Topics in log-linear models



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In this thesis we give a short introduction to log-linear models, which can be used to model higher dimensional contingency tables. Using this methodology, the logarithm of the expected frequency of each cell in a contingency table can be written in an ANOVA-type equation. Using ideas from the Ph.D. thesis of F. Rapallo (2003), if q is the number of cells in the contingency table, we consider any linear subspace of the q-dimensional Euclidean space as a possible model for the vector of logarithms of expected frequencies of the contingency table. We consider all possible models for 2X2 tables for two binary variables, and all possible hierarchical models for 2X2X2 tables for three binary variables. Using the statistical package SAS, we estimate all possible hierarchichal log-linear models for a dataset with three categorical variables that was collected by Hoblyn and Palmer (1934) and was used by Bartlett in his classic 1935 statistical paper, where he discusses the testing of no second order interaction. The experimental data we used were based on an investigation for the propagation of plum root-stocks from root cuttings.