Markov Basis For Quasi-independence Model For Two-way Incomplete Contingency Tables

Structural zero is regarded as a feature of data or a result of the structure of the data,which causes incomplete contingency table to appear repeatedly in many practical prob-lems,when using contingency tables to describe the relationships between classification variables.Monte Carlo method as an effective method to estimate the p-value,it is par-ticularly important to calculate the Markov basis for the exact test in quasi-independence model for incomplete contingency table.In this paper,we discuss the method of solving Markov basis from two aspects which are algebra and structure of Markov basis,and use the structure of Markov basis to reduce the redundant moves in Markov basis.In partic-ular,when min(I,J)? 3,max(I,J)? 4 is applied,we prove that a Markov base under the quasi-independent model of contingency table with structural zeros on diagonal cells can be composed of fundamental moves.