Inference for Ordinal Log-Linear Models Based on Algebraic Statistics

Inference for Ordinal Log-Linear Models Based on Algebraic Statistics Special Volume in honor of memory of S.E.Fienberg Pham, Thi Mui Creator Faculty kateri@isw.rwth-aachen.de Kateri, Maria Creator MATH / Applied Mathematics Illinois Institute of Technology Affiliated department Sparse contingency tables Association models Model selection Diaconis-Sturmfels algorithm Markov Chain Monte Carlo 2019 2019-04-12 Tools of algebraic statistics combined with MCMC algorithms have been used in contingency table analysis for model selection and model fit testing of log-linear models. However, this approach has not been considered so far for association models, which are special log-linear models for tables with ordinal classification variables. The simplest association model for two-way tables, the uniform (U) association model, has just one parameter more than the independence model and is applicable when both classification variables are ordinal. Less parsimonious are the row (R) and column (C) effect association models, appropriate when at least one of the classification variables is ordinal. Association models have been extended for multidimensional contingency tables as well. Here, we adjust algebraic methods for association models analysis and investigate their eligibility, focusing mainly on two-way tables. They are implemented in the statistical software R and illustrated on real data tables. Finally the algebraic model fit and selection procedure is assessed and compared to the asymptotic approach in terms of a simulation study. Article