13 Rescaling
In this section the rescaling feature is described. This feature concerns the rescaled canonical parameters (RCP) mentioned in section 5.2 of NONMEM Users Guide, Part I. These are parameters established internally by NONMEM, and the parameter estimate in each summarized iteration from the Estimation Step is given in terms of these parameters. The initial parameter estimate — the one in the summary of the zeroth iteration — is such that all of its components are 0.1. If the number of significant figures specified on the ESTIMATION record is r, then the parameter search terminates when the two estimates resulting from two successive iterations do not differ in the first r significant figures (including leading zeros after the decimal point) in any of the individual parameter components. This criterion applies to estimates in terms of the RCP.
With this background then, suppose a parameter component is initially estimated too large by one or more orders of magnitude. For example, suppose in terms of the RCP its final estimate is 0.00103, whereas its initial estimate is, of course, 0.1. Suppose further that the number of significant figures specified on the ESTIMATION record is 3. Since leading zeros after the decimal point are to be regarded as significant figures, the only figure in the final estimate that follows the leading zeros after the decimal point and that has been accurately determined is that in the thousandth place. Had the initial estimate not been so large, the final estimate could have been more accurate. In this situation the user has the opportunity to continue the parameter search and obtain greater accuracy.
There are two ways this can be done. The first is to continue the search in a subsequent NONMEM run, using the final estimate of the first run as the initial estimate of the second run. The initial estimate in terms of the RCP is now 0.1, and the (accurately determined) significant figures of the final estimate should include no leading zeros after the decimal point. It is recommended that if the user suspects before the first run that the parameter search may need to be continued in a second NONMEM run for this reason, then a Model Specification File be used. (If a Model Specification File is not used, but the initial estimate of the second run (all components considered) is very close to what will be the final estimate of the second run, then the search algorithm may not in fact be able to improve upon this initial estimate due to problems with round-off error. In this case the usual message to this effect is issued.) However, when a Model Specification File is used, the RCP in the second run are the same as those in the first run, and in terms of these the initial estimate of the second run will be no different than the final estimate of the first run, unless the rescaling feature is used. This feature allows the user to specify that a new set of RCP is to be established in the second run, and in terms of these, all components of the initial estimate are 0.1. To so specify, a 1 should be placed in field a of the FIND record. If a blank or zero is placed in this field, rescaling does not occur. (Suppose, though, that a Model Specification File is used, that a 1 is placed in field 4 of the FIND record, but that the Estimation Step is omitted i.e. a 1 is placed in field 1 of the ESTIMATION record. Then a new set of RCP are not in fact established.) The complete format for the FIND record is given in Table 1.
| Field No. | Value | Function |
|---|---|---|
| 1 | between 1 & 9999 | identifier for (existing) Model Specification File |
| 2 | between 20 & 99 | FORTRAN unit number for (existing) Model Specification File |
| 3 | 0 or blank | FORTRAN unit not to be rewound |
| 1 | FORTRAN unit to be rewound | |
| 4 | 0 or blank | estimate on file not to be rescaled |
| 1 | estimate on file to be rescaled |
There is a second way the user may continue the parameter search and obtain greater accuracy. He may specify that after the search terminates, a new set of RCP is to be established, in terms of which the components of the final estimate are 0.1, and that the search is to be automatically continued in the same NONMEM run, with the new RCP. This may be accomplished by placing a 1 in field 5 of the ESTIMATION record. The search continuation per se is regarded as a second search, and the usual three lines of summary information from the Estimation Step are given for both first and second searches. Moreover, if iterations are summarized for the first search, then they are summarized for the second search too, but the two summarizations are kept separate, and they are printed on separate pages. The value of r placed in field 3, remains in force during the second search. However, if the upper limit to the number of objective function evaluations that is placed in field 2 is M, while the number of objective function evaluations actually occurring during the first search is n, then the upper limit in force during the second search is M-n. A second search will be implemented only if the first search terminates successfully. In this case if a Model Specification File is to be generated, the final estimate from the second search is output on the file. If the first search terminates unsuccessfully, and if a Model Specification File is to be generated, then the final estimate from the first search is output on the file. The complete format of the ESTIMATION record is given in Table 2.
| Field no. | Value | Function |
|---|---|---|
| 1 | 0 or blank | Estimation Step implemented |
| 1 | Estimation Step omitted |
If the value is 1, the subsequent fields may be ignored.
| Field no. | Value | Function |
|---|---|---|
| 2 | nonnegative | Upper limit to number of objective function evaluations |
| 3 | between 1 & 8 | number of significant figures required in final estimate |
| 4 | 0 or blank | no monitoring of search routine |
| n>0 | every nth iteration summarized | |
| 5 | 0 or blank | second search not implemented |
| 1 | second search implemented | |
| 6 | 0 or blank | Model Specification File is not generated |
| 1 | Model Specification File is generated |
If the value is 0 or blank the following 2 fields may be ignored.
| Field no. | Value | Function |
|---|---|---|
| 7 | between 0 & 9999 | file identifier |
| 8 | between 20 & 99 | FORTRAN unit number for file |