|Details of the OPTEX Procedure
- GENERATE <options> ;
You use the GENERATE statement to customize the search for a design.
By default, the OPTEX procedure searches for a design as follows:
- using the exchange algorithm (METHOD=EXCHANGE)
- using D-optimality as the optimality criterion
- using a completely random initial design to
start the search (INITDESIGN=RANDOM)
- selecting candidate points only from the DATA=
data set (modified by using AUGMENT= or INITDESIGN=
- performing 10 iterations in the search (ITER=10)
- finding a design with 10+p points, where p is the number of
parameters in the model (modified by using the N= or INITDESIGN= option)
The following options can be used to modify these defaults:
specifies a data set that contains a design to be augmented, in other
words, a set of points that must be contained in the
design generated. When creating designs, the OPTEX procedure adds points
from the DATA= data set (or the last data set created, if DATA= is
not specified) to points from the AUGMENT= data set. The number of
points in the design to be augmented must be less than the number of
points specified with the N= option. For details, see
"AUGMENT= Data Set"
specifies the optimality criterion used in the search. You can specify any
one of the following:
specifies D-optimality; the optimal design maximizes the
determinant |X'X| of the information matrix for the design. This is the
specifies A-optimality; the optimal design minimizes the
sum of the variances of the estimated parameters for the model, which is the
same as minimizing the trace of (X'X)-1.
specifies U-optimality; the optimal design minimizes the
sum of the
minimum distances from each candidate point to the design. That is, if
C is the set of candidate points, D is the set of design
points, and d(x,D) is the minimum distance from x
to any point in D, then a U-optimal design minimizes
This measures how well the design "covers" the candidate set;
thus, a U-optimal design is also called a uniform coverage design.
specifies S-optimality; the optimal design maximizes the
of the minimum distance from each design point to any other design point.
Mathematically, an S-optimal design maximizes
where D is the set of design points, and ND is the number of
points in D. This measures how spread out the design points
are; thus, an S-optimal design is also called a maximum spread
For more information on the different criteria, see
"Optimality Criteria" .
specifies a method of obtaining an initial design for the search
procedure. Valid values of initialization-method are
specifies an initial design chosen by a sequential search. The
design given by INITDESIGN=SEQUENTIAL is the same as the design given by
METHOD=SEQUENTIAL. You can use the INITDESIGN=SEQUENTIAL option with other
values of the METHOD= option to specify a sequential design as the initial
design for various search methods. For details, see
specifies a completely random initial design. The initial design
generated consists of a random selection of observations from the
DATA= data set.
- PARTIAL<(m )>
specifies an initial design using a mixture of RANDOM and SEQUENTIAL methods.
A small number nr of points for the initial design are chosen at random
from the candidates, and the rest of the design points are chosen by a
sequential search. (For a definition of the sequential search,
see "Search Methods" .)
By default, nr is randomly chosen between 0 and half the number
of parameters in the linear model. You can specify the optional integer
m to modify the selection of nr. If m > 0, then nr is randomly
chosen between 0 and m
for each try. If m < 0, then nr=|m| for each try. The maximum value
for |m| is the number of points in the design. Refer to Galil and Kiefer
(1980) for notes on choosing nr.
specifies a data set that holds the initial design. Use this
initialization-method when you have a specific design that you
want to improve or when you want to evaluate an existing design.
For details, see "INITDESIGN= Data Set"
The default initialization method depends on the search procedure
as shown in Table 24.4.
Table 24.4: Default Initialization Methods
Default Initialization Method
If you specify INITDESIGN=SAS-data-set and METHOD=SEQUENTIAL, no
search is performed; the INITDESIGN= data set is taken as the final design.
By specifying these options, you can use the procedure to evaluate an
specifies the number n of searches to make. Because local optima
are common in difficult search problems, it is often a good idea to make
several tries for the optimal design with a random or partially random
method of initialization (see the preceding INITDESIGN= option). By
The n designs found are sorted by their respective efficiencies
according to the current optimality criterion (see the
option.) The most efficient design is assigned a
design-number of 1, the second most efficient design is
assigned a design-number of 2, and so on. You can then use
the design-number in the EXAMINE and OUTPUT statements to display
the characteristics of a design or to save a design in a data set.
specifies that only the best m designs are to be retained. The value
m must be less than or equal
to the value n of the ITER= option; by default m=n, so that all
iterations are kept. This option is useful when you want to
make many searches to overcome the problem of local optima but
are interested only in the results of the best m designs.
specifies the procedure used to search for the optimal design.
The default is METHOD=EXCHANGE.
the optional level gives the maximum
excursion level for the search, where level is an integer
greater than or equal to 1. Enclose the value of level in
parentheses immediately following the word DETMAX. The default
value for level is 4. In general, larger values of
level result in longer search times.
When METHOD=EXCHANGE, the optional k
specifies the k-exchange search method of Johnson
and Nachtsheim (1983), which generalizes the modified
Fedorov search algorithm of Cook and Nachtsheim (1980).
Enclose the value of k in
parentheses immediately following the word EXCHANGE.
From fastest to slowest, the methods are
In general, slower methods result in more efficient designs. While the
default method EXCHANGE always works relatively quickly, you may want to
specify a more reliable method, such as M_FEDOROV, with fast
computers or small- to moderately-sized problems.
See "Search Methods" for details on the
specifies the number of points in the final design. The default design
size is 10+p, where p is the number of parameters in the
model. If you use the INITDESIGN= option, the default number is the number
of points in the initial design. Specify N=n to search for a
design with n points. Specify N=SATURATED to search for a
design with the same number of points as there are parameters
in the model. A saturated design has no degrees of freedom to
estimate error and should be used with caution.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.