Simulation studies on model search in $3$-dimensional contingency tables. Preliminary results

Abstract

In model search procedures for multidimensional contingency tables many different measures are used for decision for the goodness of model search, for instance $\alpha$, AIC or $R^2$. Simulation studies should give us an insight into the behaviour of the measures with respect to the data, the sample size, the number of degrees of freedom and the probability given distribution. To this end different log-linear models for 3-dimensional contingency tables were given and then 1,000 contingency tables were simulated for each model and for several sample sizes and the various decision measures were computed. Summarizing the results we count empirical frequencies of the choice of the true model under various circumstances. This leads to our concluding discussion of properties of the model acceptance criteria under consideration.