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The LOGISTIC Procedure |
There are two methods of computing confidence intervals for the regression parameters. One is based on the profile likelihood function, and the other is based on the asymptotic normality of the parameter estimators. The latter is not as time-consuming as the former, since it does not involve an iterative scheme; however, it is not thought to be as accurate as the former, especially with small sample size. You use the CLPARMS= option to request confidence intervals for the parameters.
where is the set of all
with the jth
element fixed at
,and
is the log likelihood function for
.If
is the log likelihood evaluated at
the maximum likelihood estimate
, then
has a limiting chi-square
distribution with one degree of freedom
if
is the true parameter value.
Let
,where
is the
percentile
of the chi-square distribution with one degree of freedom.
A
% confidence interval for
is
Convergence is controlled by value specified with the PLCONV=
option in the MODEL statement (the default value
of
is 1E-4).
Convergence is declared on the current iteration if the following
two conditions are satisfied:
where zp is the 100pth percentile of the standard normal
distribution, is the maximum likelihood
estimate of
, and
is the standard error estimate of
.
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