PROC SEVERITY enables you to initialize parameters of a model in different ways. There can be two kinds of parameters in a model: distribution parameters and regression parameters.

The distribution parameters can be initialized by using one of the following three methods:

PARMINIT subroutine

You can define a PARMINIT subroutine in the distribution model.

INEST= data set

You can use the INEST= data set.

INIT= option

You can use the INIT= option in the DIST statement.

Note that only one of the initialization methods is used. You cannot combine them. They are used in the following order:

• The method of using the INIT= option takes the highest precedence. If you use the INIT= option to provide an initial value for at least one parameter, then other initialization methods (INEST= and PARMINIT) are not used. If you specify initial values for some but not all the parameters by using the INIT= option, then the uninitialized parameters are initialized to the default value of 0.001.

  If this option is used when regression effects are specified, then the value of the first distribution parameter must be related to the initial value for the base value of the scale or log-transformed scale parameter. See the section Estimating Regression Effects for details.

• The method of using the INEST= data set takes the second precedence. If there is a nonmissing value specified for even one distribution parameter, then the PARMINIT method is not used and any uninitialized parameters are initialized to the default value of 0.001.

• If none of the distribution parameters are initialized by using the INIT= option or the INEST= data set, but the distribution model defines a PARMINIT subroutine, then PROC SEVERITY invokes that subroutine with appropriate inputs to initialize the parameters. If the PARMINIT subroutine returns missing values for some parameters, then those parameters are initialized to the default value of 0.001.

• If none of the initialization methods are used, each distribution parameter is initialized to the default value of 0.001.

The regression parameters can be initialized by using the INEST= data set or the default method. If you use the INEST= data set, then you must specify nonmissing initial values for all the regressors. The only missing value allowed is the special missing value .R, which indicates that the regressor is linearly dependent on other regressors. If you specify .R for a regressor for one distribution in a BY group, you must specify it so for all the distributions in that BY group.

If you do not provide initial values for regressors by using the INEST= data set, then PROC SEVERITY computes them by fitting a linear regression model for on all the regressors with an intercept in the model, where denotes the response variable. If it finds any linearly dependent regressors, warnings are printed to the SAS log and those regressors are dropped from the model. Details about estimating regression effects are provided in the section Estimating Regression Effects.