The SEVERITY Procedure

Output Data Sets

PROC SEVERITY writes OUTCDF=, OUTEST=, OUTMODELINFO=, and OUTSTAT= data sets when requested with respective options. The data sets and their contents are described in the following sections.

OUTCDF= Data Set

The OUTCDF= data set records the estimates of the cumulative distribution function (CDF) of each of the specified model distributions and an estimate of the empirical distribution function (EDF).

If BY variables are specified, then the data are organized in BY groups and the data set contains variables specified in the BY statement. In addition, it contains the following variables:

<response variable>

value of the response variable. The values are sorted. If there are multiple BY groups, the values are sorted within each BY group.

_OBSNUM_

observation number in the DATA= data set.

_EDF_

estimate of the empirical distribution function (EDF). This estimate is computed by using the EMPIRICALCDF= option specified in the PROC SEVERITY statement.

<distribution1>_CDF ... <distribution $\text{[math]}$ >_CDF

estimate of the cumulative distribution function (CDF) for each of the $\text{[math]}$ candidate distributions, computed by using the final parameter estimates for that distribution. This value is missing if parameter estimation process does not converge for the given distribution.

If regressor variables are specified, then the reported estimates are from a mixture distribution. See the section CDF and PDF Estimates with Regression Effects for details.

If truncation is specified, then the data set contains the following additional variables:

<distribution1>_COND_CDF ... <distribution $\text{[math]}$ >_COND_CDF: estimate of the conditional CDF for each of the $\text{[math]}$ candidate distributions, computed by using the final parameter estimates for that distribution. This value is missing if parameter estimation process does not converge for the distribution. The conditional estimates are computed using the method described in the section Truncation and Conditional CDF Estimates.

OUTEST= Data Set

The OUTEST= data set records the estimates of the model parameters. It also contains estimates of their standard errors and optionally, their covariance structure. If BY variables are specified, then the data are organized in BY groups and the data set contains variables specified in the BY statement.

If the COVOUT option is not specified, then the data set contains the following variables:

_MODEL_

identifying name of the distribution model. The observation contains information about this distribution.

_TYPE_

type of the estimates reported in this observation. It can take one of the following two values:

EST: point estimates of model parameters
STDERR: standard error estimates of model parameters

_STATUS_

status of the reported estimates. The possible values are listed in the section _STATUS_ Variable Values.

<Parameter 1> ...<Parameter M>

$\text{[math]}$ variables, named after the parameters of all candidate distributions, containing estimates of the respective parameters. $\text{[math]}$ is the cardinality of the union of parameter name sets from all candidate distributions. In an observation, estimates are populated only for parameters that correspond to the distribution specified by the _MODEL_ variable. If _TYPE_ is EST, then the estimates are missing if the model does not converge. If _TYPE_ is STDERR, then the estimates are missing if covariance estimates cannot be obtained.

If regressors are specified, then the estimate reported for the first parameter of each distribution is the estimate of the base value of the scale or log-transformed scale parameter. See the section Estimating Regression Effects for details.

<Regressor 1> ...<Regressor K>

If $\text{[math]}$ regressors are specified in the SCALEMODEL statement, then the OUTEST= data set contains $\text{[math]}$ variables that are named for each regressor. The variables contain estimates for their respective regression coefficients. If a regressor is deemed to be linearly dependent on other regressors for a given BY group, then a warning message is printed to the SAS log and a special missing value of .R is written in the respective variable. If _TYPE_ is EST, then the estimates are missing if the model does not converge. If _TYPE_ is STDERR, then the estimates are missing if covariance estimates cannot be obtained.

If the COVOUT option is specified, then the OUTEST= data set contains additional observations that contain the estimates of the covariance structure. Given the symmetric nature of the covariance structure, only the lower triangular portion is reported. In addition to the variables listed and described previously, the data set contains the following variables that are either new or have a modified description:

_TYPE_: type of the estimates reported in this observation. For observations that contain rows of the covariance structure, the value is COV.
_STATUS_: status of the reported estimates. For observations that contain rows of the covariance structure, the status is 0 if covariance estimation was successful. If estimation fails, the status is 1 and a single observation is reported with _TYPE_=COV and missing values for all the parameter variables.
_NAME_: Name of the parameter for the row of covariance matrix reported in the current observation.

OUTMODELINFO= Data Set

The OUTMODELINFO= data set records the information about each specified distribution. If BY variables are specified, then the data are organized in BY groups and the data set contains variables specified in the BY statement. In addition, it contains the following variables:

_MODEL_: identifying name of the distribution model. The observation contains information about this distribution.
_DESCRIPTION_: descriptive name of the model. This has a nonmissing value only if the DESCRIPTION function has been defined for this model.
_PARMNAME $\text{[math]}$ ... _PARMNAME $\text{[math]}$: $\text{[math]}$ variables that contain names of parameters of the distribution model, where $\text{[math]}$ is the maximum number of parameters across all the specified distribution models. For a given distribution with $\text{[math]}$ parameters, values of variables _PARMNAME $\text{[math]}$ ( $\text{[math]}$ ) are missing.

OUTSTAT= Data Set

The OUTSTAT= data set records statistics of fit and model selection information. If BY variables are specified, then the data are organized in BY groups and the data set contains variables specified in the BY statement. The data set contains the following variables:

_MODEL_: identifying name of the distribution model. The observation contains information about this distribution.
_NMODELPARM_: number of parameters in the distribution.
_NESTPARM_: number of estimated parameters. This includes the regression parameters, if any regressors are specified.
_NOBS_: number of nonmissing observations used for parameter estimation.
_STATUS_: status of the parameter estimation process for this model. The possible values are listed in the section _STATUS_ Variable Values.
_SELECTED_: indicator of the best distribution model. If the value is 1, then this model is the best model for the current BY group according to the specified model selection criterion. This value is missing if parameter estimation process does not converge for this model.
Neg2LogLike: value of the log likelihood, multiplied by –2, that is attained at the end of the parameter estimation process. This value is missing if parameter estimation process does not converge for this model.
AIC: value of the Akaike’s information criterion (AIC) that is attained at the end of the parameter estimation process. This value is missing if parameter estimation process does not converge for this model.
AICC: value of the corrected Akaike’s information criterion (AICC) that is attained at the end of the parameter estimation process. This value is missing if parameter estimation process does not converge for this model.
BIC: value of the Schwarz Bayesian information criterion (BIC) that is attained at the end of the parameter estimation process. This value is missing if parameter estimation process does not converge for this model.
KS: value of the Kolmogorov-Smirnov (KS) statistic that is attained at the end of the parameter estimation process. This value is missing if parameter estimation process does not converge for this model.
AD: value of the Anderson-Darling (AD) statistic that is attained at the end of the parameter estimation process. This value is missing if parameter estimation process does not converge for this model.
CVM: value of the Craer-von Mises (CvM) statistic that is attained at the end of the parameter estimation process. This value is missing if parameter estimation process does not converge for this model.

_STATUS_ Variable Values

The _STATUS_ variable in the OUTEST= and OUTSTAT= data sets contains a value that indicates the status of the parameter estimation process for the respective distribution model. The variable can take the following values in the OUTEST= data set for _TYPE_=EST observations and in the OUTSTAT= data set:

0: The parameter estimation process converged for this model.
301: The parameter estimation process might not have converged for this model because there is no improvement in the objective function value. This might indicate that the initial values of the parameters are optimal, or you can try different convergence criteria in the NLOPTIONS statement.
302: The parameter estimation process might not have converged for this model because the number of iterations exceeded the maximum allowed value. You can try setting a larger value for the MAXITER= options in the NLOPTIONS statement.
303: The parameter estimation process might not have converged for this model because the number of objective function evaluations exceeded the maximum allowed value. You can try setting a larger value for the MAXFUNC= options in the NLOPTIONS statement.
304: The parameter estimation process might not have converged for this model because the time taken by the process exceeded the maximum allowed value. You can try setting a larger value for the MAXTIME= option in the NLOPTIONS statement.
400: The parameter estimation process did not converge for this model.

The _STATUS_ variable can take the following values in the OUTEST= data set for _TYPE_=STDERR and _TYPE_=COV observations:

0: The covariance and standard error estimates are available and valid.
1: The covariance and standard error estimates are not available, because the process of computing covariance estimates failed.