## 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 *s*_{j},
the estimated standard deviation of the parameter estimate
*b*_{j}.
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 *s*_{j} is the estimated standard
deviation of the parameter estimate *b*_{j}.
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,
is

where is the maximized log likelihood
under *H*_{0} 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
of freedom.
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.