Ethnic diversity fosters the social integration of refugee students

Forced migration has become a global megatrend, and many refugees are school aged. As social integration is key to their wellbeing and success, it is pivotal to determine factors that promote the social integration of refugee youth within schools. Here, using a large, nationally representative social network dataset from Germany, we examine the relationships of refugee adolescents with their peers (304 classrooms, 6,390 adolescents and 487 refugees). We find that refugee adolescents have fewer friends and are more often rejected as desk mates than their classmates. Crucially, however, they are less rejected in more diverse classrooms. This results from two basic processes: (1) more opportunities to meet other ethnic minority peers, who are more accepting of refugees in general and (2) higher acceptance of refugee adolescents by ethnic majority peers in more diverse settings. Our results can help promote the social adjustment of young refugees in school and mitigate the negative consequences of prejudice.

Supplementary Table 1 shows how the estimated probabilities of receiving friendship and rejection nominations vary between ethnic majority adolescents (the reference category), firstgeneration immigrant adolescents, second-generation immigrant adolescents, and refugee adolescents after controlling for the adolescents' gender, age, academic achievement, language skills, and length of stay in Germany. The results stem from two MRQAPs, one having the probability of receiving friendship nominations as the dependent variable and one having the probability of receiving rejection nominations as the dependent variable. The statistical procedure is described in Appendix D. The results demonstrate that refugee students, in comparison to ethnic majority students, have a lower probability of being nominated as friends (ß = -0.067, p < 0.001) and a higher probability of being rejected as desk mates (ß = 0.041, p < 0.001). Supplementary Table 1 also shows that gender, age, length of stay in Germany, and academic achievement predict the probability of being nominated as a friend, while language skills matter for the probability of being rejected as desk mates by classmates. These results confirm that the findings presented in Fig 1 in the main text are robust to controlling for possible confounders. To create Fig 2, we further restricted our sample to classrooms in which at least 15 students participated in the sociometric part of the questionnaire (i.e., the part in which the students were asked about friendships and desk-mate rejections). This procedure followed the aim of avoiding bias in our results due to nonparticipating peers who would also have nominated refugee students if they had participated. Such selection bias could be severe since, in Fig 2, we report absolute values regarding peer nominations instead of averages. Another reason for our decision was that the average valid class sizes varied across the different diversity levels, with highdiversity settings having the smallest valid class sizes. Given that the number of friendship and desk-mate rejection nominations in the different diversity settings is among the most important messages of Fig 2, we wanted to avoid bias in our results due to the differential participation rates across the different diversity levels. The resulting sample consisted of 5,328 students from 237 classrooms. Descriptive statistics of the analyzed variables by immigrant status are provided in Supplementary Table 5 In addition, we replicate the findings of Fig 2 by defining "low", "medium", and "high" settings based on the whole sample instead of based on the subsample that includes refugee students. This means that the "low" setting now includes those classrooms that are among the third of the classrooms with the lowest levels of diversity in the overall sample, the "high" setting includes classrooms that are among the highest-diversity third of the overall sample, and the "medium" setting includes the rest of the classrooms. This replication is provided in Supplementary Figure 3 and shows substantively similar tendencies to   , the total number of friends). In addition, the network plots are a proportionate representation of the ethnic composition of nominations of refugee students (e.g., the number of native friends). Note that not every bar can be represented in the network plots by the value of the closest integer to its actual mean due to our primary goal to represent the total number of nominations accurately. This sample includes classrooms in which fewer than 15 students participated in the sociometric questionnaire that included questions about friendships and rejections. N students = 6,390. N classrooms = 304.

Supplementary
Supplementary Figure 3. Typical friendship and desk-mate rejection ego networks of refugee students.
Replication of Fig 2 based on ethnic diversity settings ("low", "medium", "high") calculated from the distribution of diversity in whole sample instead of the subsample that includes refugees. The bar plots show the rounded average number of friendship (panels a, b, c) and rejection (panels d, e, f) nominations of refugee students by immigrant status group. The network plots map the average number of nominations (e.g., the total number of friends). In addition, the network plots are a proportionate representation of the ethnic composition of nominations of refugee students (e.g., the number of native friends). Note that not every bar can be represented in the network plots by the value of the closest integer to its actual mean due to our primary goal to represent the total number of nominations accurately. This sample includes classrooms in which fewer than 15 students participated in the sociometric questionnaire that included questions about friendships and rejections. N students = 5,328. N classrooms = 237.

Supplementary Figure 4.
Typical friendship and desk-mate rejection ego networks of refugee students.
Replication of Fig 2 based using diversity cut-offs 0.33 and 0.66 to create the three diversity categories ("low", "medium", "high"). The bar plots show the rounded average number of friendship (panels a, b, c) and rejection (panels d, e, f) nominations of refugee students by immigrant status group. The network plots map the average number of nominations (e.g., the total number of friends). In addition, the network plots are a proportionate representation of the ethnic composition of nominations of refugee students (e.g., the number of native friends). Note that not every bar can be represented in the network plots by the value of the closest integer to its actual mean due to our primary goal to represent the total number of nominations accurately. This sample includes classrooms in which fewer than 15 students participated in the sociometric questionnaire that included questions about friendships and rejections. N students = 5,328. N Supplementary Figure 5. Typical friendship and desk-mate rejection ego networks of refugee students.
Replication of Fig 2 based using the proportion of immigrants to create the three diversity categories ("low", "medium", "high"). The bar plots show the rounded average number of friendship (panels a, b, c) and rejection (panels d, e, f) nominations of refugee students by immigrant status group. The network plots map the average number of nominations (e.g., the total number of friends). In addition, the network plots are a proportionate representation of the ethnic composition of nominations of refugee students (e.g., the number of native friends). Note that not every bar can be represented in the network plots by the value of the closest integer to its actual mean due to our primary goal to represent the total number of nominations accurately. This sample includes classrooms in which fewer than 15 students participated in the sociometric questionnaire that included questions about friendships and rejections. N students = 5,328. N classrooms = 237.

Appendix D: Description of the Multiple Regression Quadratic Assignment Procedure
Mathematically, the Multiple Regression Quadratic Assignment Procedure (MRQAP) is defined in a similar way to linear regression models, but the data are arranged in matrices instead of vectors: .
Here, stands for the dependent matrix (that is, friendships or desk-mate rejections), with indexes i and j representing two students from this matrix. Furthermore, m shows the number of independent matrices x k (that is, the number of independent variables). Parameter k stands for a coefficient, and eij is an error term. When x k represents a friendship (rejection) network, indicates that i names j as a friend (i rejects j). The parameters of MRQAPs can be interpreted as similar to the parameters of a linear regression model because they are estimated with ordinary least squares (OLS) estimators. However, the statistical significance of the estimates is calculated using permutations to take into account dependencies between the observations (1). For this, the OLS regression results are compared to a large number of OLS regression results conducted from "random" data: data for which the dependent matrix y has been permuted. The proportion of "random" regression coefficients that are at least as large as our actual coefficient directly translates to a p-value for the given parameter. We used Y-permuted MRQAPs because they represent the most conservative method to obtain statistical inference among MRQAP models. We conducted 1,000 permutations. Cases with missing information on friendship and/or rejection nominations as well as on any of the predictor variables were excluded from the analyses. To be able to jointly analyze all classrooms in our sample, we performed multigroup QAPs. We used a multigroup MRQAP function an implemented in R by Elmer and Stadtfeld (2).

Appendix E: Robustness check of Fig 3 results
Supplementary Tables 6-10 display several models that serve us to investigate the robustness of our main results. Supplementary  Table 2 but use the proportion of immigrants in a classroom as a measure of diversity instead of the dissimilarity index and additionally consider that diversity differs across the German federal states. Supplementary Table  9 presents the results from MRQAPs in which, in addition to the variables presented in Table 2, we take it into account that students of any immigrant background but with higher socio-economic status (SES; expressed by the parents' highest occupational status) may be more likely to name refugee students as friends and less likely to reject them as desk-mates. Finally, Supplementary Table 10 presents results which extend the Table 2 results by variables accounting for students attending different school tracks to be potentially more or less likely to be friends with or reject refugee students (independent of their own immigrant background).
The diversity-related tendency of nominating refugee students in the robustness models is substantively similar to those in the main model. We see differences from the main results (Supplementary Table 2 These differences may be due to decreased statistical power (especially in case of the refugee → refugee nominations, since only few classrooms had been attended by more than two refugees). It is important to note, however, that the signs of all of these parameters are the same as the ones in the main models. Therefore, we conclude that the differences in the p-values do not affect our substantive conclusions. N students = 6,390. N classrooms = 304. "Hauptschule" is the reference category among the school tracks, preparing students for vocational training and attaining a lower secondary qualification; "Schule mit mehreren Bildungsgaengen" and "Realschule" are intermediate tracks in which student can attain lower and intermediate secondary qualifications; "Integrierte Gesamtschule" is an integrated track in which students can attain all types of qualifications. "Gymnasium" is the academic track, preparing students for a higher secondary qualification and ultimately tertiary education. Figure 7. Statistical significance of parameters capturing nominations of refugees.

Supplementary
In the subplots of each subfigure, the dots show the parameter estimates for the observed network, whereas the box plots demonstrate features of the distribution of estimates for the simulated networks. Each box represents 50% of the distribution; each error bar represents 95% of the distribution; each vertical line represents the mean of the distribution. N students = 6,390. N classrooms = 304. Panel a. Parameters for main effects of nominations of refugees in the friendship models. Panel b. Parameters for diversity interactions with nominations of refugees in the friendship models. Panel c. Parameters for main effects of nominations of refugees in the desk-mate-rejection models. Panel d. Parameters for diversity interactions with nominations of refugees in the desk-materejection models.