In spite of its currency both in academic research and political rhetoric, there are numerous attempts to define and conceptualize the social cohesion concept but there has been paid little attention to provide a rigorous and empirically tested definition. There are even fewer studies that address social cohesion in a framework of cross-cultural validation of the indicators testing the equivalence of the factorial structure across countries. Finally, as far as we know there is no study that attempt to provide an empirically tested multilevel definition of social cohesion specifying a Multilevel Structural Equation Model. This study aims to cover this gap. First, we provide a theoretical construct of social cohesion taking into account not only its multidimensionality but also its multilevel structure. In the second step, to test the validity of this theoretical construct, we perform a multilevel confirmatory factor analysis in order to verify if the conceptual structure suggested in first step holds. In addition, we test the cross-level structural equivalence and the measurement invariance of the model in order to verify if the same multilevel model of social cohesion holds across the 29 countries analysed. In the final step, we specify a second-order multilevel CFA model in order to identify the existence of a general factor that can be called “social cohesion” operating in society that accounts for the surface phenomena that we observe.
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In a MCFA the within item intercepts are allowed to be random at between-level. The within item intercepts become dependent variables at level-2.
A researcher should constrain to zero the residual variances close to zero, but in our first model we preferred to keep freely estimated the residual variances to evaluate the magnitude of these variances. In the model 2, we have constrained the negative residual variances to zero.
The Chi-square value for model-2 decreases compared with the chi-square value for model 1 (Table 4). Generally, it should be the contrary because in model 2 we have constrained the loadings to be equal across levels gaining degree of freedom. In this case, with the WLSMV estimator, it could happen that a model with more df shows a lower chi-square value. This because WLSMV produces a chi-square adjusted to the means and variances, and adjustment depends not only on data but also on the models (Muthén and Muthén 1998–2012).
Measurement invariance is an important issue in cross-cultural research because several problems can arise (translation problems, cultural biases, etc.). In addition, the measurement invariance of an instrument across groups is a necessary condition in order to compare groups with respect to the latent variables measured by that instrument (Jak et al. 2013).
The model-3 is nested in model-2 that in turn is nested in model-1. In these cases, a researcher can perform the chi-square difference test. Mplus with WLSMV estimator requires a special procedure called DIFFTEST. However, we cannot perform a chi-square difference test neither inspect the modification indices searching for misfit areas because they are not still available with WLSMV estimator in Mplus 7 for multilevel data.
In order to run the model we had to leave out the dichotomous variable “b13”. It showed extremely huge standard error caused by computation problem.
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Bottoni, G. A Multilevel Measurement Model of Social Cohesion. Soc Indic Res 136, 835–857 (2018). https://doi.org/10.1007/s11205-016-1470-7