MODEL
variable <
censorvariable(values)> <=effectlist> </ options> ;
MODEL
(variable1 variable2) <=effectlist> </ options> ;
You use the MODEL statement to fit regression models, where life is modeled as a function of explanatory variables.
You can use only one MODEL statement after a PROC RELIABILITY statement. If you specify more than one MODEL statement, only the last is used.
The MODEL statement does not produce any plots, but it enables you to analyze more complicated regression models than the ANALYZE, PROBPLOT, or RELATIONPLOT statement does. The probability distribution specified in the DISTRIBUTION statement is used in the analysis. The following are examples of MODEL statements:
model time = temp voltage; model life*censor(1) = voltage width;
See the section Analysis of Accelerated Life Test Data and the section Regression Modeling for examples that use the MODEL statement to fit regression models.
If your data are right censored lifetime data, you must specify a censorvariable and, in parentheses, the values of the censorvariable that correspond to censored data values.
If your data are recurrent events data with exact event times, you must specify a censorvariable and, in parentheses, the values of the censorvariable that correspond to the endofservice times for each unit under observation. In this case, you must also specify a UNITID statement to identify the specific unit that corresponds to each observation.
If your lifetime data contain any intervalcensored or leftcensored values, you must specify variable1 and variable2 in parentheses to provide the endpoints of the interval for each observation.
If your data are recurrent events data, and event times are not known exactly, but are known only to have occurred in intervals, you must specify variable1 and variable2 in parentheses to provide the endpoints of the interval for each observation. In this case, you must also specify a variable that determines the number of events observed in each interval with a FREQ statement, and a variable that determines the number of units under observation in each interval with a NENTER statement.
The independent variables in your regression model are specified in the effectlist. The effectlist is any combination of continuous variables, classification variables, and interaction effects.
See the section Regression Models for further information on specifying the independent variables.
The elements of the MODEL statement are described as follows.
Table 16.32: Model Statement Options
Option 
Option Description 


CONFIDENCE=number 
Specifies the confidence coefficient for all confidence intervals. Specify a number between 0 and 1. The default value is 0.95. 

CONVERGE=number 
Specifies the convergence criterion for maximum likelihood fit. See the section Maximum Likelihood Estimation for details. 

CONVH=number 
Specifies the convergence criterion for the relative Hessian convergence criterion. See the section Maximum Likelihood Estimation for details. 

CORRB 
Requests parameter correlation matrix. 

COVB 
Requests parameter covariance matrix. 

HPPTEST 
Applies only to models for recurrent events data. This option requests a likelihood ratio test for a homogeneous Poisson process. 

INEST  IN=SASdataset 
Applies only to models for recurrent events data. This option specifies a SAS data set that can contain initial values, equality constraints, upper bounds, or lower bounds for the intercept and shape parameters in a model for recurrents events data. See the section INEST Data Set for Recurrent Events Models for details. 

INITIAL=number list 
Specifies initial values for regression parameters other than the location (intercept) term. 

ITPRINT 
Requests the iteration history for maximum likelihood fit. 

LRCL 
Requests likelihood ratio confidence intervals for distribution parameters. 

LOCATION=number <LINIT> 
Specifies the fixed or initial value of the location, or intercept parameter. 

MAXIT=number 
Specifies the maximum number of iterations allowed for maximum likelihood fit. 

OBSTATS 
Requests a table that contains the XBETA, SURV, SRESID, and ADJRESID statistics in Table 16.33 or the XBETA, MCF, and INTENSITY statistics in Table 16.34. The table also contains the dependent and independent variables in the model. You can use this option to compute statistics such as survival function estimates for lifetime data or mean function estimates for recurrent events data for dependent variable values not included in the analysis. Refer to Comparison of Two Samples of Repair Data for an example of computing predicted values for recurrent events data. 

OBSTATS(statistics) 
Requests a table that contains the model variables and the statistics in the specified list of statistics. Available statistics are shown in Table 16.33. 

ORDER=DATA  FORMATTED  

FREQ  INTERNAL 
Specifies the sort order for values of the classification variables in the effectlist. 

PSTABLE=number 
Specifies stable parameterization. The number must be between zero and one. See the section Stable Parameters for further information. 

READOUT 
Analyzes data in readout structure. The FREQ statement must be used to specify the number of units that fail in each interval, and the NENTER statement must be used to specify the number of unfailed units that enter each interval. 

RELATION=transformationkeyword 

RELATION=(transformationkeyword1<,>transformationkeyword2) 
Specifies the type of relationship between independent and dependent variables. In the first form, the transformation specified is applied to the first continuous independent variable in the model. In the second form, the transformations specified within parentheses are applied to the first two continuous independent variables in the model, in the order listed. transformationkeyword, transformationkeyword1, and transformationkeyword2 can be any of the transformations listed in the following table. See Table 16.67 for definitions of the transformations. 



SCALE=number <SCINIT> 
Specifies a fixed or initial value of scale parameter. 

SHAPE=number <SHINIT> 
Specifies a fixed or initial value of shape parameter. 

SINGULAR=number 
Specifies the singularity criterion for matrix inversion. 

THRESHOLD=number 
Specifies a fixed threshold parameter. See Table 16.57 for the distributions with a threshold parameter. 

TREND=trendtest keyword  (trendtest keywords) 
Applies only to models for recurrent events data. This option requests one or more tests of trend for a Poisson process. TREND=LRHPP is equivalent to the HPPTEST option. See the section Tests of Trend for more information about the tests. The available tests are shown in the following table. 



WALDCL  NORMALCL 
Requests Wald type confidence intervals for distribution parameters. See Table 16.68 and Table 16.74 for details about the computation of Wald confidence intervals. This is the default option used if likelihood ratio confidence intervals are not requested by using the LRCL option. 
Table 16.33: Available Statistics Computed for Each Observation with the OBSTATS Option for LIfetime Data
Option 
Option Description 


CENSOR 
Is a variable that indicates the type of censoring for each opservation in the input data set. The possible values for CENSOR and their interpretations are listed in the following table. 



CONTROL=variable 
Specifies a control variable in the input data set that allows the computation of statistics for a subset of observations in the input data set. If the value of variable is 1, the statistics are computed for that observation. If the value of the control variable is not equal to 1, the statistics are not computed for that observation. 

QUANTILES  QUANTILE  

Q=numberlist 
Requests distribution quantiles for each number in numberlist for each observation. The numbers must be between 0 and 1. Estimated quantile standard errors, and upper and lower confidence limits are also tabulated. 

XBETA 
Specifies the linear predictor. 

SURVIVAL  SURV 
Specifies the fitted survival function, evaluated at the value of the dependent variable. 

RESID 
Specifies the raw residual. 

SRESID 
Specifies the standardized residual. 

GRESID 
Specifies the modified CoxSnell residual. 

DRESID 
Specifies the deviance residual. 

ADJRESID 
Specifies the adjusted standardized residuals. These are adjusted for rightcensored observations by adding the median of the lifetime greater than the rightcensored values to the residuals. 

RESIDADJ=number 
Specifies the adjustment to be added to CoxSnell residual for rightcensored data values. The default of number is 1.0, the mean of the standard exponential distribution. 

RESIDALPHA  RALPHA=number 
Specifies that the number percentile residual lifetime be used to adjust rightcensored standardized residuals. The number must be between 0 and 1. The default value is 0.5, which corresponds to the median. 
Table 16.34: Available Statistics Computed for Each Observation with the OBSTATS Option for Recurrent Events Data
Option 
Option Description 

CONTROL=variable 
Specifies a control variable in the input data set that allows the computation of statistics for a subset of observations in the input data set. If the value of variable is 1, the statistics are computed for that observation. If the value of variable is not equal to 1, the statistics are not computed for that observation. 
MCF 
Specifies the mean function, which is evaluated at the value of time for each observation. Standard errors and confidence limits are also computed. 
INTENSITY 
Specifies the intensity function, which is evaluated at the value of time for each observation. Standard errors and confidence limits are also computed. 
XBETA 
Specifies the linear predictor. 