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The RELIABILITY Procedure |

**MODEL***variable*<*censor-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.*variable*- is the dependent, or response, variable. The
*variable*must be a numeric variable in the input data set. *censor-variable(values)*- 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**nonmissing nonmissing uncensored if *variable1*=*variable2*nonmissing nonmissing interval censored if *variable1*<*variable2*nonmissing missing right censored at *variable1*missing nonmissing left censored at *variable2*

For example, if T1 and T2 represent time in hours in the input data setOBS T1 T2 1 . 6 2 6 12 3 12 24 4 24 . 5 24 24

then the statementmodel (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.

*effect-list*- 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. *options*- 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.

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. |

CONVH=number | specifies the convergence criterion for the relative Hessian convergence criterion |

CORRB | requests parameter correlation matrix |

COVB | requests parameter covariance matrix |

INITIAL=number list | specifies initial values for regression parameters other than the location, or intercept term |

ITPRINT | requests iteration history for maximum likelihood fit |

LRCL | requests likelihood ratio confidence intervals for distribution parameters |

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

MAXIT=number | specifies maximum number of iterations allowed for maximum likelihood fit |

OBSTATS | requests 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 | INTERNAL | specifies sort order for values
of the classification variables
in the effect-list |

PSTABLE=number | specifies stable parameterization.
The number must be between zero and one.
See "Stable Parameters"
for further information. |

READOUT | analyzes 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=number | specifies singularity criterion for matrix inversion |

THRESHOLD=number | specifies a fixed threshold parameter. See Table 30.37 for the distributions with a threshold parameter. |

Option |
Option Description |

CENSOR | is an indicator variable equal to 1 if an observation is censored, and 0 otherwise |

QUANTILES | QUANTILE |
Q=number list | specifies 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. |

XBETA | is the linear predictor |

SURVIVAL | SURV | is the fitted survival function, evaluated at the value of the dependent variable |

RESID | is the raw residual |

SRESID | is the standardized residual |

GRESID | is the modified Cox-Snell residual |

DRESID | is the deviance residual |

ADJRESID | is 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=number | specifies adjustment to be added to Cox-Snell residual for right-censored data values. The default is log(2) = 0.693. |

RESIDALPHA | RALPHA=number | specifies 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=variable | specifies 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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