Title: Exact tests to compare contingency tables under quasi-independence and quasi-symmetry
Authors: Fabio Rapallo - Universita del Piemonte Orientale (Italy) [presenting]
Cristiano Bocci - University of Siena (Italy)
Abstract: In the framework of contingency tables analysis, several square tables are considered under the quasi-independence (qi) or the quasi-symmetry (qs) model. Working within the class of log-linear models, a suitable model is defined and a goodness-of-fit test is introduced in order to verify if two or more tables fit a common qi (or qs) model against the alternative that each table follows a different qi (or qs) model. Such an exact test is based on classical tools of algebraic statistics, i.e., the computation of a Markov basis and a MCMC algorithm. When the comparison is limited to two tables, the Markov bases are characterized theoretically, while for larger comparisons the computations are performed through symbolic software. Applications to social mobility tables and rater agreement problems are discussed.