Method

In order to test the hypotheses in a statistically sound way, the hierarchical structure of the dataset needs to be accommodated. In multilevel data, individual error terms are likely to be correlated within groups, violating the independence assumption of single-level regression analysis. In order to relax this assumption, I run multilevel models with random intercepts (see Luke 2004; Rabe-Hesketh and Skrondal 2012). I thus end up with a fixed component indicating the mean effect of independent variables across all groups and a random component designed to absorb unobserved heterogeneity between clusters.

In addition, since the dependent variable is binary, logistic regression is used. Essentially, then, the models predict the probability of being enrolled at a university, expressed as percentages between 0 and 100 and conditional upon the explanatory covariates. Formally, the regression equation for the random intercept model can be written as:

where logit is the S-shaped link function, jPr(STUDENTS = 1l,x.,q.)} denotes the probability of Student = 1 conditional on covariates on both levels, the country-level random intercept g, fi1 + fi2x2j + ••• + f36x6j is the fixed component of the equation, and e, stands for the individual-level error term. Cross-level interactions (H3) can be estimated by simply adding the product of the two variables of interest to the fixed component to the equation.

In addition, in order to test H2, the size of the effect of parental education has to vary by country. This is generally done by supplementing the random component of the equation with a random slope for the variable of interest. In such a model the purpose of the random component is not only to absorb unobserved heterogeneity on the country level, but also to relay substantive information about country-specific slopes of the regression line. Such a model can generally be written as:

where ^PARENTAL EDUCATION^, as part of the random component of the equation, is the country-specific slope for the impact of parental education.

 
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