The SEVERITY Procedure
- Overview
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Getting Started
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Syntax
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Details
Predefined Distributions Censoring and Truncation Parameter Estimation Method Parameter Initialization Estimating Regression Effects Empirical Distribution Function Estimation Methods Statistics of Fit Defining a Distribution Model with the FCMP Procedure Predefined Utility Functions Custom Objective Functions Input Data Sets Output Data Sets Displayed Output ODS Graphics
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Examples
Defining a Model for Gaussian Distribution Defining a Model for Gaussian Distribution with a Scale Parameter Defining a Model for Mixed-Tail Distributions Estimating Parameters Using Cramér-von Mises Estimator Fitting a Scaled Tweedie Model with Regressors Fitting Distributions to Interval-Censored Data
- References
| LOSS Statement |
The LOSS statement specifies the name of the response or loss variable whose distribution needs to be modeled. You can also specify additional options to indicate any truncation or censoring of the response. The specification of response variable is optional if at least one type of censoring is specified. You must specify a response variable if no censoring is specified. If you specify more than one LOSS statement, then the first statement is used.
All the analysis variables specified in this statement must be present in the input data set that is specified by using the DATA= option in the PROC SEVERITY statement. The response variable is expected to have nonmissing values. If the variable has a missing value in an observation, then a warning is written to the SAS log and that observation is ignored.
The following censoring-truncation-options can be used in the LOSS statement:
- LEFTCENSORED | LC=variable-name
- LEFTCENSORED | LC=number
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specifies the left-censoring variable or a global left-censoring limit.
You can use the variable-name argument to specify a data set variable that contains the left-censoring limit. If the value of this variable is missing, then PROC SEVERITY assumes that such observations are not left-censored.
Alternatively, you can use the number argument to specify a left-censoring limit value that applies to all the observations in the data set. This limit must be a nonzero positive number.
By definition of left-censoring, an exact value of the response is not known when it is less than or equal to the left-censoring limit. If the response variable is specified and the value of that variable is less than or equal to the value of the left-censoring limit for some observations, then PROC SEVERITY treats such observations as left-censored and the value of the response variable is ignored. If the response variable is specified and the value of that variable is greater than the value of the left-censoring limit for some observations, then PROC SEVERITY assumes that such observations are not left-censored and the value of the left-censoring limit is ignored.
If both right-censoring and left-censoring limits are specified, then the left-censoring limit must be greater than or equal to the right-censoring limit. If both limits are identical, then the observation is assumed to be uncensored.
More details about left-censoring are provided in the section Censoring and Truncation.
- LEFTTRUNCATED | LT=variable-name <(left-truncation-option)>
- LEFTTRUNCATED | LT=number <(left-truncation-option)>
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specifies the left-truncation variable or a global left-truncation threshold.
You can use the variable-name argument to specify a data set variable that contains the left-truncation threshold. If the value of this variable is missing or 0 for some observations, then PROC SEVERITY assumes that such observations are not left-truncated.
Alternatively, you can use the number argument to specify a left-truncation threshold that applies to all the observations in the data set. This threshold must be a nonzero positive number.
It is assumed that the response variable contains the observed values. By definition of left-truncation, you can observe only a value that is greater than the left-truncation threshold. If a response variable value is less than or equal to the left-truncation threshold, a warning is printed to the SAS log, and the observation is ignored. More details about left-truncation are provided in the section Censoring and Truncation.
The following left-truncation option can be specified for an alternative interpretation of the left-truncation threshold:
- PROBOBSERVED | POBS=number
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specifies the probability of observability, which is defined as the probability that the underlying severity event is observed (and recorded) for the specified left-threshold value.
The specified number must lie in the (0.0, 1.0] interval. A value of 1.0 is equivalent to specifying that there is no left-truncation, because it means that no severity events can occur with a value less than or equal to the threshold. If you specify value of 1.0, PROC SEVERITY prints a warning to the SAS log and proceeds by assuming that LEFTTRUNCATED= option is not specified.
More details are provided in the section Probability of Observability.
- RIGHTCENSORED | RC=variable-name
- RIGHTCENSORED | RC=number
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specifies the right-censoring variable or a global right-censoring limit.
You can use the variable-name argument to specify a data set variable that contains the right-censoring limit. If the value of this variable is missing, then PROC SEVERITY assumes that such observations are not right-censored.
Alternatively, you can use the number argument to specify a right-censoring limit value that applies to all the observations in the data set. This limit must be a nonzero positive number.
By definition of right-censoring, an exact value of the response is not known when it is greater than or equal to the right-censoring limit. If the response variable is specified and the value of that variable is greater than or equal to the value of the right-censoring limit for some observations, then PROC SEVERITY treats such observations as right-censored and the value of the response variable is ignored. If the response variable is specified and the value of that variable is less than the value of the right-censoring limit for some observations, then PROC SEVERITY assumes that such observations are not right-censored and the value of the right-censoring limit is ignored.
If both right-censoring and left-censoring limits are specified, then the left-censoring limit must be greater than or equal to the right-censoring limit. If both limits are identical, then the observation is assumed to be uncensored.
More details about right-censoring are provided in the section Censoring and Truncation.
- RIGHTTRUNCATED | RT=variable-name
- RIGHTTRUNCATED | RT=number
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specifies the right-truncation variable or a global right-truncation threshold.
You can use the variable-name argument to specify a data set variable that contains the right-truncation threshold. If the value of this variable is missing for some observations, then PROC SEVERITY assumes that such observations are not right-truncated.
Alternatively, you can use the number argument to specify a right-truncation threshold that applies to all the observations in the data set. This threshold must be a nonzero positive number.
It is assumed that the response variable contains the observed values. By definition of right-truncation, you can observe only a value that is less than or equal to the right-truncation threshold. If a response variable value is greater than the right-truncation threshold, a warning is printed to the SAS log, and the observation is ignored. More details about right-truncation are provided in the section Censoring and Truncation.