Application of factor analysis to measure social capital in Slovak districts

Factor analysis is a technique particularly suitable for analysing the patterns of complex, multidimensional relationships. Given the multidimensional nature of social capital, a plethora of indicators is often utilized for measurement purposes. In this paper, we utilize factor analysis to explore patterns of social capital and to identify spatial differentiation in the level of social capital at the level of Slovak districts. Three factors have been extracted. The first factor represents low level of bridging social capital, the second factor represents activities of associations and the third factor represents low level of bonding social capital. Factor scores of extracted factors have been visualized in order to explore spatial differentiation of social capital. Visualisation shows significant differences in the levels of individual forms of social capital in Slovak districts.


INTRODUCTION
Social capital is considered to be a multidimensional concept involving relationships and contacts between actors of social groups and networks, as well as trust in other members of the group or network, the entire community or the whole society and its institutions [4,7].Since the early 1990s, the concept of social capital has become a subject of broad attention.It became popular mainly thanks to the research of Burdieu [3], Coleman [4], and Putnam, Leonardi, and Nanetti [15].The first two mentioned authors conducted analysis on a micro level (individuals, small groups).The latter authors analysed social capital on a macro level (Italian municipalities) and they considered it not as an individual asset but as an attribute of the community itself.They defined it as "features of social life -networks, norms, and trust".This concept is also perceived as a tool for explaining the differences in the economic development of the regions [6].
Measuring social capital is relatively complex.This is due to the amount of its definitions and also to a large number of its forms (especially individual and collective, bonding, bridging and linking, structural and cognitive) [12].Bonding social capital represents trust between individuals in close, homogeneous groups.Bridging social capital connects different groups of actors, who are similar in terms of hierarchical status in society.Weak ties are characteristic for this form of social capital.Weak ties and social trust in the territory facilitate access to other forms of capital [6].Linking social capital represents a network of relationships where individuals interact at different hierarchical levels and enables the acquisition of information, resources and power [18].Enhanced trust among actors in community facilitates the transfer of information and reduction of transaction costs [14].In the context of regional development, it is of paramount importance to link regional actors with actors at a higher hierarchical level, who are able to provide external resources [19].In the context of rural development, the importance of informal relations in Slovak conditions was confirmed by Melichová [11].
Multidimensional nature of social capital cannot be represented by a single indicator.Many authors (for example Putnam [14]) rely on broad sets of indicators to measure social capital.Van Deth [21] states that the most commonly used indicators are measures of voluntary association activities and measures of personal and social trust.A problem is the usage of macro indicators not directly related to social capital components.It is not clear whether they measure the social capital directly or just its outcomes.Using believed outcomes of social capital as indicators may lead to situation where we falsely attribute a change of outcome as an effect of social capital [16].The confounding number of various aspects, characteristics, indicators, or dimensions of social capital makes a common operationalization problematic [21].
Factor analysis is a technique suitable for analysing the patterns of multidimensional relationships and can be utilized to examine the underlying structure of a large number of variables and to determine whether the information can be condensed in a smaller set of factors [8].Subsequently, we can assert that variables more associated with similar factors can also be conceptually grouped with each other [20].Many authors [6,16,20] utilized factor analysis in order to assess the impact of broad set of social capital indicators more effectively.At sub-national level, this analysis has been conducted in Czech Republic [12], Poland [6] or Italy [16].

MATERIAL AND METHODS
The aim of the paper is to demonstrate the application of factor analysis in exploring and identifying patterns of social capital dimensions in Slovakia and to explore spatial differentiation of social capital at the level of Slovak districts.Due to the unavailability of part of the data, the districts of Kosice and Bratislava (missing data about voluntary associations) and remaining districts of the Bratislava region (ROP indicator not applicable), were not included in the analysis.Data of 67 districts was therefore used as an input for factor analysis.According to Hair et al. [8], an input for this analysis should have a minimum of 50 observations -we met this condition.It is also necessary that the number of observations is greater than the number of variables at least in the ratio of 5 observations to 1 variable.For 67 observations and 10 variables, this condition is met.
We have used ten indicators as an input into the analysis.The first three indicators are the number of the social and health voluntary associations, sport voluntary associations, and trade unions per 1,000 inhabitants.In order to enhance these indicators, we have used not only the residences of voluntary associations, but also their individual organizational units, which helps to reflect their spatial localisation in an improved way.The role of voluntary associations is emphasized by Putnam [13,14].He claims that they are able to link people from different social backgrounds.Bonds and contacts emerge and social networks form common norms and values.The most beneficial are activities that are undertaken directly in order to develop the local community [13].By selecting multiple types of associations, we analyse multiple types of social networks.[9,12].The indicator of electoral participation represents the institutional dimension of social capital.It reflects the level of development of civil society and can express public interest in public affairs [9].The formation of social capital is also affected by the heterogeneity of the community [4].Individual can avoid members of other social groups and limit bridging social capital [1].
In the context of Slovak Republic, the level of national fractionalizations appears to be an appropriate indicator.Some researchers consider the consequences of a lack of social capital as inverse measures of this concept.For example they use crime rates or low levels of economic growth, which point to the absence of social capital.In this way, we utilized two indicators, measuring the lack of bonding social capital.We use divorce index and suicide rates including attempts per 1,000 inhabitants.These phenomena are tied to economic and social uncertainty [20].The amount of ROP funds received in the programming period 2007 -2013 reflects the ability of different actors to receive support from this program.We consider this an indicator of linking social capital.Following Sýkora and Matoušek [19], we have chosen the unemployment rate as an indicator of the "success" of social capital in regional development.Unemployment can lead to the decline of social networks of the individual and social exclusion.Unemployed people often do not have access or resources to participation in society and have limited opportunities to interact with other people [17].

RESULTS AND DISCUSSION
Since the factor analysis assumes the existence of mutual linear dependence of the variables, we inspect the correlation matrix (Table 2).Before we utilize factor analysis it is necessary to verify the assumption that the input variables are correlated with each other.We can observe that using Pearson correlation coefficient, majority of variables are significantly correlated.This indicates suitability for factor analysis.The overall measure of suitability of the data is measured by Kaiser-Meyer-Olkin MSA statistic [8].In our case its value is 0.774.We also examined the anti-image correlation matrix and the values of MSA on the main diagonal are greater than 0.5.Bartlett's test of sphericity showed significance (p < 0.05).Based on the KMO criterion, and also based on the Bartlett's test of sphericity, we consider input data suitable for the use of factor analysis.The choice of three factors was confirmed by the scree plot.By combining these criteria, we have come to the conclusion keep three factors.After examining communalities, we assume that the factors explain a sufficient amount of variability of each of the variables.Since there were only slight variations in different rotations, we decided to apply orthogonal rotation of varimax.According to Hair et al. [8], it is necessary to take into account that with the decreasing number of observation, the value of the factor loading considered significant increases.In the case of 70 observations they consider a factor loading greater than 0.65 as significant.The resulting rotated matrix of factor loadings contains significant values for all variables.In the case of one variable (EDU), factor loadings are high two factors.However, factor loadings have different signs.Factor loadings of variables are displayed in the Table 3.
Only factor loadings greater than 0.4 are displayed.The first factor explains 38.19 % of the variability.In the case of this factor, two variables have high positive factor loadings (nationality fractionalization, unemployment rate) and two have high negative factor loadings (voter turnout, education index).This factor represents the low level of bridging social capital resources.This is caused by the combination of low level of human capital, unemployment, and high national fractionalization, resulting in a lack of weak ties, meaning a low potential of information accumulation and transfer.This leads to low civic participation and an undeveloped civil society.We refer to this factor as to "Isolation".However, considering the national fractionalization in the context of Slovakia as the cause of low bridging social capital is questionable as it is given by historical context.It is stable and not caused, for example, by sudden migration.Spatial differentiation of the extracted factors is visualized using their factor scores (Figure 1).Indeed, the least developed districts in the southern and eastern Slovakia have the highest factor scores, namely districts of Revúca, Rimavská Sobota and Rožňava.
The second factor explains additional 18.89 % of variability and it is positively correlated with four variables.Three of these variables represent activities of the chosen associationssport voluntary, associations, social and health voluntary associations and trade unions.The remaining variable is the education index, which also has a positive factor loading.This factor represents diverse social networks and in combination of high level of human capital these variables represent resources for the creation and accumulation of bridging social capital.We name this factor "Associational activity".A possible limitation of this factor may be the fact that it is only the number of associations and does not account for the number of their members or the scope of their activity.This problem may be partly alleviated by the abovementioned inclusion of organizational units of associations.Spatial differentiation of this factor is significantly different, with the highest factor scores in central Slovakia.In the context of regional development, low associational activity (districts of Detva and Poltár) may partially explain their development difficulties.The third extracted factor explains 16.02 % of variability.It comprises of negative societal phenomena -average divorce index and average number of suicides including attempts per 1,000 inhabitants have high positive factor loadings.Interesting is the fact that the amount of funds received from ROP per inhabitant has high although negative factor loading for this factor.We believe this factor may indicate the effects of low level of bonding social capital, meaning there is lower amount of strong bonds among the members of close, homogenous groups.We denote this factor as "Absence of trust".Concerning factor score differentiation in the districts, we can see that the highest values are in the western Slovakia (Hlohovec, Dunajská Streda) but also in the districts in the southern Slovakia.

CONCLUSIONS
Factor analysis has been utilized in order to explore social capital patterns and to identify spatial differentiation in the level of social capital in the districts of the Slovak Republic.The inputs for factor analysis were 10 variables, commonly used as social capital indicators.The suitability of data has been proven by Kaiser-Meyer-Olkin MSA statistic and Bartlett's test of sphericity.Factor analysis led to the extraction of three interpretable factors, with the factor scores of each factor being visualized.The first factor "Isolation" represents a low level of bridging social capital; the second factor "Associational activity" represents social networks and human capital that serve as a resource for bridging social capital accumulation.The third factor, "Absence of trust" reflects the high level of negative social phenomena resulting from the lack of bonding social capital.

Figure 1
Figure 1 Factor scores of the three extracted factors Source: own processing, ArcGis

Table 1
Selected social capital indicatorsEducation index is another indicator of bridging social capital.It represents the level of human capital.Human and social capitals are mutually contingent.By creating social networks, there is an accumulation of individual human capital and it is transformed into social capital.Strengthening the level of human capital can thus lead to strengthening the cooperative character of social and institutional networks elementary + 2*P lower secondary + 3*P upper secondary + 4*P university where P x are ratios of inhabitants in respective category.2011 SODB ELEC Voter turnout in parliamentary elections 2016 DATACUBE NFRA National fractionalisation [2] NFRA=1-(i = 1,2,..., N), where p i is a ratio of nationality on population; N is the number of nationalities.

Table 2
Correlation matrix of input variables met by three factors which together explained 73.19 % of variability, a sufficiently high percentage.

Table 3
Factor loadings after varimax rotation