Participation and Democracy: Dynamics, Causes ... - Jacobs University

to replace the five single predictors by a common factor (see Appendix A8-3 for the
result of the factor analysis). In addition, the variable “Parliamentarism” was eliminated.
The system of government is highly correlated with the variables composing the factor
score, but not conceptually related to the modernization syndrome, so that adding it to the
analysis does not have any additional value. This leads to a modified Model 2b:
Modified Model 2b:
β 0j = γ 00 + γ 01 (Modernization j ) + γ 02 (Inequality j ) + u ij .
The downside, however, of introducing a syndrome as a main predictor is that it does not
allow us anymore to attribute the effects to a single factor, or to determine the relative
strength of a single factor in predicting elite-challenging activities on the individual level.
Besides deletion or recoding of variables, HLM offers additional ways to tackle the
problem of multicollinearity. A first solution is centering, in particular of the level-1
variables. For the subsequent analysis, the level-1 variables were centered around their
group mean (except for gender which was not centered because it is a dichotomous
variable): “When group mean centering is used, the correlation between second-level
variables and both first-level variables and cross-level interactions are equal to zero, so
that only the correlations between cross-level interactions and level-1 variables remain as
a potential source of estimation problems” (SSI 2008: 84). 69 The level-2 predictors were
centered around their grand mean (exception: regime type as a dichotomous variable).
The main idea of centering is to assign a meaningful zero point to each variable
(Raudenbush and Bryk 2002: 32). 70
A second solution to detect and eliminate multicollinearity, if HLM posts a warning
message about multicollinearity, is to inspect the Tau Matrix in the output, as correlations
close to 1 or -1 (excluding the diagonal, of course) can be an indication of
69 Please see the website of Scientific Software International, Inc., the provider of the HLM software:
http://www.ssicentral.com/hlm/help6/faq/Multicollinearity.pdf .
70 Centering is central to the interpretation of any intercept β 0j, as it is the expected outcome for a person
who scores 0 in all other variables. Therefore, it is crucial that any predictor variable has a meaningful zero
point: Centering assigns the zero point to the group (or grand) mean score.
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