanities where international collaboration is far less common compared to other fields. Among the most productive humanists (and social scientists, too), women are in fact more internationally collaborative than men, but the overall contribution to gender differences is just 0.45%. Third, in the natural sciences there are no gender differences among the most productive researchers. Although this field tends to be dominated by men, the publishing behaviour of female natural scientists does not deviate from men among the most prolific researchers. In the least productive group, male natural scientists are more collaborative, while women have a higher index in the mid-productivity group (3-9 publications). Fourth, in technology there are strong gender differences (in favour of men) among researchers with few publications. Fifth, and most notably, in medical and health sciences female researchers are more internationally collaborative among the least-productive researchers, but the two single most important contributors to gender differences are found here among the more productive researchers.
Although GDCI values are higher in some other categories, these two categories contribute to the largest part of the gender inequality in favour of men (due to the high n). Despite the fact that women are equally or more internationally collaborative than men in several categories, the overall results show that men rank above women in all productivity categories.
In Table 11 we provide more detailed results where academic position is also added as an explanatory variable. This enables us to identify in which areas of research, for which type of positions, and at which productivity level gender differences are present. At first glance, it is clear that gender differences in international collaboration are very minor or not present in most categories. In the categories where women have higher GDCIs than men, the relative contribution to the total inequality tends to be small because the GDCIs in favour of women are often based on very small samples (often in combination with low GDCIs). If we arbitrarily choose a 5% size-adjusted GDCI as the threshold for significant gender inequality, there are only two categories (female postdocs in the natural sciences and associate professors in medical and health sciences with 1-2 publications) where women have a substantially higher size-adjusted international collaboration index than men. Among men, on the other hand, there are several such categories. The strongest contributions to men's higher degree of international collaboration is found for PhD students in technology and in the medical and health sciences with 1-2 publications and professors in the medical and health sciences with 10 + publications. Male PhD students contribute to 11.5% of the total size-adjusted GDCIs in technology and to 9.6% of the total size-adjusted GDCIs in the medical and health sciences.

Discussion
Our analyses have shown that the field of research is by far most important factor influencing the propensity to collaborate internationally. There are large differences from the humanities on the one hand, where international collaboration in terms of co-authorship is less common, to the natural sciences on the other, where such collaboration is very frequent. This study also demonstrates that publication productivity and academic rank are factors that are important to take into consideration when analysing scientific collaboration Table 11 Gender Difference Collaboration Index (GDCI) across fields, academic position, and publication production  at the levels of individuals, and this is also emphasised in studies by Bozeman and Gaughan (2011) and Zeng et al. (2016). Our results show that there are distinct gender differences in international research collaboration in Norway at an overall level. However, women and men are not equally distributed across the variables analysed here. First, there are relatively more female researchers in fields where the international collaboration rates generally are lower, and this might explain why the gender differences at the field level are lower than the differences at the overall level. Second, women account for higher proportions of personnel with lower academic ranks and with lower publication productivity. In these groups, the propensities to collaborate internationally are lower for both genders. As a consequence, the gender differences are smaller when academic position and productivity are taken into account. The regression analysis shows that the gender differences are not statistically significant when these variables are taken into account, with the exception of the natural sciences for the indicator of researchers involved in international collaboration. In this way, our findings confirm the assumption by Larivière et al. (2013) concerning the importance of seniority as an explanation for the gender disparities that have been identified (as described in the introduction). It is a general principle in analyses like this one that one should compare "like with like", and our study has demonstrated that gender differences in scientific collaboration might be overestimated if factors such as productivity and academic rank are not taken into consideration.
The analyses at the level of field, academic position, and productivity provide a much less distinct picture. In fact, in several categories female researchers have higher rates of international collaboration than male researchers. Still, in the majority of categories where field, academic position, and productivity are analysed separately, shares of international collaboration are slightly higher for men than for women. We find the strongest gender difference in favour of men in the medical and health sciences. The differences are particularly pronounced at an early phase of the researchers' careers-i.e. researchers in recruitment positions and researchers with a relatively low number of publications-and the differences are less pronounced at later stages.
As noted in the introduction, previous research has not provided consistent findings concerning gender differences in international research collaboration. The She Figures report (European Commission 2015) concludes that for the EU-28 overall, the female to male ratio is only marginally smaller than 1. This means that the propensity of women to publish articles with international co-authors is almost equal to men. However, at the level of individual countries, there are some differences. For Norway there is no gender gap at all, and the ratio is 1. This might appear surprising considering the results of our study showing a gender gap at the overall level. However, the She Figures report is based on analyses of corresponding authors only. This is an important limitation that is acknowledged in the report (page 162): "This indicator […] carries the risk of focusing on those women who stand out from the average population of women scientists by virtue of their more established collaboration networks. Because of this potential selection bias, this indicator might provide a more positive picture than is truly the case in the whole population of researchers with regards to gender parity".
A bibliometric analysis carried out by Elsevier (2017) concluded that women are less likely than men to collaborate internationally. This finding held for all 12 countries analysed in the study, and the differences in the period 2011-2015 ranged from 10 percentage points (Chile) to 4 percentage points (Portugal and Japan). However, this analysis was carried out at an overall level and the facts that the collaboration rates vary a lot across fields and that men and women are not equally distributed were not taken into consideration. As seen in our study, such factors might explain a significant part of the observed gender gaps.
Although our findings are based on a large dataset, they are limited to just one country. As explained in the introduction, there are large differences in the rate of international co-authorship across countries. As a small country, Norway has higher collaboration rates than many other countries, and thus analyses of other larger countries might reveal lower frequencies of such collaboration than the ones presented in this study. However, the issue concerning gender gaps might not be affected by such differences. In the She Figures report (European Commission 2015), only two countries (Cyprus and Iceland) had higher gender ratios of international collaboration than Norway. It is therefore likely that the gender gaps might be somewhat smaller in Norway compared with several other countries. Further analyses would be required in order to address this question.

Conclusions
The main contributions of our study are twofold. Methodologically, by applying two different measures of international collaboration and combining them into a single index, we have been able to provide complementary pictures of this dimension. Empirically, we have presented new evidence on gender differences in international research collaboration by applying a database with complete coverage of the scientific and scholarly publication output.
International collaboration is a crucial part of today's science and represents an important difference in how science is carried out today compared with the recent past. Such collaboration might contribute positively to the career development of individual researchers, and therefore international collaboration is an important issue to address concerning gender inequality in science. Our study has shown that there are notable gender differences at the overall level. However, when field, academic rank, and productivity are taken into consideration there are only minor and non-statistically significant sex differences in the propensity to collaborate with colleagues in other countries. Concerning gender inequality in science, the main challenge seems to be the lower productivity level of female researchers, which obviously hinders their academic career development. Differences in international collaboration are unlikely to be an important factor in this respect, at least not in the Norwegian research context as analysed in this study.  *Only disciplines with at least 50 individuals (in total) have been included in the table