Graphical Descriptions for Hierarchical Log Linear Models

  • Hyun Jip Choi (Department of Applied Statistics, Kyunggi Unicersity, Changan Gu, Suwon, 440-760, KOREA) ;
  • Chong Sun Hong (Department of Statistics, Sung Kyun Kwan University, Seoul, 110-745, KOREA)
  • Published : 1995.12.01

Abstract

We represent graphically the relationship of hierachical log linear models by regarding the values of the likelihood ratio statistics as the squared norm of the corresponding vectors. Right angled triangles, tetrahedrons, and modified polyhedrons are used for graphical description. We find that the angle between the two vectors depends on the coefficient of determination and the partial coefficent of determination. Thess graphical descriptions could be applied to the model selection method.

Keywords

References

  1. The American Statistician v.48 Model selection and R² Anderson-Sprecher,Richard
  2. Discrete Multivariate Analysis Bishop,Y.M.M.;Fienberg,S.E.;Holland,P.W.
  3. Log-Linear Model Chritensen,R.
  4. Annals of Statistics v.8 Markov-fields and log-linear models for contingency tables Darrich,J.N.;Lauritzen,S.L.;Speed,T.P.
  5. Biometrika v.70 The analysis of contingency tables by graphical models Edwards,D.;Kreiner,S.
  6. The Analysis of Cross-Classified Categorical Data Fienberg,S.E.
  7. Journal of American Statistical Association v.65 The geometry of a two by two contingency table Fienberg,S.E.;Gilbert,J.P.
  8. Journal of American Statistical Association v.65 Mosaic displays for multi-way contingency tables Friendly,M.
  9. Journal of American Statistical Association v.66 Partitioning of chi-square, analysis of marginal contingency tables, and estimation of expected frequencies on multidimensional contingency tables Goodman,L.A.
  10. Technometrics v.13 The analysis of multidimensional contingency tables : stepwise procedures and direct methods for buiding models for multiple classification Goodman,L.A.
  11. Journal of American Statistical Association v.86 Measures, model, and graphical displays in the analysis of cross-classified data Goodman,L.A.
  12. Chemical Engineering Progress v.59 The use of chi-square for preference testing in multidimensional problems Ries,P.N.;Smith,H.
  13. Ecology v.49 The anolis Lizard of Bimini : resiurce parttioning in a complex fauna Schoner,T.W.