88 Ethnic sorting in football selected at random from a population – in this case a club. For each ethnic group, this index is calculated on the basis of the other remaining eleven ethnic categories by taking the sum of each ethnic category’s respective squared proportion, multiplying it by 100 and subsequently subtracting it from 100. This results in a measure that ranges from 0 to 100 and expresses the percentual chance that two randomly selected outgroup club members differ from each other in their ethnic background. Control variables In addition to these measures, several control variables on both the individual and club level are used. On the individual level, these are: time period (separated by playing season), membership duration (in cumulative playing seasons), age (in years), gender (in male and female), and income (in tertiles of low, middle and high). On the club level, these are: club size (in total number of members) and income group share (in percentage of members within each income tertile) Modelling strategy The data for this study has a longitudinal (membership records distributed over playing seasons) as well as a hierarchical (members nested in clubs) component. To address both of these characteristics of the data structure, I use a generalized linear mixed model with a complementary log-log link function. In this model, no linear effect of consecutive playing seasons on the dependent variable is assumed, and covariates are allowed to vary between seasons (Allison, 1982). By using a complementary log-log link function, the results of this model can be interpreted as a standard proportional hazards model (Austin, 2017). Because observations are nested within clubs and are dependent on each other, a random intercept varying across the club level is included in all models. The most basic model will be a random intercept model with individual level predictors to which club level characteristics are then added in multiple steps. Because I have assumed that 1) the effect of migrant background on dropout is itself a function of the ethnic composition of clubs and 2) the effects of ingroup share and outgroup fractionalization differ between members with migrant and Dutch backgrounds, the final model includes a random effect for migrant background and cross level interaction terms for migrant background and ingroup share, and migrant background and outgroup fractionalization.
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