Estrategia para la selección de modelos gráficos en tablas de contingencia no estructuradas

• González Debén, Adalberto ^[1] ; Alfonso Sagué, Karen ^[2]
  1. [1] Instituto de Cibernética Matemática y Física

     Instituto de Cibernética Matemática y Física

     Cuba

     
  2. [2] Instituto de Higiene, Epidemiología y Microbiología, MINSAP, Departamento de Bioestadística
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 10, Nº. 1-2, 2003, págs. 37-56
• Idioma: español
• DOI: 10.15517/rmta.v10i1-2.223
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    Los modelos loglineales se utilizan con frecuencia con el objetivo de analizar lospatrones de asociaci´on entre las variables que conforman una tabla de contingenciamultidimensional. Recientemente se ha popularizado la utilizaci´on de los modelosgr´aficos discretos, que son un subconjunto de los modelos loglineales jer´arquicos cuyaestructura de independencia condicional se representa de manera ´unica por un grafo, loque facilita la interpretaci´on de los mismos. En este trabajo se describen y comparancuatro m´etodos de selecci´on de modelos gr´aficos discretos: hacia atr´as, hacia delante,paso a paso y autom´atico EH. Asimismo, se propone una estrategia general de selecci´onde modelos.Palabras clave: modelos gr´aficos, tablas de contingencia, m´etodos de selecci´on de modelos.

  • English

    Loglinear models are frequently utilized in the analysis of association patterns betweenvariables in a multidimensional contingency table. Discrete graphical modelsare fashionable. They are a subset of the hierarchical loglinear models and its conditionalindependence structures are represented by a graph. Because of that they canbe more easily interpreted. In this work four models selection methods are describedand compared: stepwise selection (backward, forward and in two steps) and the EHprocedure.A strategy for model selection is proposed.Keywords: graphical models, contingency tables, model selection methods

• Referencias bibliográficas
  • Alfonso, K. (1999) Análisis de Tablas de Contingencia Vía Modelos Gráficos. Tesis de Licenciatura en Matemática, Universidad de La Habana.
  • Acid, S.; Campos, L.M. (1999) “Fast algorithms for learning simplified graphical models”, in: Proceedings of the Second Symposium on Artificial...
  • Agresti, A. (1990) Categorical Data Analysis. Wiley, New York.
  • Asmussen, S.; Edwards, D. (1983) “Collapsability and response variables in contingency tables”, Biometrika 70(3): 566–578.
  • Darroch, J. N.; Lauritzen, S. L.; Speed, T. P. (1980) “Markov fields and log-linear models for contingency tables”, Annals of Statistics 8:...
  • Edwards, D. (1990) “Hierarchical interaction models (with discussion)”, J.Royal Stat. Soc. B 52: 3–20, 51-72.
  • Edwards, D. (1995a) Introduction to Graphical Modelling. Springer Texts in Statistics, New York.
  • Edwards, D. (1995b) “Graphical Modelling”, in: J. Krazanowski (Ed.) Recent Advances in Descriptive Multivariate Analysis. Clarendon Press,...
  • Edwards, D.; Kreiner, S. (1983) “The analysis of contingency tables by graphical models”, Biometrika 70: 553–565.
  • Larrañaga, P.; Etxeberŕıa, R.; Lozano, J.A.; Sierra, B.; Inza, I.; Peña, J. (1999) “A review of the cooperation between evolutionary computation...
  • Lauritzen, S.L. (1989) “Lectures on contingency tables”, (3rd edn). Technical Report R-89-29, Institute for Electronic Systems, Aalborg University.
  • Lauritzen, S.L.; Spiegelhalter, D.J. (1988) “Local computations with probabilities on graphical structures and their application to expert...
  • Lauritzen, S. L.; Wermuth, N. (1989) “Graphical model for associations between variables, some of which are qualitative and some quantitative”,...
  • Lauritzen, S.L. (1996) Graphical Models. Oxford Science Publications, New York.
  • Mühlenbein, H.; Mahning, T. (1999) “The Factorized distribution algorithm for additively decomposed functions”, in: Proceedings of the Second...
  • Mühlenbein, H.; Mahning, T.; Ochoa, A. (1999) “Schemata, distribution and graphical models in evolutionary optimization”, Journal of Heuristics...
  • Wermuth, N.; Lauritzen, S.L. (1983) “Graphical and recursive models for contingency tables”, Biometrika 70: 537–552.
  • Wermuth, N.; Lauritzen, S.L. (1990) “On substantive research hypotheses, conditional independence graphs and chains models (with discussion)”,...
  • Wickens, T.D. (1989) Multiway Contingency Tables Analysis for the Social Sciences. LEA, New Jersey.
  • Whittaker, J. (1990) Graphical Models in Applied Multivariate Statistics. Wiley, New York.