The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Comparison of TERGM and SAOM : Statistical analysis of student network data

TERGM과 SAOM 비교 : 학생 네트워크 데이터의 통계적 분석

  • Yujin Han (Department of Statistics, Duksung Women's University) ;
  • Jaehee Kim (Department of Statistics, Duksung Women's University)
  • 한유진 (덕성여자대학교 정보통계학과) ;
  • 김재희 (덕성여자대학교 정보통계학과)
  • Received : 2022.10.08
  • Accepted : 2022.11.27
  • Published : 2023.02.28
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Abstract

The purpose of this study was to find out what attributes are valid for the edge between students through longitudinal network analysis, and the results of TERGM (temporal exponential random graph model) and SAOM (stochastic actor-oriented model) statistical models were compared. The TERGM model interprets the research results based on the edge formation of the entire network, and the SAOM model interprets the research results on the surrounding networks formed by specific actors. The TERGM model expressed the influence of a previous time through a time term, and the SAOM model considered temporal dependence by implementing a network that evolves by an actor's opportunity as a ratio function.

본 연구는 학생 간의 연결에 어떤 속성이 유효한지 종단 네트워크 분석을 통해 알아보고자 하였으며, 종단 네트워크 모형인 TERGM (temporal exponential random graph model)과 SAOM (stochastic actor-oriented model) 통계적 모형을 사용하고 결과를 비교하였다. TERGM 모형은 네트워크 전체의 연결 형성을 바탕으로, SAOM 모형은 특정 행위자가 형성하는 주변 네트워크를 대상으로 연구 결과를 해석하였다. TERGM 모형은 시간 항을 통해 이전 시점의 영향을 표현하였으며, SAOM 모형은 비율 함수로 행위자의 기회에 의해 진화하는 네트워크를 구현해 시간적 종속성을 고려하였다.

Keywords

Acknowledgement

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1A4A5028907) and Basic Research (No. 2021R1F1A1054968)

References

  1. Airoldi EM, Blei D, Fienberg S, and Xing E (2008). Mixed membership stochastic blockmodels, Advances in Neural Information Processing Systems, 9, 1981-2014.
  2. Andrieu C, De Freitas N, Doucet A, and Jordan MI (2003). An introduction to MCMC for machine learning, Machine Learning, 50, 5-43. https://doi.org/10.1023/A:1020281327116
  3. Barnett NP, DiGuiseppi GT, Tesdahl EA, and Meisel MK (2022). Peer selection and influence for marijuana use in a complete network of first-year college students, Addictive Behaviors, 124, 107087.
  4. Batagelj V and Mrvar A (2001). A subquadratic triad census algorithm for large sparse networks with small maximum degree, Social Networks, 23, 237-243. https://doi.org/10.1016/S0378-8733(01)00035-1
  5. Bonacich P (1987). Power and centrality: A family of measures, American Journal of Sociology, 92, 1170-1182. https://doi.org/10.1086/228631
  6. Brewe E, Kramer L, and Sawtelle V (2012). Investigating student communities with network analysis of interactions in a physics learning center, Physical Review Special Topics-Physics Education Research, 8, 010101.
  7. Czarna AZ, Leifeld P, Smieja M, Dufner M, and Salovey P (2016). Do narcissism and emotional intelligence win us friends? modeling dynamics of peer popularity using inferential network analysis, Personality and Social Psychology Bulletin, 42, 1588-1599. https://doi.org/10.1177/0146167216666265
  8. De Jong P, Sprenger C, and Van Veen F (1984). On extreme values of Moran's I and Geary's c, Geographical Analysis, 16, 17-24. https://doi.org/10.1111/j.1538-4632.1984.tb00797.x
  9. Desmarais BA and Cranmer SJ (2012). Statistical mechanics of networks: Estimation and uncertainty, Physica A: Statistical Mechanics and its Applications, 391, 1865-1876. https://doi.org/10.1016/j.physa.2011.10.018
  10. Desmarais BA and Cranmer SJ (2017). Statistical inference in political networks research, The Oxford Handbook of Political Networks (pp. 203-219), Oxford University Press, Oxford.
  11. Dokuka S, Valeeva D, and Yudkevich M (2020). How academic achievement spreads: The role of distinct social networks in academic performance diffusion, Plos One, 15, e0236737, Available from: 10.1371/journal.pone.0236737
  12. Duque MG (2018). Recognizing international status: A relational approach, International Studies Quarterly, 62, 577-592. https://doi.org/10.1093/isq/sqy001
  13. Eklund L and Roman S (2017). Do adolescent gamers make friends offline? identity and friendship formation in school, Computers in Human Behavior, 73, 284-289. https://doi.org/10.1016/j.chb.2017.03.035
  14. Faris R, Felmlee D, and McMillan C (2020). With friends like these: Aggression from amity and equivalence, American Journal of Sociology, 126, 673-713. https://doi.org/10.1086/712972
  15. Flakus M, Danieluk B, Baran L, Kwiatkowska K, Rogoza R, and Schermer JA (2021). Are intelligent peers liked more? assessing peer-reported liking through the network analysis, Personality and Individual Differences, 177, 110844.
  16. Freeman LC (1977). A set of measures of centrality based on betweenness, Sociometry, 40, 35-41. https://doi.org/10.2307/3033543
  17. Freeman LC (1978). Centrality in social networks conceptual clarification, Social Networks, 1, 215-239. https://doi.org/10.1016/0378-8733(78)90021-7
  18. Fruchterman TMJ and Reingold EM (1991). Graph drawing by force-directed placement, Software - Practice and Experience, 21, 1129-1164. https://doi.org/10.1002/spe.4380211102
  19. Goeyvaerts N, Santermans E, Potter G et al. (2018). Household members do not contact each other at random: Implications for infectious disease modelling, Proceedings of the Royal Society B, 285, 20182201, Available from: 10.1098/rspb.2018.2201
  20. Handcock MS, Raftery AE, and Tantrum JM (2007). Model-based clustering for social networks, Journal of the Royal Statistical Society: Series A (Statistics in Society), 170, 301-354. https://doi.org/10.1111/j.1467-985X.2007.00471.x
  21. Hanneke S, Fu W, and Xing EP (2010). Discrete temporal models of social networks, Electronic Journal of Statistics, 4, 585-605. https://doi.org/10.1214/09-EJS548
  22. Hoff PD, Raftery AE, and Handcock MS (2002). Latent space approaches to social network analysis, Journal of the American Statistical Association, 97, 1090-1098. https://doi.org/10.1198/016214502388618906
  23. Holme P and Saramaki J (2012). Temporal networks, Physics Reports, 519, 97-125. https://doi.org/10.1016/j.physrep.2012.03.001
  24. Hunter DR, Goodreau SM, and Handcock MS (2008). Goodness-of-fit of social network models, Journal of the American Statistical Association, 103, 248-258. https://doi.org/10.1198/016214507000000446
  25. Kang YK, Bae SY, and Hong SH (2021). Analysis of middle school students' friends network in class using ERGM: Homophily and relationship in gender, grade, academic achievement and family economic status, Forum for Youth Culture, 67, 5-27. https://doi.org/10.17854/ffyc.2021.07.67.5
  26. Kim JE and Lee HJ (2021). Analysis of female students' helping networks in a secondary school, The Journal of Learner-Centered Curriculum and Instruction, 21 ,921-942. https://doi.org/10.22251/jlcci.2021.21.2.921
  27. Kolaczyk ED and Csardi G (2014). Statistical Analysis of Network Data with R, Springer, New York.
  28. Kretschmer D, Leszczensky L, and Pink S (2018). Selection and influence processes in academic achievement-more pronounced for girls?, Social Networks, 52, 251-260. https://doi.org/10.1016/j.socnet.2017.09.003
  29. Krivitsky PN and Handcock MS (2014). A separable model for dynamic networks, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76, 29-46. https://doi.org/10.1111/rssb.12014
  30. Krivitsky PN, Handcock MS, and Morris M (2011). Adjusting for network size and composition effects in exponential-family random graph models, Statistical Methodology, 8, 319-339. https://doi.org/10.1016/j.stamet.2011.01.005
  31. Kwon HB and Kim JS (2019). An analysis of forming positive relationships depending on classroom seat arrangement by social network analysis, The Journal of the Korea Contents Association, 19, 114-124. https://doi.org/10.5392/JKCA.2019.19.06.114
  32. Lee J, Li G, and Wilson JD (2020). Varying-coefficient models for dynamic networks, Computational Statistics and Data Analysis, 152, 107052.
  33. Leifeld P, Cranmer SJ, and Desmarais BA (2018). Temporal exponential random graph models with btergm: Estimation and bootstrap confidence intervals, Journal of Statistical Software, 83, 1-36. https://doi.org/10.18637/jss.v083.i06
  34. Leifeld P and Cranmer SJ (2019). A theoretical and empirical comparison of the temporal exponential random graph model and the stochastic actor-oriented model, Network Science, 7, 20-51. https://doi.org/10.1017/nws.2018.26
  35. Li M and Stone HN (2018). A social network analysis of the impact of a teacher and student community on academic motivation in a science classroom, Societies, 8, 68.
  36. Loyal JD and Chen Y (2020). Statistical network analysis: A review with applications to the coronavirus disease 2019 pandemic, International Statistical Review, 88, 419-440. https://doi.org/10.1111/insr.12398
  37. Mastrandrea R, Fournet J, and Barrat A (2015). Contact patterns in a high school: A comparison between data collected using wearable sensors, contact diaries and friendship surveys, Plos One, 10, e0136497, Available from: 10.1371/journal.pone.0136497
  38. McCann M, Jordan JA, Higgins K, and Moore L (2019). Longitudinal social network analysis of peer, family, and school contextual influences on adolescent drinking frequency, Journal of Adolescent Health, 65, 350-358. https://doi.org/10.1016/j.jadohealth.2019.03.004
  39. McMillan C, Kreager DA, and Veenstra R (2022). Keeping to the code: How local norms of friendship and dating inform macro-structures of adolescents' romantic networks, Social Networks, 70, 126-137. https://doi.org/10.1016/j.socnet.2021.11.012
  40. Park YJ, Um JM, Hong SB, Han YJ, and Kim JH (2022). Statistical ERGM analysis for consulting company network data, The Korean Journal of Applied Statistics, 35, 527-541. https://doi.org/10.5351/KJAS.2022.35.4.527
  41. Ripley RM, Snijders TA, Boda Z, Voros A, and Preciado P (2011). Manual for RSIENA, University of Oxford, Department of Statistics, Nuffield College, Oxford.
  42. Schaefer DR, Simpkins SD, Vest AE, and Price CD (2011). The contribution of extracurricular activities to adolescent friendships: New insights through social network analysis, Developmental Psychology, 47, 1141- 1152. https://doi.org/10.1037/a0024091
  43. Shin H (2022). Social contagion of academic behavior: Comparing social networks of close friends and admired peers, Plos One, 17, e0265385, Available from: 10.1371/journal.pone.0265385
  44. Snijders TAB (2001). The statistical evaluation of social network dynamics, Sociological Methodology, 31, 361- 395. https://doi.org/10.1111/0081-1750.00099
  45. Snijders TAB (2005). Models for longitudinal network data, Models and Methods in Social Network Analysis, (pp. 215-247), Cambridge University Press, Cambridge.
  46. Snijders TAB, Van de Bunt GG, and Steglich CEG (2010). Introduction to stochastic actor-based models for network dynamics, Social Networks, 32, 44-60. https://doi.org/10.1016/j.socnet.2009.02.004
  47. Sokal RR and Oden NL (1978). Spatial autocorrelation in biology: 1. Methodology, Biological Journal of the Linnean Society, 10, 199-228. https://doi.org/10.1111/j.1095-8312.1978.tb00013.x
  48. Steglich C, Snijders TAB, and Pearson M (2010). Dynamic networks and behavior: Separating selection from influence, Sociological Methodology, 40, 329-393. https://doi.org/10.1111/j.1467-9531.2010.01225.x
  49. Valente TW, Fujimoto K, Chou CP, and Spruijt-Metz D (2009). Adolescent affiliations and adiposity: A social network analysis of friendships and obesity, Journal of Adolescent Health, 45, 202-204. https://doi.org/10.1016/j.jadohealth.2009.01.007
  50. Vogtle EM and Windzio M (2016). Networks of international student mobility: Enlargement and consolidation of the European transnational education space?, Higher Education, 72, 723-741. https://doi.org/10.1007/s10734-015-9972-9
  51. Wasserman S and Faust K (1994). Social Network Analysis: Methods and Applications, Cambridge University Press, Cambridge.
  52. Weber H, Schwenzer M, and Hillmert S (2020). Homophily in the formation and development of learning networks among university students, Network Science, 8, 469-491. https://doi.org/10.1017/nws.2020.10
  53. Weerman FM (2011). Delinquent peers in context: A longitudinal network analysis of selection and influence effects, Criminology, 49, 253-286. https://doi.org/10.1111/j.1745-9125.2010.00223.x
  54. Xing EP, Fu W, and Song L (2010). A state-space mixed membership blockmodel for dynamic network tomography, The Annals of Applied Statistics, 4, 535-566. https://doi.org/10.1214/09-AOAS311