Method – Multilevel modelling

In contrast to studies understanding social reality as o te t f ee or fully o te t ou d (Hantrais, 1999, p. 94), this thesis aims to treat the context as an explanatory variable that helps to examine social reality by understanding countries as a contextual framework. Using countries or nations as a framework, the researcher faces several limitations. As argued by Hantrais (1999), national borders change and thus do not necessarily reflect cultural or ideological differences within countries. Comparing employment patterns, care and income between women in eastern and western Germany, Pfau-Effinger and Smidt (2011) for example find that differences between eastern and western German women can be largely explained by diffe e es in the cultural values and models of the family […] and their interaction with institutional and economic fa to s (p. 217).

Secondly, with countries being embedded in supranational organisations, any change in the membership structure causes socio-cultural change in the organisation per se. Additionally, the key problem for cross-national comparisons based on countries as a contextual framework is likely to ignore within-country differences. Jobert (1996) highlights the difficulties when comparing the education, training and employment in Germany, France, Italy and the UK, due to diversity within the countries (as cited in Hantrais, 1999), with for example Germany deciding at the federal state-level on education policies and thus having not one, but several education systems.

To summarize, choosing countries as the level of observation is problematic, as cross- national comparisons appear to be unable in taking into account within country diversity. However, the discussed shortcomings can be overcome by using an approach that takes advantages of both macro- and micro-level differences, while still associating cases with

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commonly used identities, such as multilevel modelling (MLM). MLM is the method of choice as it takes into account political, legal, socio-cultural and economic systems, but at the same time takes social and cultural diversity of the individuals beyond their nationality into account (Hantrais, 1999).

In general, multilevel analysis examines elatio s between variables measured at different levels of the multilevel data st u tu e (Hox, 2002, p. viii). Multilevel analysis enables us to examine data that is ested within each other, therefore violates the independence assumption statistical analyses such as ANOVA and ordinary least-squares (OLS) require (Peugh, 2010, p. 86). However, as Peugh (2010) for example argues, not every nested dataset requires MLM. The key reason for engaging in multilevel modelling is the assumption of high variation at level-2, which is the context-level variable (schools or countries for example). Only if there is enough variation at level-2 or the context level, MLM can be useful. In our example with countries being the level-2 variable and the i di iduals job levels being our level-1, we expect high cross- national variation in vertical segregation and not only variation between individuals. MLM allows us to examine not only individual determinants, but also the context factors that impact individual level behaviour (Muijs, 2011). Applying Peugh s (2010) example of MLM for educational data to my research question, the variation at the context level is expressed and calculated by the intraclass correlation (ICC) score which is the proportion of vertical occupational segregation that can be explained at the country level (level-2), and the expected correlation between vertical segregation of two individuals from the same country. Therefore, if the ICC is too low or even zero, the mean of occupational levels of women does not vary much across countries (level-2), and therefore varies only across individuals. In this case, other statistical methods might be more useful. However, for this thesis the ICC is irrelevant as we are not interested in the variation of individuals to reach top position and whether this varies across countries, but more importantly whether the gender gap varies across countries. Thus, while the first question would require random intercept models, the second one requires random slope models as it will be discussed later in this section. For now this means however, that ICC is irrelevant to seeing whether there is a cross-national variance in the extent to which there is a

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gender gap in obtaining top positions for workers.What is more important is the significance of the random slope variance, and whether the impact labour market institutions and family policies have on i di iduals access to managerial positions is different for women than for men. This will be measured by comparing explained variance in the models and by comparing logged likelihood changes to see whether adding more variables improves the model fit.

As mentioned above, this thesis examines the potential associations between labour market institutions, family policies and o e s likelihood to work in top jobs. Thus, in a first step we need to establish our null or empty model of our multilevel model. Because we take into account the nested nature of our data, we need to allow countries to have different means of our dependent variable. The dependent variable is binary – with 1 being the chances to reach a top position and 0 all other positions. Thus, the first model needs to indicate that individuals at the level 1 are nested within countries at level 2. Here, the main drawback of the analysis is the limited number of level-2 country cases and thus the statistical power. This issue is addressed by adding a maximum of two cross-level interaction terms per model.

In order to show which country an individual belongs to, in multilevel models we do not only add the subscript i and j to our dependent variable yij, indicating the value the individual i has in the country j. Furthermore, since we have J countries with nj individuals, the sample size is:

Since this thesis only looks at two levels – the country and the individuals –, we need to establish a two-level model with the residual including two components – the country-level residuals or random effects uj and the individual-level residuals eij. This leads to the following model:

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In this empty model, y is our dependent variable – the likelihood of an individual i nested within country j to obtain a top positions with being the global average. In other words, is the overall mean of Y across all countries or the average chances for an individual to reach a top position across all included countries. uj on the other hand is the random effect component

and shows how much in country j the likelihood of an individual to reach a top position varies from the global average . The average likelihood to reach a top position Y for an individual i nested within country j therefore is the overall mean across all countries and the additional random element, the group-level residual, thus . However, in this model we do not allow

the likelihood to reach top positions

Starting with the empty model, which serves as a comparison, the analysis starts with random intercept model with explanatory independent variables. In contrast to empty models, these random intercept models aim to examine whether the independent variables discussed in the previous sections have an impact on i di iduals likelihood to reach top positions. Because this thesis investigates cross-national variation of the gender gap in top positions, the key explanatory independent variable therefore is gender. Thus, after running the empty models, gender is added to the model and it will be examined whether the gender of an individual i living in a country j increases or decreases the average likelihood for an individual i living in a country j to reach top positions. Here, we therefore allow the intercept to vary across countries depending on gender. In other words, does gender have an impact on i di iduals likelihood to reach top positions? What is more, in order to exclude the possibility that the gender impacts i di iduals likelihood to reach top positions only because of the individual and job characteristics between genders as discussed in the previous section, the models also include individual-level control variables. These are all summarised by in the equations. The impact individual-level variables have is assumed to be the same across countries and is therefore fixed for these models.

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The following equation summarizes these random intercept models with individual control and explanatory variables.

However, the general assumption in this thesis, is not only that gender impacts career perspectives and women are disadvantaged, even after controlling for various individual-level characteristics. More importantly, this effect is expected to vary across countries. In other words, the assumption here is that the gender gap is significantly smaller or bigger in different European countries. Wo e s likelihood to reach top positions relative to e s is expected to vary between countries and therefore the impact gender has on access to top positions is not fixed.

For each country, we get the following regression model.

The intercept includes the following:

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Lastly, bringing both models together for all countries, we get the following random slope model:

As indicated by j, we can see that the latter part of the equation is the random element which indicates that the impact individual-level variables have is allowed to vary across countries.

These models can help us understand whether the gender gap varies across countries and which individual-level variables have an impact. In order to be able to address the other research questions however, we need to add independent context-level variables to the equations. To recap, this thesis aims to understand drivers of the gender gap in managerial positions, and further investigates to what extent family policies or labour market institutions have an impact on vertical segregation.

Therefore, we now need to include the intercept variation with Z being our context level variables for country j.

However, in this case Z only describes the impact of a context-level variable on our dependent variable, which is an i di idual s likelihood to reach a top position. Because this thesis investigates whether family policies and labour market institutions affect women differently than men, we need to add cross-level interaction terms in order to understand how macro-level variables impact the effect gender has on career chances. This is summarised by the following equation with being the cross-level interaction term.

In contrast to random slope models, random intercept models do not allow us to examine whether context variables have influence the varying impact of our key independent variable/gender on our dependent variable across countries.

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For the random slope model with cross-level interaction, we therefore have the following model with Z being family policy or labour market institution variables and 01Zj being the

variance of slopes for the independent variables across countries: