+--------------------------------------------------------------------+
| |
| $THETA |
| |
+--------------------------------------------------------------------+
MEANING: Gives initial estimates and bounds for thetas
CONTEXT: NM-TRAN Control Record
USAGE:
$THETA value1 [value2] [value3] ...
[(value)xn] ...
[label=value] ...
[NAMES (label ...)value ...]
[NUMBERPOINTS=n]
[ABORT|NOABORT|NOABORTFIRST]
SAMPLE:
$THETA (0,3) 2 FIXED (0,.6,1) 10 (-INF,-2.7,0) (37 FIXED)
DISCUSSION:
Gives initial estimates and bounds for elements of the THETA matrix.
Thetas are numbered in the order in which they are defined.
OPTIONS:
Each value defines a theta and gives its initial estimate and bounds.
A value has one of 4 forms:
init [FIXED]
Init is the initial estimate. If FIXED is used, the final param-
eter estimate is to be constrained to equal the initial parameter
estimate.
([low,] init [,up] [FIXED])
Low and up are lower and upper bounds respectively. They are the
boundaries for the minimization search. Commas are optional. If
an upper bound is used, a lower bound must also be used (e.g.,
-INF; see below). The lower and upper bounds (or if just the
lower bound is used, then just this bound) may be omitted, in
which case this form differs from the one described above only in
so far as with this form, the initial estimate and the FIXED
attribute are enclosed in parentheses. When FIXED is used, and a
bound appears the bound must equal the initial estimate. FIXED
is implied when all three values are equal. The lower bound can
be -INF (i.e., -infinity), and the upper bound can be INF (i.e.,
+infinity). These are the defaults for lower and upper bounds.
They are communicated to NONMEM as numeric values -1000000 and
1000000.
([low,] init [,up]) [FIXED]
This is just like the form described above except that if the
FIXED attribute is used, the attribute occurs outside the paren-
theses, and then if moreover, a bound appears, the bound need not
equal the initial estimate.
(low,,up)
The commas are required. Because no initial estimate is given, a
search for an initial estimate (the Initial Estimates Step) is
undertaken by NONMEM. With NONMEM 7.4, when initial thetas are
to be estimated, evaluations can now be done for FOCE and
Laplace, not just for FO.
(value)xn
Any initial value or group of initial values may be enclosed in |
parentheses and followed by "xn", which means to replicate the |
values within parentheses n times ("repeated value"). The values |
within the parenthesis may have any of the above forms. For |
example, the following two are equivalent: |
$THETA 2 2 2 2 (0.001,0.1,1000) (0.001,0.1,1000) (0.001,0.1,1000) |
(0.5 FIXED) (0.5 FIXED) |
$THETA (2)x4 (0.001,0.1,1000)x3 (0.5 FIXED)x2 |
UNINT (NM75)
UNINT is used during the Optimal Design Step to identify a theta
as uninteresting. UNINT may be used anywhere that FIXED may be
used.
label=value [FIXED] (NM75)
This is a compact method of defining an element of theta, speci-
fying its initial estimate, and specifying a symbolic subscript
for this element of THETA. The symbolic subscript may be used
for THETA in abbreviated code, and will also identify this ele-
ment of THETA in the NONMEM output. (Only the first 9 characters
of the label will appear). If new $THETA records change the
ordering, the abbreviated code does not have to be changed. For
example, suppose the third element of THETA that is defined hap-
pens to be
$THETA CL=(0.0,7.0)
The abbreviated code can use this symbolic subscript instead of
the numeric subscript, e.g.,
TVCL=THETA(CL)
The NONMEM report will describe the relationship, e.g.,
LABELS FOR THETAS THETA(3)=THETA(CL)
and THETA(CL) rather than TH 3 will appear in the NONMEM report.
It is also possible to specify the label using the
$ABBR REPLACE THETA(CL)=THETA(3)
control record but the NONMEM report will not identify the rela-
tionship and will not generate the symbolic label THETA(CL) in
the report. For dynamic, or implicit mapping of labels, such as
for various occasions, these still need to be done via the $ABBR
REPLACE record.
$THETA records must be placed ahead of any records that use the
symbolic label. Therefore these records must be placed before
$THETAI, $THETAR, and abbreviated code.
NAMES (label ...)value ... (NM75)
A compact way of defining one or more thetas with labels and ini-
tial values. For example
$THETA NAMES(V1,CL,Q,V2) (0.0,7.0) (0.0,7.0) (0.0,7.0) 7
NUMBERPOINTS=n
During NONMEM's search for an initial estimate, a number of
points will be examined. This number will be automatically
determined by NONMEM, or it can be specified with this option.
May also be coded NUMBERPTS, NUMPOINTS, NUMPTS.
ABORT
During the Initial Estimates step, NONMEM is to abort when PRED
sets the error return code to 1. (The PRED error return code n
is set by the statement "EXIT n [k]" in abbreviated code, or by
the statement IERPRD=n in user-supplied code, or by PREDPP when
it detects an error.) This is the default.
NOABORT
During the Initial Estimates step, NONMEM is simply to ignore
values of the theta vector that result in PRED error return code
1. (Ordinarily the first value of the theta vector is never
ignored.) These will not be feasible values for an initial esti-
mate.
NOABORTFIRST
Same as NOABORT option, but also applies to the first value of
the theta vector that is tried. It cannot be shortened; all
characters must be coded. May be used with the NOABORT option,
in which case the stronger condition (NOABORTFIRST) takes prece-
dence.
REFERENCES: Guide IV Section III.B.9
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