For a given set of covariates, x (including the
intercept term), the pth
quantile of the log response, yp, is given by
where wp is the pth quantile of the baseline distribution.
The estimated quantile is computed by replacing the unknown
parameters with their estimates, including any shape
parameters on which the baseline distribution might depend.
The estimated quantile of the original response is obtained by
taking the exponential of the estimated log quantile unless the
NOLOG option is specified in the preceding MODEL statement.
The standard errors of the quantile estimates are computed
using the estimated covariance matrix of the parameter estimates
and a Taylor series expansion of the quantile estimate.
The standard error is computed as
where V is the estimated covariance matrix of the
parameter vector ,
and z is the vector
where is the vector of the shape parameters.
Unless the NOLOG option is specified, this standard
error estimate is converted into a standard error
estimate for exp(yp) as STD.
It may be more desirable to compute confidence limits for the log
response and convert them back to the original response variable
than to use the standard error estimates for exp(yp) directly.
See Example 36.1 for a 90% confidence interval
of the response constructed by exponentiating
a confidence interval for the log response.
The variable, CDF, is computed as
where the residual
CDFi = F(wi)
and F is the baseline cumulative distribution function.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.