Key points are not available for this paper at this time.
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 (1971) studied this question.