On the Backward Selection Procedure for Graphical Log-linear Models - Monte Carlo Results

Abstract

The analysis of categorical data by means of log-linear models is one of the most useful statistical tools available, particularly in the social and medical sciences, thus in all the sciences where we deal with collection of large amounts of qualitative data. They are also widely applied in expert systems (see Lauritzen and Spiegelhalter (1988), Matzkevich andAbramson (1995)). Qualitative data are often analysed by cross-classifying two variables at a time only, i.e. examining all the two way marginal tables of the underlying multidimensional table. It is well known that this approach may often produce misleading results. The analysis of multidimensional contingency tables by means of log-linear models allows to avoid most of such problems. However, the number of possible log-linear model for multidimensional tables is so large that one must use some form of stepwise selection strategy to chose a model, which fits to the data and satisfies some additional conditions. In the paper some statistical properties of the backward selection procedure by means of Monte Carlo methods are studied.

W pracy przedstawione są wyniki analizy Monte Carlo przeprowadzonej na podstawie 5-wymiarowych tablic kontyngencyjnych. Celem analizy jest oszacowanie frakcji graficznych modeli logarytmo-liniowych poprawnie wybranych przez tzw. procedurę selekcji wstecz.