Necessary and sufficient conditions for collapsibility of a directed acyclic graph (DAG) model for a contingency table are derived. By applying the conditions, we can easily check collapsibility over any variable in a given model either by using the joint probability distribution or by using the...

We show that, when the three-way association level among the three binary variables, X, U₁ and U₂ is fixed, D_P = pr(X = 1¦U₁ = 1) - pr(X = 1¦U₁ = 0) increases as the cross-product ratio of U₁ and U₂ increases under the assumption that X is positively associated with U₁ and U₂. We then discuss...

The Pearson's chi-squared statistic (X2) does not in general follow a chi-square distribution when it is used for goodness-of-fit testing for a multinomial distribution based on sparse contingency table data. We explore properties of [Zelterman, D., 1987. Goodness-of-fit tests for large sparse...