Abstract
In this paper we extend and improve a recently proposed method for the measurement of the cultural distance between strata. In the original version, strata meant countries: respondents from different countries were clustered on the basis of their answers to a set of questions and their resulting distribution among the K clusters thus formed was used to calculate the “position” of each country as a point in a K-dimensional space. The proposed improvements are as follows. First, the notion of “strata” is enlarged: not only geographic units, but also gender, age, education, religious attitudes and rural/urban residence. Second, clustering is now based on EM, or Expectation Maximization, which automatically determines the optimal number of clusters, thus overcoming one of the major limitations of the previous version of the method. Third, since this optimal number of clusters turns out to be small, a principal component analysis is used to capture most of the variability and draw a very telling, two-dimensional representation of how (culturally) distant strata are from one another. Fourth, since two types of distances between strata can be computed, a cultural and an “objective” one (e.g., kilometers between regions or years between age groups), their correlation can be calculated. On our Istat (Indagine multiscopo, Aspetti della vita quotidiana, Rome, 2013) data, expectations are confirmed: the farther strata are, the greater their cultural distance. The same happens for the (rural/urban) type of commune of residence. Religion, instead, is rarely, and gender is never, associated to any measurable cultural difference.
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Notes
Let the composite variable X be the sum of Z elementary (manifest) variables YZ, and let \(\sigma_{X}^{2}\) and \(\sigma_{{Y_{z} }}^{2}\) be their variances. Cronbach’s alpha, which is considered acceptable for values above 0.6 and good for values above 0.7, is defined as \(\alpha = \frac{Z}{Z - 1}\left( {1 - \frac{{\sum\nolimits_{z = 1}^{Z} {\sigma_{{Y_{z} }}^{2} } }}{{\sigma_{X}^{2} }}} \right)\).
Note, incidentally, that since we did not sum our elementary variables, a low value of Cronbach’s alpha (which we obtained in one case out of four: environmental concern—see further in the text) is not necessarily an indicator of poor performance of our method: it may simply depend on the fact that the elementary indicators focus on different aspects of the general topic under consideration.
With tenfold cross-validation, which is the standard way of measuring the error rate of a learning scheme on a (large) dataset.
Our own acronym: the authors did not give any name or acronym to their method.
This linear constraint implies that in a space with K dimensions, all the points (strata) will actually lie in a sub-space with K−1 dimensions. But we need not worry about this peculiarity, here.
Obviously, we dropped duplications (the distance from i to j coincides with the distance from j to i, and must be considered only once) and ignored the distance of each point (stratum) from itself. This is why S points originate S(S−1)/2 distances instead of S 2. See, e.g., Table 3, further in the text.
The theoretical maximum distance between two strata is √2: this happens when all the observations from the first stratum belong to only one cluster, and all the observations from the other stratum belong to a unique, different cluster (we thank Prof. Mauro Maltagliati for pointing this out to us). In practice this is very unlikely to happen, especially with a large number of clusters.
Regional differences are generally considered important in Italy, especially along the North–South divide.
Very young cohorts, instead, have the problem of truncation: teen-agers, by definition, cannot (yet) hold a university degree. This was kept into account in the present analysis.
Gender proved (mildly) significant only when the domain politics was split into “active participation” and “interest, trust and the like” (not shown here). In this case, and solely for “active participation”, men and women appeared to be slightly different, especially at older ages.
The question was “How often to you go to places of religious worship” (which means “Catholic Mass”, in Italy), and the six possible answers ranged from “Never” to “Every day”.
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Mucciardi, M., De Santis, G. Cultural Versus Objective Distances: The DBS-EM Approach. Soc Indic Res 130, 867–882 (2017). https://doi.org/10.1007/s11205-015-1213-1
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DOI: https://doi.org/10.1007/s11205-015-1213-1