Диссертация (1136614), страница 17
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It was shown that school-entry academic skillshave large predictive power for later academic performance [55], and that academic performance might be heritable [56]. We find the persistence of performance in our data. Theaverage GPA over high school students (3.85 ± 0.55) and its variance do practically notchange over time, see S2 Fig. The average absolute difference between two consecutive timepoints h|Gi(t) − Gi(t − 1)|ii is 0.130, which means that the variation between GPAs of thesame student at different time points is much smaller than the variation across students.Similar results are observed for the university students, with an average GPA of 7.41 ± 1.03and a mean absolute difference 0.40.2.
The second argument why the socialization/adaptation mechanism can be ruled out is dueto the observation that if we fix the GPAs for the high school students and do not let evolve i ), we observe practically thethem over time (we use the average GPA over all trimesters Gsame homophily increase as for the co-evolving GPAs, Fig 4(a).3.
Finally, we use a regression model to explain the GPA of students Gi(t) by the explanatoryvariables: GPA at the previous trimester/semester Gi(t − 1), by the influence of friends’GPAs, by gender and by age (see S1 Text). The results are presented in S2 Table. For highschool and university alike we find that the coefficients for Gi(t − 1) (α1) and gender (γ) aresignificant and the coefficient for friends’ GPA (α2) is not. Again, this suggests that GPAsare rather stable over time and are almost fully determined by the GPA at the previous timepoint. The regression shows no evidence for an adaptation effect.PLOS ONE | https://doi.org/10.1371/journal.pone.0183473 August 30, 20178 / 16Formation of homophily in academic performanceSocial selection and network re-organizationDue to the second argument above the explanation of the observed homophily increase canonly come through changes in social networks over time, i.e.
the social selection mechanism,where students preferentially select new friends that are similar in performance. A simplemodel allows us to understand the situation. It assumes that whenever students select newfriends they prefer students who are more similar to them than their current friends. Every stu i (constant). There exists an initial friendship networkdent i is endowed with a fixed GPA Gthat we initialize with the observed network at timestep 1, Amodelð1Þ ¼ Aij ð1Þ. From time t to tij+ 1 the model runs through the following steps• Pick a student i at random,• Pick a random friend j of i, (AmodelðtÞ ¼ 1),ij• Pick a random potential new friend k (AmodelðtÞ ¼ 0),ik• If k is closer to i than j, i.e.
if |Gi − Gk| |Gi − Gj|, rewire the link from ij to ik. Otherwise,rewire the link from ij to ik anyhow, with probability θ,• Repeat until all students are updated, then continue with next timestep until t = T.Clearly, if θ = 0, rewiring happens only if a potential friend is closer in GPA than a current one(strict homophily increase); if θ = 1 we have pure random rewiring. For a fixed θ we computethe Homophily Index Hmodel(t) based on model networks. θ is fitted from the data such thatPT2modelðtÞ HðtÞÞ is minimized.t¼1 ðHWe find θ values within the range of 0.55 and 0.61 for all groups. This means that studentschoose new friends among those who are similar about 64%-81% more often than amongthose who are not similar. The results of the model are presented in Fig 4 (boxes).
The experimental homophily increase is recovered. Remarkably, for all student groups, the model is ableto reproduce even details in the empirical GPA distances between stable, discontinued, andnew friendships, see S3 Table.We have to show that the homophily increase is not explained as a trivial consequence ofnetwork densification. In both datasets we observe that friendship networks are dynamicallychanging over time. In Fig 5 the relative change of the average degree and the clustering coefficient of the networks are shown in comparison with the relative change of homophily.
To seethat the observed homophily increase is not a trivial consequence of network densification,observe that while for the high school degree and clustering increase, for university (seniors)they decrease. In both cases homophily increases. This is a first indication that degree and clustering are not the drivers of homophily change. As a second indication we test if H and IX aresignificant with respect to a permutation test that preserves network topology. This is indeedthe case (see Methods). Thirdly, by re-defining time intervals in a way that for each time interval the average degree is approximately the same, we find the same homophily increase (seeS3 Fig), indicating that the degree is not an explanatory variable.Finally, in S4 Fig we show that there exist slight gender differences in the homophilyincrease.
While both genders show about the same increase over time, the homophily index His slightly larger for females in the sophomore and senior groups, and larger for males for thehigh school students and juniors. However, the noise in our data is too large to confirm thathomophily indeed peaks in early adolescence, as seen in [57].PLOS ONE | https://doi.org/10.1371/journal.pone.0183473 August 30, 20179 / 16Formation of homophily in academic performanceFig 5. The network properties degree and clustering change over time (relative changes are shown, first timepoint is 1). While the network of seniors becomes sparser, there is a densification of the high school network (inset).Therefore degree and clustering coefficients can not be the drivers behind the observed homophily increase in bothgroups.https://doi.org/10.1371/journal.pone.0183473.g005DiscussionWe studied a unique dataset containing the academic performance of high school and university students together with detailed information about the evolution of their social ties.
Inaccordance with previous research [2, 4, 5, 50] we found strong homophily in academic performance. The strength of academic homophily is found to be stronger than for homophily insexual activity [58] or alcohol abuse among adolescents [59] but weaker than for homophily insmoking marijuana [59], or for age [54].We are not only able to demonstrate the strong homophily in academic performance butalso to monitor how it emerges from a homogenous population and how it solidifies overtime. We show that the observed gradual homophily increase can be explained predominantlyby the process of social selection, meaning that students re-arrange their local social networksPLOS ONE | https://doi.org/10.1371/journal.pone.0183473 August 30, 201710 / 16Formation of homophily in academic performanceto form ties and clusters of individuals that have similar performance levels.
We could excludethe alternative explanations of social adaptation and co-evolution of social ties and performance. With a series of tests we ruled out the possibility that the increase of homophily resultsfrom adapting their academic performance to the one by their close friends. As an importantconsequence, this means that there are no indications for a pull effect, where groups of friendswith good grades stimulate poor performing friends to increase their performance. The opposite effect of a negative group influence on students is also not found.
It can be concluded thatacademic homophily in the studied groups arises and strengthens almost entirely through network re-linking.We are able to understand the social-selection based homophily increase with a simpledynamical one-parameter model. The estimate of the parameter from the data means that students choose a new friend among those who are similar to them 64%-81% more often than dissimilar ones.Note that even though this model is much simpler than others previously used [60],remarkably it is able to recover the increase over the whole time period for all groups, andeven allows to understand details of the dynamics. It would be interesting to see in furtherwork if these findings hold more generally also true for other student groups with differentsocial contexts and in different countries.It is important to note that the observed changes in social ties might be driven or facilitatedby various factors. In the absence of ability tracking, other institutional factors may play a rolein the segregation by academic achievements.
For example extracurricular activities may provide an additional opportunity for similar individuals to meet and to from friendship ties [61].Future research is needed to clarify the role of such specific factors.Our findings might shed light or even confirm that access does not necessarily lead toequity. We find indications that physical mixing of students in the same educational institutiondoes not lead to a homogeneous mixing of social ties. Even if the initial distribution is ratherhomogenous, students constantly re-organize their social network during the studies, whicheventually results in segregation by academic performance. It is possible to conjecture that thismechanism is potentially reinforced by the accessibility of modern information technologieswhere maintaining links does not require physical presence anymore.Academic achievements are the result of various factors, ranging from innate abilities toteacher qualification and family background.
Regardless of these factors, it is the achievementsthat have direct implications for the students’ future success. For example, Russian universitiesselect students solely on the basis of their final school examination. Thus, academic achievements determine which students are selected for elite universities and which are not.
As socialnetworks play a crucial role in social mobility [62, 63], a selective university may provide aunique opportunity to create ties that will benefit students in the future. However, if initiallylow-performing students from a disadvantaged background predominantly create ties withother lower-performing students it significantly reduces their upward social mobility and mayexplain the persistence of inequality in societies.MethodsHomophily indexWe introduce a Homophily Index, H, as the Pearson correlation coefficient between the vectorof students’ GPAs, Gi(t), and the vector of the average of the GPAs of their direct friends,!Pj Aij ðtÞGj ðtÞHðtÞ ¼ corr Gi ðtÞ; P:ð1Þj Aij ðtÞPLOS ONE | https://doi.org/10.1371/journal.pone.0183473 August 30, 201711 / 16Formation of homophily in academic performanceIf students’ grades are independent from average grades of their friends than H(t) = 0.
PositiveH(t) means that better average grades of friends lead to better average grades of students andnegative H(t) means that better average grades of friends lead to worse students’ performance.H(t) = 1 means a linear relation between students’ performance and average performance oftheir friends.Randomization testOne of the challenges in understanding correlations of traits between connected individuals isto test if the observed homophily effect is significant or if it results trivially from the topologyof the underlying network. To test for this we employ a typical permutation test, see e.g.
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