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Mapping Perceptions: A Bayesian Framework for Cognitive Social Structure Analysis
Mapeo de percepciones: un marco Bayesiano para el análisis de estructuras sociales cognitivas
DOI:
https://doi.org/10.15446/rce.v49n2.118473Keywords:
Bayesian hierarchical model; , Cognitive social structure; , Latent space models; , Multinetwork analysis;, Social network analysis. (en)Análisis de redes sociales;, Análisis multired;, Estructura social cognitiva;, Modelo Bayesiano jerárquico;, Modelos de espacio latente. (es)
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This paper presents a hierarchical Bayesian framework for analyzing cognitive social structure data, consisting of multiple undirected, binary networks. The proposed model incorporates fixed and random effects within a probit regression structure, combined with latent multiplicative interaction effects, enabling the characterization of social relationships. Through Bayesian estimation using Markov chain Monte Carlo methods, the model generates shrinkage estimators that borrow information across networks, providing an interpretable spatial representation of actor interactions and a robust framework for predicting missing links. Key contributions include the identification of essential network features, the exploration of latent dimensions, and a comprehensive evaluation of the model's predictive performance. Applications to real CSS data demonstrate the flexibility and utility of the proposed approach, highlighting its capacity to address challenges such as network dependencies, latent position identifiability, and model selection.
Este artículo presenta un marco Bayesiano jerárquico para analizar datos de estructuras sociales cognitivas, conformados por múltiples redes binarias no dirigidas. El modelo propuesto incorpora efectos fijos y aleatorios dentro de una estructura de regresión probit, junto con efectos latentes de interacción multiplicativa, lo que permite caracterizar relaciones sociales entre actores. Mediante estimación Bayesiana con métodos de Monte Carlo vía cadenas de Markov, el modelo genera estimadores con contracción que toman prestada información entre redes, proporciona una representación espacial interpretable de las interacciones entre actores y ofrece un marco robusto para predecir enlaces faltantes. Las contribuciones principales incluyen la identificación de características esenciales de la red, la exploración de dimensiones latentes y una evaluación integral del desempeño predictivo del modelo. Las aplicaciones a datos reales de estructuras sociales cognitivas muestran la flexibilidad y utilidad del enfoque propuesto, así como su capacidad para abordar desafíos relacionados con dependencias de red, identificabilidad de posiciones latentes y selección de modelos.
References
Aguiar, I. & Ugander, J. (2024), 'The latent cognitive structures of social networks', Network Science 12(3), 202-233.
Airoldi, E. M., Blei, D. M., Fienberg, S. E. & Xing, E. P. (2009), Mixed membership stochastic blockmodels, in 'Advances in Neural Information Processing Systems', pp. 33-40.
Aldous, D. J. (1985), Exchangeability and related topics, Springer.
Bernardo, J. M. & Smith, A. F. (2001), 'Bayesian theory'.
Borg, I. & Groenen, P. J. (2005), Modern multidimensional scaling: Theory and applications, Springer Science & Business Media.
Brands, R. A. (2013), 'Cognitive social structures in social network research: A review', Journal of Organizational Behavior 34(S1), S82-S103.
Butts, C. T. (2003), 'Network inference, error, and informant (in) accuracy: a Bayesian approach', Social Networks 25(2), 103-140.
D'Angelo, S., Alfò, M. & Brendan Murphy, T. (2020), 'Modeling node heterogeneity in latent space models for multidimensional networks', Statistica Neerlandica 74(3), 324-341.
D'Angelo, S., Murphy, T. B. & Alfò, M. (2019), 'Latent space modelling of multidimensional networks with application to the exchange of votes in Eurovision Song Contest', The Annals of Applied Statistics 13(2), 900-930.
De Bacco, C., Contisciani, M., Cardoso-Silva, J., Safdari, H., Borges, G. L., Baptista, D., Sweet, T., Young, J.-G., Koster, J., Ross, C. T., McElreath, R., Redhead, D. & Power, E. A. (2023), 'Latent network models to account for noisy, multiply reported social network data', Journal of the Royal Statistical Society Series A: Statistics in Society 186(3), 355-375.
De Bacco, C., Contisciani, M., Cardoso-Silva, J., Safdari, H., Lima Borges, G., Baptista, D., Sweet, T., Young, J.-G., Koster, J., Ross, C. T. et al. (2023), 'Latent network models to account for noisy, multiply reported social network data', Journal of the Royal Statistical Society Series A: Statistics in Society 186(3), 355-375.
Durante, D. & Dunson, D. B. (2018), 'Bayesian inference and testing of group differences in brain networks', Bayesian Analysis 13(1), 29-58.
D'Angelo, S., Alfò, M. & Fop, M. (2023), 'Model-based clustering for multidimensional social networks', Journal of the Royal Statistical Society Series A: Statistics in Society 186(3), 481-507.
Eddelbuettel, D. (2013), Seamless R and C++ Integration with Rcpp, Springer, New York. ISBN 978-1-4614-6867-7.
Fienberg, S. E., Meyer, M. M. & Wasserman, S. S. (1985), 'Statistical analysis of multiple sociometric relations', Journal of the American Statistical association 80(389), 51-67.
Galaskiewicz, J. & Marsden, P. V. (1978), 'Interorganizational resource networks: Formal patterns of overlap', Social Science Research 7(2), 89-107.
Gamerman, D. & Lopes, H. F. (2006), Markov chain Monte Carlo: stochastic simulation for Bayesian inference, Chapman and Hall/CRC.
Gelman, A., Hwang, J. & Vehtari, A. (2014), 'Understanding predictive information criteria for Bayesian models', Statistics and Computing 24(6), 997-1016.
Goldenberg, A., Zheng, A., Fienberg, S. & Airoldi, E. (2010), 'A survey of statistical network models', Foundations and Trends® in Machine Learning 2(2), 129-233.
Gollini, I. & Murphy, T. B. (2016), 'Joint modeling of multiple network views', Journal of Computational and Graphical Statistics 25(1), 246-265.
Handcock, M. S., Raftery, A. E. & Tantrum, J. M. (2007), 'Model-based clustering for social networks', Journal of the Royal Statistical Society: Series A (Statistics in Society) 170(2), 301-354.
Hoff, P. D. (2005), 'Bilinear mixed-effects models for dyadic data', Journal of the American Statistical Association 100(469), 286-295.
Hoff, P. D. (2008), Modeling homophily and stochastic equivalence in symmetric relational data, in 'Advances in Neural Information Processing Systems', pp. 657-664.
Hoff, P. D. (2009), 'Multiplicative latent factor models for description and prediction of social networks', Computational and Mathematical Organization Theory 15(4), 261-272.
Hoff, P. D., Raftery, A. E. & Handcock, M. S. (2002), 'Latent space approaches to social network analysis', Journal of the American Statistical Association 97(460), 1090-1098.
Hoover, D. N. (1982), 'Row-column exchangeability and a generalized model for probability', Exchangeability in Probability and Statistics (Rome, 1981) pp. 281-291.
Kolaczyk, E. D. (2009), Statistical Analysis of Network Data: Methods and Models, Springer Series in Statistics, Springer. https://books.google.com/books?id=QGNLsqq7QwC
Kolaczyk, E. D. & Csárdi, G. (2014), Statistical analysis of network data with R, Vol. 65, Springer.
Krackhardt, D. (1987), 'Cognitive social structures', Social Networks 9(2), 109-134.
Krackhardt, D. & Kilduff, M. (1986), Culture, cultural construals, and social net-works: The task of organizing diversity, Vol. 86, Johnson Graduate School of Management.
Li, W.-J., Yeung, D.-Y. & Zhang, Z. (2011), Generalized latent factor models for social network analysis, in 'Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI), Barcelona, Spain'.
Newman, M. (2003), 'The structure and function of complex networks', SIAM review 45(2), 167-256.
Nowicki, K. & Snijders, T. (2001), 'Estimation and prediction for stochastic blockstructures', Journal of the American Statistical Association 96(455), 1077-1087.
Rodriguez, A. (2015), A Bayesian nonparametric model for exchangeable multinetwork data based on fragmentation and coagulation processes, Technical report, University of California, Santa Cruz.
Roethlisberger, F. J. & Dickson, W. J. (1939), 'Management and the worker', Cambridge: Cambridge University Press.
Salter-Townshend, M. & McCormick, T. H. (2017), 'Latent space models for Multiview network data', The Annals of Applied Statistics 11(3), 1217.
Sampson, S. F. (1968), A novitiate in a period of change: An experimental and case study of social relationships, PhD thesis, Cornell University, September.
Schweinberger, M. & Snijders, T. (2003), 'Settings in social networks: A measurement model', Sociological Methodology 33(1), 307-341.
Sewell, D. K. (2019), 'Latent space models for network perception data', Network Science 7(2), 160-179.
Snijders, T. (2011), 'Statistical models for social networks', Annual Review of Sociology 37, 131-153.
Sosa, J. & Betancourt, B. (2022), 'A latent space model for multilayer network data', Computational Statistics & Data Analysis 169, 107432.
Sosa, J. & Rodríguez, A. (2021), 'A latent space model for cognitive social structures data', Social Networks 65, 85-97.
Swartz, T. B., Gill, P. S. & Muthukumarana, S. (2015), 'A Bayesian approach for the analysis of triadic data in cognitive social structures', Journal of the Royal Statistical Society Series C: Applied Statistics 64(4), 593-610.
Wang, L., Zhang, Z. & Dunson, D. (2019), 'Common and individual structure of brain networks', The Annals of Applied Statistics 13(1), 85.
Wilson, J. D., Cranmer, S. & Lu, Z.-L. (2020), 'A hierarchical latent space network model for population studies of functional connectivity', Computational Brain & Behavior 3(4), 384-399.
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