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Elementary Analysis of Multidimensional Contingency Tables. Application to a Medical Example 1/2
Author(s) -
Enke H.
Publication year - 1986
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710280309
Subject(s) - contingency table , pairwise comparison , independence (probability theory) , simple (philosophy) , conditional independence , notation , table (database) , hierarchical database model , mathematics , computer science , contingency , algorithm , data mining , statistics , arithmetic , philosophy , epistemology , linguistics
By the aid of analysing a medical example a three—step procedure for analysing multi—dimensional contingency tables is introduced. This procedure has some good properties. Step one is due to catch the relationship structure between the variables connected by the contingency table. Hereby only so—called graphical models, a subclass of hierarchical models in regard of the parameters of the log—linear model, are admitted. The models can be generated by combination of hypotheses of pairwise conditional independence. Hereby a so‐called Extended Combination Procedure is proposed using the position of the Chain of (hierarchical) Hypotheses. A useful symbolic notation for ‘Dependence Models’ in addition to that in form of ‘Independence Models’ and ‘Minimal Sets’ is proposed. Step two analyses the significant conditional pairs in regard to the question for what attribute level combinations of the condition complexes the relations remain significant. Step three investigates those tables recognised as significant in step two more closely to get ideas about the ‘sources’ of dependencies and possibilities of collapsing parts of the table. The procedure is mostly used in explorative data analysis although the simple steps can be used to test hypotheses, too.