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The conditions are defined under which collapsing multidimensional contingency tables, by adding over variables, will affect the apparent interaction between the remaining variables. This leads to a simple method of distinguishing those log-linear models for which the cell estimates may be obtained by direct multiplication, from those requiring iterative fitting. The implications of fitting over-parametrized models are discussed with particular reference to the 'partial association' model used implicitly (a) when information from separate two-dimensional tables is combined to test the association between the two variables, and (b) when rates are adjusted by indirect standardization.
Yvonne Bishop (Wed,) studied this question.