Parameterization Used in PROC GENMOD

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The GENMOD Procedure

Parameterization Used in PROC GENMOD

Design Matrix

The linear predictor part of a generalized linear model is

${\eta}= X {\beta}$

where ${\beta}$ is an unknown parameter vector and X is a known design matrix. By default, all models automatically contain an intercept term; that is, the first column of X contains all 1s. Additional columns of X are generated for classification variables, regression variables, and any interaction terms included in the model. PROC GENMOD parameterizes main effects and interaction terms using the same ordering rules that PROC GLM uses. This is important to understand when you want to construct likelihood ratios for custom contrasts using the CONTRAST statement. See Chapter 30, "The GLM Procedure," for more details on model parameterization.

Some columns of X can be linearly dependent on other columns due to specifying an overparameterized model. For example, when you specify a model consisting of an intercept term and a class variable, the column corresponding to any one of the levels of the class variable is linearly dependent on the other columns of X. PROC GENMOD handles this in the same manner as PROC GLM. The columns of X'X are checked in the order in which the model is specified for dependence on preceding columns. If a dependency is found, the parameter corresponding to the dependent column is set to 0 along with its standard error to indicate that it is not estimated. The order in which the levels of a class variable are checked for dependencies can be set by the ORDER= option in the PROC GENMOD statement.

You can exclude the intercept term from the model by specifying the NOINT option in the MODEL statement.

Missing Level Combinations

All levels of interaction terms involving classification variables may not be represented in the data. In that case, PROC GENMOD does not include parameters in the model for the missing levels.

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