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In model search procedures for multidimensional contingency tables many different measures are used for decision for the goodness of model search, for instance , AIC or . 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...