Iterative adjustment

 

Syntax

BD>itadjust : [ B / X IL]

where is the name of a base or element, X is the name of a component, and is an index list.

The ITADJUST:  command uses an iterative adjustment algorithm, an alternative to our standard adjustment algorithm which increases the potential size of the fitting set, subject to certain limitations on the availability of some results. An example syntax is:

BD>itadjust :[B / X.i.j.k ]

where the intention is to adjust by a number of quantities for some range of values .

The basic syntax is essentially the same, and implies the same, as the corresponding syntax for standard adjustments using the ADJUST:  command. For example, these commands do redefine the current operator, and may also be used to define (or prepare) the collection being adjusted. Similarly, the collection being adjusted may have been prepared beforehand.

The second argument in the command consists of only one named quantity, X, with an index list. Notice that different quantities can be associated with different indices, if necessary. For example you might take to represent and to represent .

B is a base or single element which constitutes the collection to be adjusted, and which must carry beliefs that have already been specified. Beliefs specified between B and the quantities intended by X can be accessed or generated as follows:

1. Each element in B can be related directly to the X quantities via functional variance-covariance specifications using the FVAR:  command.
2. Otherwise, if an element in B itself contains value indices (for example, if the first element in B is Y.1.3), then the program deduces whether the element plus its indices constitutes recognisable input to a FVAR:  specification. For example, we might have defined

   BD>fvar : v(2, Y.i.j, X.r.s.t ) = E

   and this would be used to generate the requisite beliefs.

The second argument X represents the collection to be used for the adjustment. It is the name of a quantity whose beliefs have been specified functionally, using FVAR:  and FE:  commands, and which has an index list. The indices in the index list are given values by issuing an INDEX:  command. For example, we might issue the following commands:

BD>index :i=1,1,2

BD>index :j=1,1,2

BD>index :k=1,1,2

BD>itadjust  [ B / X.i.j.k]

to mean that the base B should be adjusted by in turn by . Note that the order of adjustment is given by the final indices changing fastest. Functional beliefs should have been specified beforehand, although the index characters used in the definition need not be the same. For example, we might have made the definitions:

BD>fvar : v(2, B.1, X.r.s.t)=E1

BD>fvar : v(1, X.i.j.k, X.r.s.t)=E2

BD>fvar : v(2, X.i.j.k, X.r.s.t)=E3

BD>fe : e(1,X.j.k.r)=E4

where E1, E2, E3 and E4 are equations, usually containing varying indices, and is one of the elements in B. If we dont include functional specifications for the expectations for the quantities to be used in the adjustment, the expectations are taken to be zero.

As far as the expectation specifications are concerned, only the current default expectation store is ever referenced; the remainder are ignored. The default expectation store can be changed by using the e  argument to the CONTROL:  command. In the above piece of example code, expectation store number one has been used - this is the default expectation store number.

Belief store numbers are treated in the same way as for the standard algorithm, and so too are the various controls affecting adjustment which we discussed in §9.1.2. If a prospective sample size of greater than unity is used, then beliefs appropriate to an exchangeable adjustment must be available, and have been specified functionally. Location of the correct belief store is determined by the priorvar , betweenvar , infovar , and modelvar  controls as for standard adjustments. The exchangeable  control has no effect on the iterative algorithms, and commands which require varying the sample size are not available. Hence, the VARYSIZE:  command is not available thereafter.

We use the ITADJUST:  command where data is available, as follows. Using the same example, we need to set up the data system thus:

1. Arrange the data so that it exists on the data-carrier of the same name, X.
2. Introduce data carriers whose names are i, j, and k, to relate to the indices in the index list, .
3. Use these data-carriers (i,j,k) to define a selection over X as follows: is selected if equals the current value of index AND if matches the current value of index AND if matches the current value of index . The average of the selected data is taken as the datum for the element to be fitted.
4. The average for each element added must be based on the same sample size.
5. The FACTOR:  command makes such data/index definition very simple.
6. Data selection is not governed by the usual selection facilities.

The output available is exactly the same as that under the standard ADJUST:  command, and is obtained by setting the same options. In general, the iterative adjustment algorithm is slower than the standard adjustment algorithm, and production of the adjusted expectation is particularly time-consuming.

Some of the output for each successive iteration of the ITADJUST:  command can be retained as data by setting various arguments to the KEEP:  command. Results corresponding to consecutive iterations are stored in consecutive data locations. The results that can be retained are:

1. The expected sizes of consecutive adjustments, by using the itsize  argument.
2. The observed sizes of consecutive adjustments, by using the itesize  argument.
3. The path correlation between consecutive adjustments, by setting the itpath  argument.