SAS/STAT 9.2 User's Guide: The MIXED Procedure (Book Excerpt)

3900 ✦ Chapter 56: The MIXED Procedure
CL< =WALD >
requests confidence limits for the covariance parameter estimates. A Satterthwaite approximation
is used to construct limits for all parameters that have a lower boundary constraint of
zero. These limits take the form
b2 2
;1 ˛=2
2
b 2
2
;˛=2
where D 2Z 2 , Z is the Wald statistic b 2 =se.b 2 /, and the denominators are quantiles of
the 2 -distribution with degrees of freedom. See Milliken and Johnson (1992) and Burdick
and Graybill (1992) for similar techniques.
For all other parameters, Wald Z-scores and normal quantiles are used to construct the limits.
Wald limits are also provided for variance components if you specify the NOBOUND option.
The optional =WALD specification requests Wald limits for all parameters.
The confidence limits are displayed as extra columns in the “Covariance Parameter Estimates”
table. The confidence level is 1 ˛ D 0:95 by default; this can be changed with the ALPHA=
option.
CONVF< =number >
requests the relative function convergence criterion with tolerance number. The relative function
convergence criterion is
jf k f k 1j
jf kj
number
where f k is the value of the objective function at iteration k. To prevent the division by jf kj,
use the ABSOLUTE option. The default convergence criterion is CONVH, and the default
tolerance is 1E 8.
CONVG < =number >
requests the relative gradient convergence criterion with tolerance number. The relative gradient
convergence criterion is
maxj jg jkj
jf kj
number
where f k is the value of the objective function, and g jk is the j th element of the gradient
(first derivative) of the objective function, both at iteration k. To prevent division by jf kj,
use the ABSOLUTE option. The default convergence criterion is CONVH, and the default
tolerance is 1E 8.
CONVH< =number >
requests the relative Hessian convergence criterion with tolerance number. The relative Hessian
convergence criterion is
g k 0 H 1
k g k
jf kj
number
where f k is the value of the objective function, g k is the gradient (first derivative) of the
objective function, and H k is the Hessian (second derivative) of the objective function, all at
iteration k.