## Independence in Contingency Tables Using Simplicial Geometry

Egozcue, Juan José
Templ, Matthias
Hron, Karel
##### Text Complet​
Independence-in-Contingency.pdf
##### Sol·licita còpia a l'autor de l'article
En omplir aquest formulari esteu demanant una còpia de l'article dipositat al repositori institucional (DUGiDocs) al seu autor o a l'autor principal de l'article. Serà el mateix autor qui decideixi lliurar una còpia del document a qui ho sol•liciti si ho creu convenient. En tot cas, la Biblioteca de la UdG no intervé en aquest procés ja que no està autoritzada a facilitar articles quan aquests són d'accés restringit.
##### Compartir​
Frequently, contingency tables are generated in a multinomial sampling. Multinomial probabilities are then organized in a table assigning probabilities to each cell. A probability table can be viewed as an element in the simplex. The Aitchison geometry of the simplex identifies independent probability tables as a linear subspace. An important consequence is that, given a probability table, the nearest independent table is obtained by orthogonal projection onto the independent subspace. The nearest independent table is identified as that obtained by the product of geometric marginals, which do not coincide with the standard marginals, except in the independent case. The original probability table is decomposed into orthogonal tables, the independent and the interaction tables. The underlying model is log-linear, and a procedure to test independence of a contingency table, based on a multinomial simulation, is developed. Its performance is studied on an illustrative example ​
​Tots els drets reservats