Model selection in social interaction frameworks: a bayesian approach.
Se propone una metodología para la selección de modelos de interacción social, considerando la complejidad en su especificación. Los modelos de interacción social presentan dos tipos de variables explicativas, las interdependencias entre individuos, denotadas por una matriz de adyacencia, y las cara...
- Autores:
-
Almonacid Hurtado, Paula María
- Tipo de recurso:
- Doctoral thesis
- Fecha de publicación:
- 2020
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/79934
- Palabra clave:
- 519 - Estadísticas
Procesos de Markov
Método de Montecarlo
Teoría bayesiana de decisiones estadísticas
Bayesian Model Averaging
Markov chain Monte Carlo model composition
Modelos de interacción social
- Rights
- openAccess
- License
- Atribución-NoComercial-SinDerivadas 4.0 Internacional
| id |
UNACIONAL2_5d191b20ac6f101df0e46449f17bbac5 |
|---|---|
| oai_identifier_str |
oai:repositorio.unal.edu.co:unal/79934 |
| network_acronym_str |
UNACIONAL2 |
| network_name_str |
Universidad Nacional de Colombia |
| repository_id_str |
|
| dc.title.eng.fl_str_mv |
Model selection in social interaction frameworks: a bayesian approach. |
| dc.title.translated.spa.fl_str_mv |
Selección de modelos en el marco de modelos de interacción social: un enfoque bayesiano |
| title |
Model selection in social interaction frameworks: a bayesian approach. |
| spellingShingle |
Model selection in social interaction frameworks: a bayesian approach. 519 - Estadísticas Procesos de Markov Método de Montecarlo Teoría bayesiana de decisiones estadísticas Bayesian Model Averaging Markov chain Monte Carlo model composition Modelos de interacción social |
| title_short |
Model selection in social interaction frameworks: a bayesian approach. |
| title_full |
Model selection in social interaction frameworks: a bayesian approach. |
| title_fullStr |
Model selection in social interaction frameworks: a bayesian approach. |
| title_full_unstemmed |
Model selection in social interaction frameworks: a bayesian approach. |
| title_sort |
Model selection in social interaction frameworks: a bayesian approach. |
| dc.creator.fl_str_mv |
Almonacid Hurtado, Paula María |
| dc.contributor.advisor.none.fl_str_mv |
Salazar Uribe, Juan Carlos Ramírez Hassan, Andrés |
| dc.contributor.author.none.fl_str_mv |
Almonacid Hurtado, Paula María |
| dc.contributor.researchgroup.spa.fl_str_mv |
Grupo de Investigación en Estadística Universidad Nacional de Colombia, Sede Medellín |
| dc.subject.ddc.spa.fl_str_mv |
519 - Estadísticas |
| topic |
519 - Estadísticas Procesos de Markov Método de Montecarlo Teoría bayesiana de decisiones estadísticas Bayesian Model Averaging Markov chain Monte Carlo model composition Modelos de interacción social |
| dc.subject.lemb.none.fl_str_mv |
Procesos de Markov Método de Montecarlo Teoría bayesiana de decisiones estadísticas |
| dc.subject.proposal.eng.fl_str_mv |
Bayesian Model Averaging Markov chain Monte Carlo model composition |
| dc.subject.proposal.spa.fl_str_mv |
Modelos de interacción social |
| description |
Se propone una metodología para la selección de modelos de interacción social, considerando la complejidad en su especificación. Los modelos de interacción social presentan dos tipos de variables explicativas, las interdependencias entre individuos, denotadas por una matriz de adyacencia, y las características específicas de dichos individuos. De acuerdo con esto, los investigadores deben considerar un número significativo de modelos posibles dados por 2^(k−1) × Z, que representa el número de combinaciones de k variables menos el intercepto en grupos de tamaños 2 a (k − 1), multiplicado por el número de posibles matrices de interacción social Z. La metodología propuesta permite seleccionar simultáneamente las covariables y las matrices de interacción social mediante la implementación de métodos bayesianos tales como Markov chain Monte Carlo model composition (MC3) y Bayesian Averaging Model (BMA). A grandes rasgos, estos métodos permiten obtener estimaciones e inferencias a partir de un promedio de modelos seleccionados luego de reducir su espacio al de mayor probabilidad. Se realizaron varios ejercicios de simulación con el fin evaluar la metodología, así como dos casos de aplicación. Adicionalmente, estos modelos fueron estimados utilizando los enfoques Bayesiano y de Máxima verosimilitud. Después de comparar los resultados, se encontró que el enfoque Bayesiano ofrece múltiples ventajas, ya que es posible, a diferencia del método de Máxima verosimilitud, obtener la distribución posterior de los parámetros, incluir información a priori, en caso de ser necesario, e introducir incertidumbre asociada al espacio de elección de los modelos. (Tomado de la fuente) |
| publishDate |
2020 |
| dc.date.issued.none.fl_str_mv |
2020-08-12 |
| dc.date.accessioned.none.fl_str_mv |
2021-08-12T20:55:18Z |
| dc.date.available.none.fl_str_mv |
2021-08-12T20:55:18Z |
| dc.type.spa.fl_str_mv |
Trabajo de grado - Doctorado |
| dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
| dc.type.version.spa.fl_str_mv |
info:eu-repo/semantics/acceptedVersion |
| dc.type.coar.spa.fl_str_mv |
http://purl.org/coar/resource_type/c_db06 |
| dc.type.content.spa.fl_str_mv |
Text |
| dc.type.redcol.spa.fl_str_mv |
http://purl.org/redcol/resource_type/TD |
| format |
http://purl.org/coar/resource_type/c_db06 |
| status_str |
acceptedVersion |
| dc.identifier.uri.none.fl_str_mv |
https://repositorio.unal.edu.co/handle/unal/79934 |
| dc.identifier.instname.spa.fl_str_mv |
Universidad Nacional de Colombia |
| dc.identifier.reponame.spa.fl_str_mv |
Repositorio Institucional Universidad Nacional de Colombia |
| dc.identifier.repourl.spa.fl_str_mv |
https://repositorio.unal.edu.co/ |
| url |
https://repositorio.unal.edu.co/handle/unal/79934 https://repositorio.unal.edu.co/ |
| identifier_str_mv |
Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia |
| dc.language.iso.spa.fl_str_mv |
spa |
| language |
spa |
| dc.relation.references.spa.fl_str_mv |
Ahelegbey, D. F. (2015). The Econometrics of Networks: A Review. Working Papers, 13:27. Anselin, L. and Griffith, D. A. (1988). Do spatial effecfs really matter in regression analysis? Papers in Regional Science, 65(1):11–34. Arias, A. S. (2015). Apalancamiento. https://economipedia.com/definiciones/apalancamiento-financiero.html Athanasoglou, P. P., Brissimis, S. N., and Delis, M. D. (2008). Bank-specific, industry-specific and macroeconomic determinants of bank profitability. Journal of international financial Markets, Institutions and Money, 18(2):121–136. Berger, J. and Pericchi, L. (2015). Bayes Factors. In Wiley StatsRef: Statistics Reference Online, pages 1–14. John Wiley & Sons, Ltd, Chichester, UK. Blondel, V. D., Guillaume, J.-L., Lambiotte, R., and Lefebvre, E. (2008). Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment, 2008(10):P10008. Blume, L. E., Brock, W. A., Durlauf, S. N., and Ioannides, Y. M. (2011). Identification of social interactions. In Handbook of Social Economics, volume 1, pages 853–964. Elsevier B.V. Blume, L. E., Brock, W. A., Durlauf, S. N., and Jayaraman, R. (2015). Linear social interactions models. Journal of Political Economy, 123(2):444–496. Bourke, P. (1989). Concentration and other determinants of bank profitability in europe, north america and australia. Journal of Banking & Finance, 13(1):65–79. Bramoullé, Y., Djebbari, H., and Fortin, B. (2009). Identification of peer effects through social networks. Journal of econometrics, 150(1):41–55. Bramoullé, Y., Djebbari, H., and Fortin, B. (2020). Peer effects in networks: A survey. In Annual Review of Economics, volume 12, pages 603–629. Annual Reviews Inc. Brock, W. A. and Durlauf, S. N. (2001). Discrete choice with social interactions. The Review of Economic Studies, 68(2):235–260. Brueckner, J. K. (2003). Strategic interaction among governments: An overview of empirical studies. International regional science review, 26(2):175–188. Case, A. C., Rosen, H. S., and Hines Jr, J. R. (1993). Budget spillovers and fiscal policy interdependence: Evidence from the states. Journal of public economics, 52(3):285–307. Chandrasekhar, A. and Lewis, R. (2011). Econometrics of sampled networks. Unpublished manuscript, MIT.[422]. Chipman, H., George, E., McCulloch, R., Clyde, M., Foster, D., and Stine, R. (2001). The Practical Implementation of Bayesian Model Selection on JSTOR. Lecture Notes-Monograph Series, 38:65–134. Cingano, F. and Rosolia, A. (2012). People i know: job search and social networks. Journal of Labor Economics, 30(2):291–332. Cliff, A. D. (1973). Spatial autocorrelation. Technical report. Comola, M. and Prina, S. (2020). Treatment Effect Accounting for Network Changes *. The Review of Economics and Statistics, pages 1–25. Cotteleer, G., Stobbe, T., and van Kooten, G. C. (2011). Bayesian model averaging in the context of spatial hedonic pricing: an application to farmland values. Journal of Regional Science, 51(3):540–557. Crespo Cuaresma, J. and Feldkircher, M. (2013). Spatial filtering, model uncertainty and the speed of income convergence in europe. Journal of Applied Econometrics, 28(4):720–741. Csárdi and Nepusz (2006). The igraph software package for complex network research. Interjournal Complex Systems, page 1695. De Oliveira, V. and Song, J. J. (2008). Bayesian analysis of simultaneous autoregressive models. Sankhya: The Indian Journal of Statistics, Series B (2008-) ¯, pages 323–350. De Paula, A. (2016). Econometrics of network models (no. cwp06/16). Technical report, cemmap working paper, Centre for Microdata Methods and Practice. Draper, D. (1995). Assessment and propagation of model uncertainty. Journal of the Royal Statistical Society: Series B (Methodological), 57(1):45–70. Durlauf, S. (2006). Groups, social influences, and inequality. In Bowles, S., Durlauf, S. N., and Hoff, K., editors, Poverty Traps, chapter 6, pages 141–175. Princeton University Press. Eicher, T. S., Papageorgiou, C., and Raftery, A. E. (2011). Default priors and predictive performance in bayesian model averaging, with application to growth determinants. Journal of Applied Econometrics, 26(1):30–55. Elhorst, J. P. (2014). Spatial econometrics: from cross-sectional data to spatial panels, volume 479. Springer. Fan, J. and Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American statistical Association, 96(456):1348–1360. Fernandez, C., Ley, E., and Steel, M. F. (2001). Benchmark priors for bayesian model averaging. Journal of Econometrics, 100(2):381–427. Friedman, J., Hastie, T., Tibshirani, R., et al. (2000). Additive logistic regression: a statistical view of boosting (with discussion and a rejoinder by the authors). The annals of statistics, 28(2):337– 407. Gelfand, A. E. and Smith, A. F. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American statistical association, 85(410):398–409. George, E. I. (2010). Dilution priors: Compensating for model space redundancy. In Berger, J. O., Cai, T. T., and Iain M. Johnstone, editors, Borrowing Strength: Theory Powering Applications - A Festschrift for Lawrence D. Brown, volume 6, chapter 21, pages 158–165. Institute of Mathematical Statistics. Gilks, W. R., Best, N. G., and Tan, K. (1995). Adaptive rejection metropolis sampling within gibbs sampling. Journal of the Royal Statistical Society: Series C (Applied Statistics), 44(4):455–472. Goddard, J., Molyneux, P., and Wilson, J. O. (2004). The profitability of european banks: a crosssectional and dynamic panel analysis. The Manchester School, 72(3):363–381. Griffith, D. A. and Lagona, F. (1998). On the quality of likelihood-based estimators in spatial autoregressive models when the data dependence structure is misspecified. Journal of Statistical Planning and Inference, 69(1):153–174. Hartmann, W. R., Manchanda, P., Nair, H., Bothner, M., Dodds, P., Godes, D., Hosanagar, K., and Tucker, C. (2008). Modeling social interactions: Identification, empirical methods and policy implications. Marketing letters, 19(3-4):287–304. Hassan, A. R. (2017). The interplay between the bayesian and frequentist approaches: a general nesting spatial panel data model. Spatial Economic Analysis, 12(1):92–112. Hastings, W. K. (1970). Monte carlo sampling methods using markov chains and their applications. Biometrika, 57(1):97–109. Held, P., Krause, B., and Kruse, R. (2016). Dynamic clustering in social networks using louvain and infomap method. In 2016 Third European Network Intelligence Conference (ENIC), pages 61–68. IEEE. Hepple, L. W. (1995). Bayesian techniques in spatial and network econometrics: 2. computational methods and algorithms. Environment and Planning A, 27(4):615–644. Hodges, J. S. (1987). Uncertainty, policy analysis and statistics. Statistical science, 2(3):259–275. Hsieh, C.-S. and Lee, L. F. (2016). A social interactions model with endogenous friendship formation and selectivity. Journal of Applied Econometrics, 31(2):301–319. Huber, P. J. (2004). Robust Statistics. John Wiley & Sons, Hoboken, New Jersey. Jackson, M. O. (2010). Social and economic networks. Princeton university press. Junker, N. (2020). Community Detection with Louvain and Infomap | R-bloggers. Kelejian, H. H. (2008). A spatial j-test for model specification against a single or a set of nonnested alternatives. Letters in Spatial and Resource Sciences, 1(1):3–11. Kelejian, H. H. and Piras, G. (2011). An extension of kelejian’s j-test for non-nested spatial models. Regional Science and Urban Economics, 41(3):281–292. Kelejian, H. H. and Piras, G. (2014). Estimation of spatial models with endogenous weighting matrices, and an application to a demand model for cigarettes. Regional Science and Urban Economics, 46:140–149. Kiziryan, M. (2015). Flujo de caja. https://economipedia.com/definiciones/flujo-de-caja.html Koop, G. M. (2003). Bayesian econometrics. John Wiley & Sons Inc. Krisztin, T. (2017). The determinants of regional freight transport: a spatial, semiparametric approach. Geographical Analysis, 49(3):268–308. Kuan, C.-M. and Liu, T. (1995). Forecasting exchange rates using feedforward and recurrent neural networks. Journal of applied econometrics, 10(4):347–364. Lancaster, T. (2000). The incidental parameter problem since 1948. Journal of econometrics, 95(2):391–413. Leamer, E. E. and Leamer, E. E. (1978). Specification searches: Ad hoc inference with nonexperimental data, volume 53. Wiley New York. Lee, L.-f. (2007). Identification and estimation of econometric models with group interactions, contextual factors and fixed effects. Journal of Econometrics, 140(2):333–374. Lee, L.-f., Liu, X., and Lin, X. (2010). Specification and estimation of social interaction models with network structures. The Econometrics Journal, 13(2):145–176. LeSage, J. P. (2008). An introduction to spatial econometrics. Revue d’Économie Industrielle, (123):19–44. LeSage, J. P. and Fischer, M. M. (2008). Spatial growth regressions: model specification, estimation and interpretation. Spatial Economic Analysis, 3(3):275–304. LeSage, J. P. and Parent, O. (2007a). Bayesian model averaging for spatial econometric models. Geographical Analysis, 39(3):241–267. LeSage, J. P. and Parent, O. (2007b). Bayesian model averaging for spatial econometric models. Geographical Analysis, 39(3):241–267. Lin, X. (2005). Peer effects and student academic achievement: an application of spatial autoregressive model with group unobservables. Unpublished manuscript, Ohio State University. Lin, X. (2010). Identifying peer effects in student academic achievement by spatial autoregressive models with group unobservables. Journal of Labor Economics, 28(4):825–860. Madigan, D. and Raftery, A. E. (1994). Model selection and accounting for model uncertainty in graphical models using occam’s window. Journal of the American Statistical Association, 89(428):1535–1546. Madigan, D., York, J., and Allard, D. (1995). Bayesian Graphical Models for Discrete Data. International Statistical Review / Revue Internationale de Statistique, 63(2):215–232. Manjares, A. (2020). EBITDA. https://mispropiasfinanzas.com/concepto/ebitda/ Manski, C. F. (1993). Identification of endogenous social effects: The reflection problem. The Review of Economic Studies, 60(3):531–542. Marden, J. I. (2000). Hypothesis testing: from p values to bayes factors. Journal of the American Statistical Association, 95(452):1316–1320. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953). Equation of state calculations by fast computing machines. The journal of chemical physics, 21(6):1087–1092. Moffitt, R. A. et al. (2001). Policy interventions, low-level equilibria, and social interactions. Social dynamics, 4(45-82):6–17. Molyneux, P. and Thornton, J. (1992). Determinants of european bank profitability: A note. Journal of banking & Finance, 16(6):1173–1178. Moser, M. and Hofmarcher, P. (2014). Model priors revisited: Interaction terms in bma growth applications. Journal of Applied Econometrics, 29(2):344–347. Moulton, L. H. and Zeger, S. L. (1991). Bootstrapping generalized linear models. Computational Statistics & Data Analysis, 11(1): 63-63. Neyman, J. and Scott, E. L. (1948). Consistent Estimates Based on Partially Consistent Observations. Econometrica, 16(1):1–32. Piribauer, P. and Crespo Cuaresma, J. (2016). Bayesian variable selection in spatial autoregressive models. Spatial Economic Analysis, 11(4):457–479. Piribauer, P. and Fischer, M. M. (2015). Model uncertainty in matrix exponential spatial growth regression models. Geographical Analysis, 47(3):240–261. Raftery, A. E. (1988). Inference for the binomial n parameter: A hierarchical bayes approach. Biometrika, 75(2):223–228. Raftery, A. E. (1995). Bayesian model selection in social research. Sociological Methodology, 25:111–164. Raftery, A. E. (1996). Approximate bayes factors and accounting for model uncertainty in generalised linear models. Biometrika, 83(2):251–266. Raftery, A. E., Madigan, D., and Hoeting, J. A. (1997). Bayesian model averaging for linear regression models. Journal of the American Statistical Association, 92(437):179–191. Rosvall, M. and Bergstrom, C. T. (2008). Maps of random walks on complex networks reveal community structure. Proceedings of the National Academy of Sciences of the United States of America, 105(4):1118–23. Sacerdote, B. (2011). Peer effects in education: How might they work, how big are they and how much do we know thus far? In Handbook of the Economics of Education, volume 3, pages 249–277. Elsevier. Short, B. K. (1979). The relation between commercial bank profit rates and banking concentration in canada, western europe, and japan. Journal of Banking & Finance, 3(3):209–219. Song, Y., Liang, X., Zhu, Y., and Lin, L. (2021). Robust variable selection with exponential squared loss for the spatial autoregressive model. Computational Statistics and Data Analysis, 155:107094. Stakhovych, S. and Bijmolt, T. H. (2009). Specification of spatial models: A simulation study on weights matrices. Papers in Regional Science, 88(2):389–408. Steel, M. F. and Ley, E. (2007). On the effect of prior assumptions in Bayesian model averaging with applications to growth regression. The World Bank. Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58(1):267–288. Topa, G. (2001). Social interactions, local spillovers and unemployment. The Review of Economic Studies, 68(2):261–295. Wang, X., Jiang, Y., Huang, M., and Zhang, H. (2013). Robust variable selection with exponential squared loss. Journal of the American Statistical Association, 108(502):632–643. Weisbrod, B. A. (1964). External Benefits of Public Education. PhD thesis, Princeton University, Princeton. Westreicher, G. (2018). Rentabilidad de los activos, ROA. https://economipedia.com/definiciones/rentabilidad-de-los-activos-roa.html Westreicher, G. , S. (2020). Capital de trabajo. https://economipedia.com/definiciones/capital-de-trabajo.html Wilson, J. H. (1975). The student expenditure impact of a university on the local economy. The Annals Of Regional Science, 9(1):122–126. Withers, S. D. (2002). Quantitative methods: Bayesian inference, bayesian thinking. Progress in Human Geography, 26(4):553–566. Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data. MIT Press, London, second edition. Zellner, A. (1986). On assessing prior distributions and Bayesian regression analysis with g-prior distributions. Elsevier Science. Zellner, A. (1999). Bayesian and non-bayesian approaches to scientific modeling and inference in economics and econometrics. Technical report. Zhang, X. and Yu, J. (2018). Spatial weights matrix selection and model averaging for spatial autoregressive models. Journal of Econometrics, 203(1):1–18. Zou, H. (2006). The adaptive lasso and its oracle properties. Journal of the American statistical association, 101(476):1418–1429. |
| dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
| dc.rights.license.spa.fl_str_mv |
Atribución-NoComercial-SinDerivadas 4.0 Internacional |
| dc.rights.uri.spa.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| dc.rights.accessrights.spa.fl_str_mv |
info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
Atribución-NoComercial-SinDerivadas 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ http://purl.org/coar/access_right/c_abf2 |
| eu_rights_str_mv |
openAccess |
| dc.format.extent.spa.fl_str_mv |
90 páginas |
| dc.format.mimetype.spa.fl_str_mv |
application/pdf |
| dc.publisher.spa.fl_str_mv |
Universidad Nacional de Colombia Universidad Nacional de Colombia |
| dc.publisher.program.spa.fl_str_mv |
Medellín - Ciencias - Doctorado en Ciencias - Estadística |
| dc.publisher.department.spa.fl_str_mv |
Escuela de estadística |
| dc.publisher.faculty.spa.fl_str_mv |
Facultad de Ciencias |
| dc.publisher.place.spa.fl_str_mv |
Medellín, Colombia |
| dc.publisher.branch.spa.fl_str_mv |
Universidad Nacional de Colombia - Sede Medellín |
| institution |
Universidad Nacional de Colombia |
| bitstream.url.fl_str_mv |
https://repositorio.unal.edu.co/bitstream/unal/79934/1/license.txt https://repositorio.unal.edu.co/bitstream/unal/79934/3/43164806.2020.pdf https://repositorio.unal.edu.co/bitstream/unal/79934/4/43164806.2020.pdf.jpg |
| bitstream.checksum.fl_str_mv |
cccfe52f796b7c63423298c2d3365fc6 9be36951faece8c917f94ac397af1331 9812569a9e825bc63df8cabaf0893e11 |
| bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 |
| repository.name.fl_str_mv |
Repositorio Institucional Universidad Nacional de Colombia |
| repository.mail.fl_str_mv |
repositorio_nal@unal.edu.co |
| _version_ |
1814089365511471104 |
| spelling |
Atribución-NoComercial-SinDerivadas 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Salazar Uribe, Juan Carlosdd5849a37723fe30e64e55863468d8a0600Ramírez Hassan, Andréscb0a3d0282e6e8121788a379b1d07987600Almonacid Hurtado, Paula Maríaa974d3b450f205193b80c3d5b752d5f0Grupo de Investigación en Estadística Universidad Nacional de Colombia, Sede Medellín2021-08-12T20:55:18Z2021-08-12T20:55:18Z2020-08-12https://repositorio.unal.edu.co/handle/unal/79934Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/Se propone una metodología para la selección de modelos de interacción social, considerando la complejidad en su especificación. Los modelos de interacción social presentan dos tipos de variables explicativas, las interdependencias entre individuos, denotadas por una matriz de adyacencia, y las características específicas de dichos individuos. De acuerdo con esto, los investigadores deben considerar un número significativo de modelos posibles dados por 2^(k−1) × Z, que representa el número de combinaciones de k variables menos el intercepto en grupos de tamaños 2 a (k − 1), multiplicado por el número de posibles matrices de interacción social Z. La metodología propuesta permite seleccionar simultáneamente las covariables y las matrices de interacción social mediante la implementación de métodos bayesianos tales como Markov chain Monte Carlo model composition (MC3) y Bayesian Averaging Model (BMA). A grandes rasgos, estos métodos permiten obtener estimaciones e inferencias a partir de un promedio de modelos seleccionados luego de reducir su espacio al de mayor probabilidad. Se realizaron varios ejercicios de simulación con el fin evaluar la metodología, así como dos casos de aplicación. Adicionalmente, estos modelos fueron estimados utilizando los enfoques Bayesiano y de Máxima verosimilitud. Después de comparar los resultados, se encontró que el enfoque Bayesiano ofrece múltiples ventajas, ya que es posible, a diferencia del método de Máxima verosimilitud, obtener la distribución posterior de los parámetros, incluir información a priori, en caso de ser necesario, e introducir incertidumbre asociada al espacio de elección de los modelos. (Tomado de la fuente)We propose a methodology oriented towards the selection of social interaction models taking into account the complexity in its specification. This type of models considers as explaining variables the inter-dependencies between individuals, represented by an adjacency matrix and the economic characteristics of a group of individuals. In this sense, researchers have to consider a significant number of possible models given by 2^(k−1) × Z, which represents the number of combinations of k variables without the intercept in groups of sizes from 2 to (k − 1) times the number of potential social interaction matrices W. This new methodology enables the process of simultaneous selection of the covariables and the social interaction matrices, through the application of the Markov Chain Monte Carlo Model Composition (MC3) and Bayesian Model Averaging methods, which are based on the Bayesian approach. These methods produce estimates and inferences from an average of models, which are selected after reducing the probability model space to the highest probability possible. Several simulation exercises were carried out to test the methodology, as well as two applications. Additionally, these Social Interaction Models were estimated, using Bayesian and Maximum Likelihood approaches. After comparing the results, we find that the Bayesian approach offers multiple advantages; such as finding the posterior distribution of the parameters, including prior information, if it is necessary, and introducing model uncertainty. (Tomado de la fuente)DoctoradoDoctora en Ciencias-EstadísticaAnálisis multivariado y Estadística bayesiana90 páginasapplication/pdfspaUniversidad Nacional de ColombiaUniversidad Nacional de ColombiaMedellín - Ciencias - Doctorado en Ciencias - EstadísticaEscuela de estadísticaFacultad de CienciasMedellín, ColombiaUniversidad Nacional de Colombia - Sede Medellín519 - EstadísticasProcesos de MarkovMétodo de MontecarloTeoría bayesiana de decisiones estadísticasBayesian Model AveragingMarkov chain Monte Carlo model compositionModelos de interacción socialModel selection in social interaction frameworks: a bayesian approach.Selección de modelos en el marco de modelos de interacción social: un enfoque bayesianoTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttp://purl.org/redcol/resource_type/TDAhelegbey, D. F. (2015). The Econometrics of Networks: A Review. Working Papers, 13:27.Anselin, L. and Griffith, D. A. (1988). Do spatial effecfs really matter in regression analysis? Papers in Regional Science, 65(1):11–34.Arias, A. S. (2015). Apalancamiento. https://economipedia.com/definiciones/apalancamiento-financiero.htmlAthanasoglou, P. P., Brissimis, S. N., and Delis, M. D. (2008). Bank-specific, industry-specific and macroeconomic determinants of bank profitability. Journal of international financial Markets, Institutions and Money, 18(2):121–136.Berger, J. and Pericchi, L. (2015). Bayes Factors. In Wiley StatsRef: Statistics Reference Online, pages 1–14. John Wiley & Sons, Ltd, Chichester, UK.Blondel, V. D., Guillaume, J.-L., Lambiotte, R., and Lefebvre, E. (2008). Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment, 2008(10):P10008.Blume, L. E., Brock, W. A., Durlauf, S. N., and Ioannides, Y. M. (2011). Identification of social interactions. In Handbook of Social Economics, volume 1, pages 853–964. Elsevier B.V.Blume, L. E., Brock, W. A., Durlauf, S. N., and Jayaraman, R. (2015). Linear social interactions models. Journal of Political Economy, 123(2):444–496.Bourke, P. (1989). Concentration and other determinants of bank profitability in europe, north america and australia. Journal of Banking & Finance, 13(1):65–79.Bramoullé, Y., Djebbari, H., and Fortin, B. (2009). Identification of peer effects through social networks. Journal of econometrics, 150(1):41–55.Bramoullé, Y., Djebbari, H., and Fortin, B. (2020). Peer effects in networks: A survey. In Annual Review of Economics, volume 12, pages 603–629. Annual Reviews Inc.Brock, W. A. and Durlauf, S. N. (2001). Discrete choice with social interactions. The Review of Economic Studies, 68(2):235–260.Brueckner, J. K. (2003). Strategic interaction among governments: An overview of empirical studies. International regional science review, 26(2):175–188.Case, A. C., Rosen, H. S., and Hines Jr, J. R. (1993). Budget spillovers and fiscal policy interdependence: Evidence from the states. Journal of public economics, 52(3):285–307.Chandrasekhar, A. and Lewis, R. (2011). Econometrics of sampled networks. Unpublished manuscript, MIT.[422].Chipman, H., George, E., McCulloch, R., Clyde, M., Foster, D., and Stine, R. (2001). The Practical Implementation of Bayesian Model Selection on JSTOR. Lecture Notes-Monograph Series, 38:65–134.Cingano, F. and Rosolia, A. (2012). People i know: job search and social networks. Journal of Labor Economics, 30(2):291–332.Cliff, A. D. (1973). Spatial autocorrelation. Technical report. Comola, M. and Prina, S. (2020). Treatment Effect Accounting for Network Changes *. The Review of Economics and Statistics, pages 1–25.Cotteleer, G., Stobbe, T., and van Kooten, G. C. (2011). Bayesian model averaging in the context of spatial hedonic pricing: an application to farmland values. Journal of Regional Science, 51(3):540–557.Crespo Cuaresma, J. and Feldkircher, M. (2013). Spatial filtering, model uncertainty and the speed of income convergence in europe. Journal of Applied Econometrics, 28(4):720–741.Csárdi and Nepusz (2006). The igraph software package for complex network research. Interjournal Complex Systems, page 1695.De Oliveira, V. and Song, J. J. (2008). Bayesian analysis of simultaneous autoregressive models. Sankhya: The Indian Journal of Statistics, Series B (2008-) ¯, pages 323–350.De Paula, A. (2016). Econometrics of network models (no. cwp06/16). Technical report, cemmap working paper, Centre for Microdata Methods and Practice.Draper, D. (1995). Assessment and propagation of model uncertainty. Journal of the Royal Statistical Society: Series B (Methodological), 57(1):45–70.Durlauf, S. (2006). Groups, social influences, and inequality. In Bowles, S., Durlauf, S. N., and Hoff, K., editors, Poverty Traps, chapter 6, pages 141–175. Princeton University Press.Eicher, T. S., Papageorgiou, C., and Raftery, A. E. (2011). Default priors and predictive performance in bayesian model averaging, with application to growth determinants. Journal of Applied Econometrics, 26(1):30–55.Elhorst, J. P. (2014). Spatial econometrics: from cross-sectional data to spatial panels, volume 479. Springer.Fan, J. and Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American statistical Association, 96(456):1348–1360.Fernandez, C., Ley, E., and Steel, M. F. (2001). Benchmark priors for bayesian model averaging. Journal of Econometrics, 100(2):381–427.Friedman, J., Hastie, T., Tibshirani, R., et al. (2000). Additive logistic regression: a statistical view of boosting (with discussion and a rejoinder by the authors). The annals of statistics, 28(2):337– 407.Gelfand, A. E. and Smith, A. F. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American statistical association, 85(410):398–409.George, E. I. (2010). Dilution priors: Compensating for model space redundancy. In Berger, J. O., Cai, T. T., and Iain M. Johnstone, editors, Borrowing Strength: Theory Powering Applications - A Festschrift for Lawrence D. Brown, volume 6, chapter 21, pages 158–165. Institute of Mathematical Statistics.Gilks, W. R., Best, N. G., and Tan, K. (1995). Adaptive rejection metropolis sampling within gibbs sampling. Journal of the Royal Statistical Society: Series C (Applied Statistics), 44(4):455–472.Goddard, J., Molyneux, P., and Wilson, J. O. (2004). The profitability of european banks: a crosssectional and dynamic panel analysis. The Manchester School, 72(3):363–381.Griffith, D. A. and Lagona, F. (1998). On the quality of likelihood-based estimators in spatial autoregressive models when the data dependence structure is misspecified. Journal of Statistical Planning and Inference, 69(1):153–174.Hartmann, W. R., Manchanda, P., Nair, H., Bothner, M., Dodds, P., Godes, D., Hosanagar, K., and Tucker, C. (2008). Modeling social interactions: Identification, empirical methods and policy implications. Marketing letters, 19(3-4):287–304.Hassan, A. R. (2017). The interplay between the bayesian and frequentist approaches: a general nesting spatial panel data model. Spatial Economic Analysis, 12(1):92–112.Hastings, W. K. (1970). Monte carlo sampling methods using markov chains and their applications. Biometrika, 57(1):97–109.Held, P., Krause, B., and Kruse, R. (2016). Dynamic clustering in social networks using louvain and infomap method. In 2016 Third European Network Intelligence Conference (ENIC), pages 61–68. IEEE.Hepple, L. W. (1995). Bayesian techniques in spatial and network econometrics: 2. computational methods and algorithms. Environment and Planning A, 27(4):615–644.Hodges, J. S. (1987). Uncertainty, policy analysis and statistics. Statistical science, 2(3):259–275.Hsieh, C.-S. and Lee, L. F. (2016). A social interactions model with endogenous friendship formation and selectivity. Journal of Applied Econometrics, 31(2):301–319.Huber, P. J. (2004). Robust Statistics. John Wiley & Sons, Hoboken, New Jersey.Jackson, M. O. (2010). Social and economic networks. Princeton university press.Junker, N. (2020). Community Detection with Louvain and Infomap | R-bloggers.Kelejian, H. H. (2008). A spatial j-test for model specification against a single or a set of nonnested alternatives. Letters in Spatial and Resource Sciences, 1(1):3–11.Kelejian, H. H. and Piras, G. (2011). An extension of kelejian’s j-test for non-nested spatial models. Regional Science and Urban Economics, 41(3):281–292.Kelejian, H. H. and Piras, G. (2014). Estimation of spatial models with endogenous weighting matrices, and an application to a demand model for cigarettes. Regional Science and Urban Economics, 46:140–149.Kiziryan, M. (2015). Flujo de caja. https://economipedia.com/definiciones/flujo-de-caja.htmlKoop, G. M. (2003). Bayesian econometrics. John Wiley & Sons Inc.Krisztin, T. (2017). The determinants of regional freight transport: a spatial, semiparametric approach. Geographical Analysis, 49(3):268–308.Kuan, C.-M. and Liu, T. (1995). Forecasting exchange rates using feedforward and recurrent neural networks. Journal of applied econometrics, 10(4):347–364.Lancaster, T. (2000). The incidental parameter problem since 1948. Journal of econometrics, 95(2):391–413.Leamer, E. E. and Leamer, E. E. (1978). Specification searches: Ad hoc inference with nonexperimental data, volume 53. Wiley New York.Lee, L.-f. (2007). Identification and estimation of econometric models with group interactions, contextual factors and fixed effects. Journal of Econometrics, 140(2):333–374.Lee, L.-f., Liu, X., and Lin, X. (2010). Specification and estimation of social interaction models with network structures. The Econometrics Journal, 13(2):145–176.LeSage, J. P. (2008). An introduction to spatial econometrics. Revue d’Économie Industrielle, (123):19–44.LeSage, J. P. and Fischer, M. M. (2008). Spatial growth regressions: model specification, estimation and interpretation. Spatial Economic Analysis, 3(3):275–304.LeSage, J. P. and Parent, O. (2007a). Bayesian model averaging for spatial econometric models. Geographical Analysis, 39(3):241–267.LeSage, J. P. and Parent, O. (2007b). Bayesian model averaging for spatial econometric models. Geographical Analysis, 39(3):241–267.Lin, X. (2005). Peer effects and student academic achievement: an application of spatial autoregressive model with group unobservables. Unpublished manuscript, Ohio State University.Lin, X. (2010). Identifying peer effects in student academic achievement by spatial autoregressive models with group unobservables. Journal of Labor Economics, 28(4):825–860.Madigan, D. and Raftery, A. E. (1994). Model selection and accounting for model uncertainty in graphical models using occam’s window. Journal of the American Statistical Association, 89(428):1535–1546.Madigan, D., York, J., and Allard, D. (1995). Bayesian Graphical Models for Discrete Data. International Statistical Review / Revue Internationale de Statistique, 63(2):215–232.Manjares, A. (2020). EBITDA. https://mispropiasfinanzas.com/concepto/ebitda/Manski, C. F. (1993). Identification of endogenous social effects: The reflection problem. The Review of Economic Studies, 60(3):531–542.Marden, J. I. (2000). Hypothesis testing: from p values to bayes factors. Journal of the American Statistical Association, 95(452):1316–1320.Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953). Equation of state calculations by fast computing machines. The journal of chemical physics, 21(6):1087–1092.Moffitt, R. A. et al. (2001). Policy interventions, low-level equilibria, and social interactions. Social dynamics, 4(45-82):6–17.Molyneux, P. and Thornton, J. (1992). Determinants of european bank profitability: A note. Journal of banking & Finance, 16(6):1173–1178.Moser, M. and Hofmarcher, P. (2014). Model priors revisited: Interaction terms in bma growth applications. Journal of Applied Econometrics, 29(2):344–347.Moulton, L. H. and Zeger, S. L. (1991). Bootstrapping generalized linear models. Computational Statistics & Data Analysis, 11(1): 63-63.Neyman, J. and Scott, E. L. (1948). Consistent Estimates Based on Partially Consistent Observations. Econometrica, 16(1):1–32.Piribauer, P. and Crespo Cuaresma, J. (2016). Bayesian variable selection in spatial autoregressive models. Spatial Economic Analysis, 11(4):457–479.Piribauer, P. and Fischer, M. M. (2015). Model uncertainty in matrix exponential spatial growth regression models. Geographical Analysis, 47(3):240–261.Raftery, A. E. (1988). Inference for the binomial n parameter: A hierarchical bayes approach. Biometrika, 75(2):223–228.Raftery, A. E. (1995). Bayesian model selection in social research. Sociological Methodology, 25:111–164.Raftery, A. E. (1996). Approximate bayes factors and accounting for model uncertainty in generalised linear models. Biometrika, 83(2):251–266.Raftery, A. E., Madigan, D., and Hoeting, J. A. (1997). Bayesian model averaging for linear regression models. Journal of the American Statistical Association, 92(437):179–191.Rosvall, M. and Bergstrom, C. T. (2008). Maps of random walks on complex networks reveal community structure. Proceedings of the National Academy of Sciences of the United States of America, 105(4):1118–23.Sacerdote, B. (2011). Peer effects in education: How might they work, how big are they and how much do we know thus far? In Handbook of the Economics of Education, volume 3, pages 249–277. Elsevier. Short,B. K. (1979). The relation between commercial bank profit rates and banking concentration in canada, western europe, and japan. Journal of Banking & Finance, 3(3):209–219.Song, Y., Liang, X., Zhu, Y., and Lin, L. (2021). Robust variable selection with exponential squared loss for the spatial autoregressive model. Computational Statistics and Data Analysis, 155:107094.Stakhovych, S. and Bijmolt, T. H. (2009). Specification of spatial models: A simulation study on weights matrices. Papers in Regional Science, 88(2):389–408.Steel, M. F. and Ley, E. (2007). On the effect of prior assumptions in Bayesian model averaging with applications to growth regression. The World Bank.Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58(1):267–288.Topa, G. (2001). Social interactions, local spillovers and unemployment. The Review of Economic Studies, 68(2):261–295.Wang, X., Jiang, Y., Huang, M., and Zhang, H. (2013). Robust variable selection with exponential squared loss. Journal of the American Statistical Association, 108(502):632–643.Weisbrod, B. A. (1964). External Benefits of Public Education. PhD thesis, Princeton University, Princeton.Westreicher, G. (2018). Rentabilidad de los activos, ROA. https://economipedia.com/definiciones/rentabilidad-de-los-activos-roa.htmlWestreicher, G. , S. (2020). Capital de trabajo. https://economipedia.com/definiciones/capital-de-trabajo.htmlWilson, J. H. (1975). The student expenditure impact of a university on the local economy. The Annals Of Regional Science, 9(1):122–126.Withers, S. D. (2002). Quantitative methods: Bayesian inference, bayesian thinking. Progress in Human Geography, 26(4):553–566.Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data. MIT Press, London, second edition.Zellner, A. (1986). On assessing prior distributions and Bayesian regression analysis with g-prior distributions. Elsevier Science.Zellner, A. (1999). Bayesian and non-bayesian approaches to scientific modeling and inference in economics and econometrics. Technical report.Zhang, X. and Yu, J. (2018). Spatial weights matrix selection and model averaging for spatial autoregressive models. Journal of Econometrics, 203(1):1–18.Zou, H. (2006). The adaptive lasso and its oracle properties. Journal of the American statistical association, 101(476):1418–1429.EspecializadaLICENSElicense.txtlicense.txttext/plain; charset=utf-83964https://repositorio.unal.edu.co/bitstream/unal/79934/1/license.txtcccfe52f796b7c63423298c2d3365fc6MD51ORIGINAL43164806.2020.pdf43164806.2020.pdfTesis Doctora en Ciencias-Estadísticaapplication/pdf3975595https://repositorio.unal.edu.co/bitstream/unal/79934/3/43164806.2020.pdf9be36951faece8c917f94ac397af1331MD53THUMBNAIL43164806.2020.pdf.jpg43164806.2020.pdf.jpgGenerated Thumbnailimage/jpeg4021https://repositorio.unal.edu.co/bitstream/unal/79934/4/43164806.2020.pdf.jpg9812569a9e825bc63df8cabaf0893e11MD54unal/79934oai:repositorio.unal.edu.co:unal/799342023-07-25 23:04:33.921Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.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 |