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MODEL Statement

MODEL variable<\astcensor-variable(values)> <=effect-list> < / options >;

MODEL (variable1 variable2) <=effect-list> </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 "Analysis of Accelerated Life Test Data" and "Regression Modeling" for examples of fitting regression models using the MODEL statement.

If your data are right censored, you must specify a censor-variable and, in parentheses, the values of the censor-variable that correspond to censored data values.

If your data contain any interval-censored or left-censored values, you must specify variable1 and variable2 in parentheses to provide the endpoints of the interval for each observation.

The independent variables in your regression model are specified in the effect-list. The effect-list is any combination of continuous variables, classification variables,

See Regression Models for further information on specifying the independent variables.

The elements of the MODEL statement are described as follows.

is the dependent, or response, variable. The variable must be a numeric variable in the input data set.

indicates which observations in the input data set are right censored. You specify the values of censor-variable that represent censored observations by placing those values in parentheses after the variable name. If your data are not right censored, then you can omit the specification of a censor-variable; otherwise, censor-variable must be a numeric variable in the input data set.

(variable1 variable2)
is another method of specifying the dependent variable in the regession model. You can use this syntax in a situation where uncensored, interval-censored, left-censored and right-censored values occur in the same set of data. Table 30.20 shows how you use this syntax to specify different types of censoring by using combinations of missing and nonmissing values.

Table 30.20: Specifying Censored Values
Variable1 Variable2 Type of Censoring
nonmissingnonmissinguncensored if variable1 = variable2
nonmissingnonmissinginterval censored if variable1 < variable2
nonmissingmissingright censored at variable1
missingnonmissingleft censored at variable2

For example, if T1 and T2 represent time in hours in the input data set
   OBS    T1    T2

    1      .     6
    2      6    12
    3     12    24
    4     24     .
    5     24    24
then the statement
      model (t1 t2);

specifies a model in which observation 1 is left censored at 6 hours, observation 2 is interval censored in the interval (6, 12), observation 3 is interval censored in (12,24), observation 4 is right censored at 24 hours, and observation 5 is an uncensored lifetime of 24 hours.

is a list of variables in the input data set representing the values of the independent variables in the model for each observation, and combinations of variables representing interaction terms. If a variable in the effect-list is also listed in a CLASS statement, an indicator variable is generated for each level of the variable. An indicator variable for a particular level is equal to 1 for observations with that level, and equal to 0 for all other observations. This type of variable is called a classification variable. Classification variables can be either character or numeric. If a variable is not listed in a CLASS statement, it is assumed to be a continuous variable, and it must be numeric.

control how the model is fit and what output is produced. All options are specified after a slash (/) in the MODEL statement. The "Summary of Options" section, which follows, lists all options by function.

Summary of Options

Table 30.21: Model Statement Options
Option Option Description
CONFIDENCE=numberspecifies the confidence coefficient for all confidence intervals. Specify a number between 0 and 1. The default value is 0.95
CONVERGE=numberspecifies the convergence criterion for maximum likelihood fit.
CONVH=numberspecifies the convergence criterion for the relative Hessian convergence criterion
CORRBrequests parameter correlation matrix
COVBrequests parameter covariance matrix
INITIAL=number listspecifies initial values for regression parameters other than the location, or intercept term
ITPRINTrequests iteration history for maximum likelihood fit
LRCLrequests likelihood ratio confidence intervals for distribution parameters
LOCATION=number < LINIT >specifies fixed or initial value of the location, or intercept parameter
MAXIT=numberspecifies maximum number of iterations allowed for maximum likelihood fit
OBSTATSrequests a table containing the XBETA, SURV, SRESID, and ADJRESID statistics in Table 30.22. The table also contains the dependent and independent variables in the model.
OBSTATS(statistics)requests a table containing the model variables and the statistics in the specified list of statistics. Available statistics are shown in Table 30.22.
ORDER=DATA | FORMATTED | FREQ | INTERNALspecifies sort order for values of the classification variables in the effect-list
PSTABLE=numberspecifies stable parameterization. The number must be between zero and one. See "Stable Parameters" for further information.
READOUTanalyzes data in readout structure. The FREQ statement must be used to specify the number of units failing in each interval, and the NENTER statement must be used to specify the number of unfailed units entering each interval
RELATION=ARRHENIUS | ARRHENIUS2 | POWER RELATION=(ARRHENIUS | ARRHENIUS2 | POWER < , > ARRHENIUS | ARRHENIUS2 | POWER )specifies 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.
SCALE=number < SCINIT >specifies fixed or initial value of scale parameter
SHAPE=number < SHINIT >specifies fixed or initial value of shape parameter
SINGULAR=numberspecifies singularity criterion for matrix inversion
THRESHOLD=numberspecifies a fixed threshold parameter. See Table 30.37 for the distributions with a threshold parameter.

Table 30.22: Observation Statistics Available in the OBSTATS Option
Option Option Description
CENSORis an indicator variable equal to 1 if an observation is censored, and 0 otherwise
QUANTILES | QUANTILE | Q=number listspecifies distribution quantiles for each number in number list for each observation. The numbers must be between 0 and 1. Estimated quantile standard errors, and upper and lower confidence limits are also tabulated.
XBETAis the linear predictor
SURVIVAL | SURVis the fitted survival function, evaluated at the value of the dependent variable
RESIDis the raw residual
SRESIDis the standardized residual
GRESIDis the modified Cox-Snell residual
DRESIDis the deviance residual
ADJRESIDis the adjusted standardized residuals. These are adjusted for right-censored observations by adding the median of the lifetime above the right-censored values to the residuals.
RESIDADJ=numberspecifies adjustment to be added to Cox-Snell residual for right-censored data values. The default is log(2) = 0.693.
RESIDALPHA | RALPHA=numberspecifies number ×100% percentile residual lifetime used to adjust right-censored standardized residuals. The number must be between 0 and 1. The default value is 0.5, corresponding to the median.
CONTROL=variablespecifies a control variable in the input data set. If the value of the control variable is 1, the observation statistics are computed. If the value of the control variable is not equal to 1, the statistics are not computed for that observation.

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Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.