Quantitive Evalution of Involvement of Countries of the World in the International Open Access Movement

The article presents the developed method for the quantitative evaluation of involvement of countries of the world in the international open access movement. It consists in the identification of eight country open access indicators initially connected with the open access initiatives and instruments, their weighing, normalization and aggregation in the form of a weighted average value. In a second more strict approximation the number of indicators has been reduced up to six for the account of discarding the data duplicated in ROAR and Open DOAR. Budapest initiative and Berlin declaration were considered as the ОА-initiatives, and data from the international registers DOAJ, SHERPA/RoMEO, ROAR MAP and the Webometrics ОА-repositories ranking was considered as the instruments. The calculation is done on the basis of the developed method for 133 countries


Introduction
A fair number of scientific works are devoted to the problem of movement of the open access to scientific knowledge launched at the turn of the century. In the advanced search "Google Scholar" we find 394 responses to the request of the term "Open access to scientific knowledge" in the exact word combination line (8 June, 2017). At the same time there are very few works dedicated to the quantitative analysis of involvement of countries in this movement. Among the above-mentioned responses we managed to single out five articles which considered the distribution of the open access repositories and journals on a country-by-country basis. The work (Wani et al., 2009). gives the distribution of OAR (Open Access Repositories) in the Open DOAR register across the leading countries of the world (Tab. 1). More up-to-date data on the OAR distribution in the Open DOAR and ROAR registers are shown in the   Open DOAR  ROAR  USA  395  547  Great Britain  209  249  Germany  165  193  Japan  138  166  Spain  98  153  Poland  75  106  France  71  82  Italy  70  88  Canada  58  85  India  54  94 Having compared these tables, we see what fold the OAR has increased in the Open DOAR for four and a half years. The greatest increase of the OAR has been observed for the USA. Also this article describes the growth dynamics of the number of the ОА-journals (OAJ) in the DOAJ register for the period from 2002 to 2013. Let's give the data obtained at the ends of this time interval (Sokolov and Sungatullina, 2015). (Tab.3). As we can see from the built tables, the number of the ОАJ grows much faster than of the ОАR. The work provides the OAR distribution across 11 leading countries distinguishing those of them which function within the frameworks of the Open Archives Initiative Protocol for Metadata Harvesting (РМН ОАI), and the work gives the distribution of a wider set of the open access resources and instruments for the Sub-Saharan African countries. The work describes the data of distribution of the OAR and OAJ number across the CIS countries (Roy et al., 2013;Sizyoongo et al., 2014;Zakharyan et al., 2015).

Materials and Methods
We will characterize the involvement of countries in the international open access movement by statistic data from registers of the largest open access initiatives and instruments. We will consider Budapest initiative "Open access" (2002) and Berlin Declaration of the open access to scientific and humanities knowledge (2003) as such initiatives, and the international registers ROAR, Open DOAR, SHERPA/RoMEO, ROAR MAP, DOAJ and Webometrics ranking for the ОА-repositories as instruments. In total, we will use 8 quantitative indicators (a number of organisations which have signed Budapest initiative and Berlin declaration shall be taken for the first two). Values of these eight indicators are also recorded in a form of a matrix (table) for fifteen ex-USSR countries and based on it the average values for each index per one country and the total quantitative potential of the open access initiatives and instruments on a country-by-country basis shall be calculated by summation of lines of this matrix. As far as all these indicators are not equal worth, and some of them replicate each other, so we will offer the following procedure for more precise calculation of the quantitative potential of involvement of countries in the open access. Let's choose one most essential index out of three indicators which relate to the ОА-repositories. It should be understood here that organisations usually register their ОА-repositories simultaneously in two registers -ROAR and Open DOAR, provided that the first register is more popular. Besides, the actual number of records in these registers usually exceeds the real number of functioning ОА-repositories. Replication of records takes place, for examples, due to the change of an ОА-repository name or its re-registration. At the same time, the real number of functioning ОАrepositories which data is indexed by search engines is disclosed reliably in the Webometrics ranking. We will take this index as a basis. Let's break down six selected indicators into three groups in order of importance with assignment weighting coefficients to them (Tab. 5). When distributing weighs for these six indicators, we proceeded from the following considerations. Groups were chosen with the uniform indicators (carriers of the ОА-results, ОА-policy, ОА-initiatives), that is why there were taken equal weighting coefficients among indicators of one group. The significance of the very groups (summary weighting coefficient for a group) was supposed to be increasing with the uniform interval according to the procedure specified in the table 5. Herewith the sum of group weighting coefficients was taken to be equal to one. Thus, the integrated index of involvement of countries in the international open access movement can be calculated using the weighted average value.
(1) Where, Ii maxmaximum value of i index over the whole sampling of countries. There is carried out the correlation analysis between IOA and indicators normalized to the maximum value according to the sampling of countries N´=N/N . The total number of estimated countries turned out to be 133.

Results and Discussion
Initial values of eight indicators of involvement of fifteen ex-USSR countries in the international open access movements, which were collected by us on 24-26 June, 2017 from the ОА -initiatives and OA-instruments Websites are shown in the Table 6. This table shows calculated values of N, N´=N /N and IOA. Countries in the table are ranked by values of the index N (N´). There has been obtained a good correlation relationship between N´ and IOA (Fig. 1).

Figure-1. Linear regression equation between
5% of the total number of the ОА-initiatives and ОА-instruments is accounted for by 20% of countries (27 countries) (Tab. 6), i.e. we obtained the distribution closed to Pareto distribution.
If we break all countries into 5 groups, accordingto the five-level uniform classification scale by N´ index, so we can see their very non-uniform distribution. Only USA will fall into a group of countries with very high level of involvement in the ОА-movement (0.8 < N´ ≤ 1.0), the United Kingdom will fall into a group of countries with a high level (0.6 < N´ ≤ 0.8), Brazil will fall into a group of countries with the average level (0.4 < N´ ≤ 0.6), Spain, Germany, Indonesia, Japan, Poland, Italy, India, Egypt, France will fall into a group of countries with a low level (0.2 < N´ ≤ 0.4). The rest of countries (121 countries) falls into a group with a very low level of involvement in the ОА-movement, which amounts to 91% of their total number (Ike and Lee, 2014;Usova, 2009).

Conclusion
Thus, this article presents the developed method of the quantitative evaluation of involvement of countries in the international open access movement which principle consists in the identification of indicators of involvement of countries in the open access, their weighing, normalization and aggregation on the weighted average value basis. Two global initiatives -Budapest initiative and Berlin declaration were considered as the ОА-initiative, and particularly, databases according to their subscribers. The international registers according to the ОА-repositories (ROAR, Open DOAR), OA-journals (DOAJ), ОА-policies (SHERPA/RoMEO, ROAR MAP) and ranking of the ОА-repositories in Webometrics were considered initially as the ОА-instruments. During more strict selection of indicators we excluded from consideration the data of ROAR and Open DOAR registers due to their errors and duplication. Finally, six quantitative indicators were broken down into three groups (ОА-carriers, ОА-policies, ОАinitiatives) with different weighting coefficients. Weighing and normalization of these indicators provided the opportunity to obtain the weighted average integrated index of involvement of countries in the open access which varies from 0 to 1. There has been obtained a high correlation relationship between values of this index and the total number of the ОА-initiatives and ОА-instruments. It is shown that 76.5% of the total number of these initiatives and instruments is accounted for by the first 20% of countries. Use of the uniform five-level classification scale according to N´ index shows that 91% of countries (121 countries) falls into the group with very low level of involvement of countries in the ОА-movement (Shishkina et al., 2015).