Incomplete Tables, Separability and Collapsibility

An observed contingency table is incomplete if it contains zeros in certain cells. Such zeros are of two types, random zeros and structural zeros. A cell has a random zero, if the observed value in the cell is zero, but the expected value is positive. A cell has a structural zero if the expected number is zero, i.e. if it is known a priori that the cell will contain a zero. Random or structural zeros does not impaire the log-linear structure of a given model. It means, however, that certain log-linear parameters can not be estimated.