Zero Frequencies

The CATMOD Procedure

Zero Frequencies

There are two types of zero cells in a contingency table: structural and sampling. A structural zero cell has an expected value of zero, while a sampling zero cell may have nonzero expected value.

For any log-linear model analysis, PROC CATMOD creates response profiles only for the observed profiles. Thus, for an analysis with one population (the usual case), the resulting contingency table does not contain zero or missing cells, which means that these cells are treated as structural zeros. However, for a WLS or ML=NR analysis on more than one population, a zero or missing cell in the body of the contingency table is treated as a sampling zero (as long as some population has a nonzero count for that profile).

If you want to treat zero frequencies as sampling zeros, you can specify the ZERO=SAMPLING and MISSING=SAMPLING options in the MODEL statement. Alternatively, you can include a statement in the DATA step creating your SAS data set that changes each zero to a very small number (such as 1E-20).

Refer to Bishop, Fienberg, and Holland (1975) and Christensen (1997) for a discussion of the issues. See Example 1.1 for an illustration of a log-linear model analysis of data that contain both structural and sampling zeros.

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