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Measuring Social Capital with Aggregated Indicators: A Case of Ecological Fallacy?

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Abstract

Social capital has become a highly successful concept in social science despite widely perceived shortcomings in conceptualization and operationalization. The latter is frequently performed as a principal component analysis of individual survey data with subsequent aggregation to regional or national levels. The central focus of this paper is the interpretation of the diverging correlations observed between the dimensions elaborated on an individual and an aggregate level. We illustrate that the correlations of regionally aggregated components are the result of an improper application of a single-level model to a multilevel structure. This mechanism is demonstrated empirically by adopting results from the European Social Survey and elaborating dimensions of social capital from both individual and aggregate survey data for European regions. The findings clearly indicate that the observed ecological correlations are not simply spurious or inconsistent due to an ecological fallacy condition, but rather reflect the influence of regional driving forces. Researchers need to be more careful in taking account of the multilevel nature of the data in order to produce valid results. In fact, the often applied procedure of individual factorization and subsequent aggregation of data provides a mixture of the two level effects with potentially misleading implications.

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Notes

  1. For an overview of possible conceptions of the term, see Adler and Kwon (2002), Bjørnskov and Sønderskov (2013), Portes (1998) or Sønderskov (2009).

  2. From a conceptual perspective, components of social capital need not be uncorrelated and thus may also be computed accordingly. In order to test for robustness of the main findings, all analyses were repeated with a PCA with an oblique Oblimin rotation, which reconfirmed the results of the orthogonal approach. Thus, the findings of this paper are not affected by the rotation type chosen. Therefore, in the empirical section of this paper only the findings for the orthogonally rotated PCA are shown as this is the preferred approach in the current social capital literature. The detailed results of the obliquely rotated PCA are shown in the “Appendix”.

  3. This wave is chosen because all important facets of social capital are covered in this first wave and not in the subsequent versions.

  4. Nomenclature of Territorial Units for Statistics (NUTS) is the regional classification used by Eurostat.

  5. The analyses were repeated on the basis of the 81 corresponding NUTS1 regions and reconfirmed the results.

  6. Note that the indicator “Politics too complicated to understand” is coded so that a high score represents a high degree of (purported) understanding.

  7. The cross-validation of the components on the individual level requires an in-depth proficiency in psychological sciences, so that such further examination would exceed the authors' expertise.

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Authors and Affiliations

  1. Department of Economics, University of Innsbruck, Universitaetsstr 15, 6020, Innsbruck, Austria

    Sibylle Puntscher, Christoph Hauser & Gottfried Tappeiner

  2. Department of Statistics, University of Innsbruck, Universitaetsstr 15, 6020, Innsbruck, Austria

    Janette Walde

Authors
  1. Sibylle Puntscher
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  2. Christoph Hauser
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  3. Janette Walde
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  4. Gottfried Tappeiner
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Correspondence to Sibylle Puntscher.

Appendix: Results of PCA with Oblique Oblimin Rotation

Appendix: Results of PCA with Oblique Oblimin Rotation

In this appendix the previous calculations are repeated with a PCA with an oblique Oblimin rotation. The results are briefly compared to the findings of the main part of the paper.

Table 8 indicates that a PCA with an oblique Oblimin rotation conducted on the individual-level ESS indicators generates four components with very similar loadings as in Table 2. Thus, the four components can be interpreted again as the four social capital aspects Political Interest, Trust, Weak Ties and Strong Ties. The oblique component Weak Ties shows, however, negative component loadings. This does not change the main findings, but is important to remember when considering the correlation coefficients presented later in the Tables 10, 11 and 12 of this appendix.

Table 8 Rotated component matrix of the PCA with oblique rotation of individual indicators
Full size table

Further, the results of the PCA with Oblimin rotation conducted on the individual-level mean-centred ESS indicators illustrated in Table 9 are very similar to those in Table 4. Again, the component Weak Ties shows negative component loadings.

Table 9 Rotated component matrix of the PCA with oblique rotation of mean-centred individual indicators (i.e. individual deviations from regional means)
Full size table

The following Table 10 indicates the correlation coefficients of the oblique rotated components calculated with the original ESS data (Table 8). Components that are generated with a PCA with orthogonal Varimax rotation are by definition uncorrelated (unity matrix). As these components are, however, calculated with an oblique rotation, they show some statistically significant correlation coefficients.

Table 10 Pearson’s correlation coefficient of the oblique component values obtained with original individual-level indicators (oblique rotation)
Full size table

Subsequently, Table 11 indicates the correlation coefficients after the regional aggregation of the obliquely rotated social capital components (cf. Table 8) and can, thus, be compared to Table 3. Similarly as for the orthogonally rotated components in Table 3, an increase in the correlation coefficients between the oblique components is detected after the aggregation process.

Table 11 Pearson’s correlation coefficient of the oblique component values obtained with original (individual-level) indicators after regional aggregation (oblique rotation)
Full size table

Table 12 shows the correlation coefficient of the aggregated oblique component values obtained with mean-centred indicators (cf. Table 5, which is based on orthogonally rotated PCA on mean-centred indicators).

Table 12 Pearson’s correlation coefficient of the aggregated component values obtained with mean-centred (individual-level) indicators after regional aggregation (oblique rotation)
Full size table

Testing whether these correlation coefficients (Table 10 compared to Table 12) differ from each other, no empirical evidence is given for a statistically significant difference after a Bonferroni correction in order to keep the significance level at 5 % (cf. Table 13). This means that by calculating the oblique PCA on mean-centred indicators we are again able to segregate the regional effect. In this case, it is important to remember that the statistical significance of the correlation coefficients between the aggregated oblique components (cf. Table 12) is not a sign of aggregation effects (as in the orthogonal case), as the individual-level components are already correlated (cf. Table 10).

Table 13 Test on differences between correlation coefficients obtained with original indicators (Table 10) and correlation coefficients obtained with mean-centred indicators (Table 12)
Full size table

Thus, an oblique rotation does not qualitatively change the obtained conclusions.

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Puntscher, S., Hauser, C., Walde, J. et al. Measuring Social Capital with Aggregated Indicators: A Case of Ecological Fallacy?. Soc Indic Res 125, 431–449 (2016). https://doi.org/10.1007/s11205-014-0843-z

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