C.I. for Parameters
The C.I. for Parameters table gives
a confidence interval for each parameter for
each confidence coefficient specified.
You choose the confidence interval for parameters
either in the fit output options dialog or from the
Tables menu, as shown in Figure 39.19.
Figure 39.19: C.I. for Parameters Menu
Selecting 95% C.I. / C.I.(Wald) for Parameters
or 95% C.I.(LR) for Parameters
in the fit output options dialog produces a table
with a 95% confidence interval for the parameters.
This is the equivalent of choosing
Tables:C.I. / C.I.(Wald) for Parameters:95%
or Tables:C.I.(LR) for Parameters:95%
from the Tables menu.
You can also choose other confidence
coefficients from the Tables menu.
Figure 39.20 illustrates a 95% confidence intervals
table for the parameters in a linear model.
Figure 39.20: C.I. for Parameters Table
For linear models, a confidence interval has upper and lower limits
where is the critical value of the Student's t statistic
with degrees of freedom n-p, used in computing sj,
the estimated standard deviation of the parameter estimate
For generalized models, you can specify the confidence interval
based on either a Wald type statistic or the likelihood function.
A Wald type
confidence interval is constructed from
where is the critical value of the
statistic with one degree of
freedom, and sj is the estimated standard
deviation of the parameter estimate bj.
Thus, upper and lower limits are
where is the critical
value of the standard normal statistic.
A table of 95% Wald type confidence intervals for the
parameters is shown in Figure 39.21.
Figure 39.21: C.I. for Parameters Tables
The likelihood ratio test statistic for the null hypothesis
where is a specified value,
where is the maximized log likelihood
under H0 and is the maximized
log likelihood over all .
In large samples, the hypothesis is rejected at level if
the test statistic is greater than the critical value of the chi-squared statistic with one degree
Thus a likelihood-based confidence interval
is constructed using restricted maximization to find
upper and lower limits satisfying
An iterative procedure is used to obtain these limits.
A 95% likelihood-based confidence interval table for
the parameters is illustrated in Figure 39.21.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.