Accessing the results of observed adjustments and partial adjustments

Consider the following scenario: Suppose that the base has been adjusted by the base . Occasionally we will be concerned with partial adjustments, and to this purpose for the partial adjustment results we suppose that we adjust initially by the base baseE, and then partially by base ; and that represents the complete adjustment . Suppose that we might observe , , and so too (otherwise, data-related results - and thus these options - are not available).

Observed adjusted expectations

   

Usage

• BD>option  a  switches on standard observed adjusted expectation output.

• BD>option  a+  switches on extended observed adjusted expectation output.

• BD>option  -a  switches off observed adjusted expectation output.

• BD>show  (a ) displays standard observed adjusted expectation output for the current adjustment.

• BD>show  (a+ ) displays extended observed adjusted expectation output for the current adjustment.

The a  and a+  options are used for the output of observed adjustments, delivering standard and extended output respectively. The extended output shown depends upon whether or not results are (or will be) available for both an adjustment and a partial adjustment.    

Minimal output for an adjustment

For a single adjustment the standard output consists of, for every element , the name of the element and its observed adjusted expectation . (See [31][section 4].)

Extended output for an adjustment

For a single adjustment the extended output consists of, for every element , the name of the element; its initial expectation ; its observed adjusted expectation ; and its standardised adjustment . (See [31][section 4.2].)

Extended output for an additional partial adjustment

For a partial adjustment the extended output consists of the extended output for a single adjustment listed above, together with the change in observed adjusted expectation:

and the standardised value of the change: . (See [48][sections 6.2.3, 13.2.3].)

Bearing

 

Usage

• BD>option  b  switches on bearing output.

• BD>option  -b  switches off bearing output.

• BD>show  (b ) displays bearing output for the current adjustment.

The b  option is used to display output relating to the size and bearing for the adjustment, and for the partial adjustment if any. (See [31][sections 4.4, 5.4].) Similar output is available using the b*  option. Both the bearing and the partial bearing may be retained interactively as assignments by using respectively the b  and pb  arguments to the KEEP:  command. The output shown consists of one or more columns, each representing a linear combination of the elements of :

• firstly, the bearing for the current adjustment, ;
• secondly, in the case of partial adjustment, the bearing for the partial adjustment, ;
• thirdly, in the case of partial adjustment, the bearing for the initial adjustment, .

Beneath each column are summary quantities for the observed adjustment: the size of the adjustment, the expected size of the adjustment, and the size ratio respectively. Hence the values reported are (assuming that the partial results are available, otherwise only the first column is reported):

• for the current adjustment, , , and . The first is available as the operand size , and the second is available as the operand rmtr .
• for the partial adjustment, , , and . The first is available as the operand psize , and the second is available as the operand prmtr .
• for the previous adjustment, , , and .

 

Standardised bearing

 

Usage

• BD>option  b*  switches on standardised bearing output.

• BD>option  -b*  switches off standardised bearing output.

• BD>show  (b* ) displays standardised bearing output for the current adjustment.

The b*  option is used to display output relating to the size and standardised bearing for the adjustment, and for the partial adjustment if any. (See [31][sections 4.4, 5.4].) Similar output is available using the b  option. Both the bearing and the partial bearing may be retained interactively as assignments by using respectively the b  and pb  arguments to the KEEP:  command, but they cannot be retained in standardised form. The output shown consists of one or more columns, each representing a linear combination of the standardised elements of , where each element is standardised to have expectation zero and prior variance unity:

• firstly, the standardised bearing for the current adjustment, .
• secondly, in the case of partial adjustment, the standardised bearing for the partial adjustment, .
• thirdly, in the case of partial adjustment, the standardised bearing for the initial adjustment, .

Beneath each column are summary quantities for the observed adjustment: the size of the adjustment, the expected size of the adjustment, and the size ratio respectively. Hence the values reported are (assuming that the partial results are available, otherwise only the first column is reported):

• for the current adjustment, , , and . The first is available as the operand size , and the second is available as the operand rmtr .
• for the partial adjustment, , , and . The first is available as the operand psize , and the second is available as the operand prmtr .
• for the previous adjustment, , , and .

 

Correlations between bearings and elements

 

Usage

• BD>option  becorr  switches on bearing-element correlation output.

• BD>option  -becorr  switches off bearing-element correlation output.

• BD>show  (becorr ) displays bearing-element correlation output for the current adjustment.

The becorr  option yields the prior correlation between the bearing for the current adjustment, , and every element . If a partial adjustment has been made, then the prior correlations for the bearings for the previous and partial adjustments, and , with every element are given.  

Correlations between bearings

 

Usage

• BD>option  bcorr  switches on bearing inter-correlation output.

• BD>option  -bcorr  switches off bearing inter-correlation output.

• BD>show  (bcorr ) displays bearing inter-correlation output for the current adjustment.

When the results of a partial adjustment are available, the bcorr  option yields the prior correlations between the three kinds of bearing: the bearing for the current adjustment, ; the previous adjustment, ; and the partial adjustment, . One of these three correlations (depending upon the type of fit) is the path correlation, also available using the pc  option. In the case of model fitting, the path correlation is the prior correlation between the bearings for the previous and partial adjustments, and in the case of model reduction, it is the prior correlation between the bearings for the current and partial adjustments.  

Discrepancy vector

 

Usage

• BD>option  dv  switches on discrepancy vector output.

• BD>option  -dv  switches off discrepancy vector output.

• BD>show  (dv ) displays discrepancy vector output for the current adjustment.

The dv  option is used to display output relating to the adjustment discrepancy and discrepancy vector for the adjustment, and for the partial adjustment if any. Similar output is available using the dv*  option. Both the discrepancy vector and the partial discrepancy vector may be retained interactively as assignments by using respectively the dv  and pdv  arguments to the KEEP:  command. The output shown consists of one or more columns, each representing a linear combination of the elements of :

• firstly, the discrepancy vector for the current adjustment, B.
• secondly, in the case of partial adjustment, the discrepancy vector for the partial adjustment, B.
• thirdly, in the case of partial adjustment, the discrepancy vector for the initial adjustment, B.

Beneath each column are summary quantities for the observed adjustment: the discrepancy for the adjustment, the prior expected size of the discrepancy for the adjustment (the expected size of this discrepancy is equal to the rank of the corresponding resolution matrix), and the discrepancy ratio respectively. This summary is also given with the dv*  option. Hence the values reported are (assuming that the partial results are available, otherwise only the first column is reported):

• for the current adjustment, , , and . The first is available as the operand dvsize , and the second is available as the operand rmrank .
• for the partial adjustment, , , and . The first is available as the operand pdvsize , and the second is available as the operand prmrank .
• for the previous adjustment, , , and .

 

Standardised discrepancy vector

 

Usage

• BD>option  dv*  switches on standardised discrepancy vector output.

• BD>option  -dv*  switches off standardised discrepancy vector output.

• BD>show  (dv* ) displays standardised discrepancy vector output for the current adjustment.

The dv*  option is used to display output relating to the size and standardised discrepancy vector for the adjustment, and for the partial adjustment if any. Similar output is available using the dv  option. Both the discrepancy vector and the partial discrepancy vector may be retained interactively as assignments by using respectively the dv  and pdv  arguments to the KEEP:  command, but they cannot be retained in standardised form. The output shown consists of one or more columns, each representing a linear combination of the standardised elements of , where each element is standardised to have expectation zero and prior variance unity:

• firstly, the standardised discrepancy vector for the current adjustment, B.
• secondly, in the case of partial adjustment, the standardised discrepancy vector for the partial adjustment, B.
• thirdly, in the case of partial adjustment, the standardised discrepancy vector for the initial adjustment, B.

Beneath each column are summary quantities for the observed adjustment: the discrepancy for the adjustment, the prior expected size of the discrepancy for the adjustment (the expected size of this discrepancy is equal to the rank of the corresponding resolution matrix), and the discrepancy ratio respectively. This summary is also given with the dv  option. Hence the values reported are (assuming that the partial results are available, otherwise only the first column is reported):

• for the current adjustment, , , and . The first is available as the operand dvsize , and the second is available as the operand rmrank .
• for the partial adjustment, , , and . The first is available as the operand pdvsize , and the second is available as the operand prmrank .
• for the previous adjustment, , , and .

 

Correlations between discrepancy vectors and elements

 

Usage

• BD>option  dvecorr  switches on discrepancy vector-element correlation output.

• BD>option  -dvecorr  switches off discrepancy vector-element correlation output.

• BD>show  (dvecorr ) displays discrepancy vector-element correlation output for the current adjustment.

The dvecorr  option yields the prior correlation between the discrepancy vector for the current adjustment, B, and every element . If a partial adjustment has been made, then the prior correlations for the discrepancy vectors for the previous and partial adjustments, B and B, with every element are given.  

Correlations between discrepancy vectors

 

Usage

• BD>option  dvcorr  switches on discrepancy vector inter-correlation output.

• BD>option  -dvcorr  switches off discrepancy vector inter-correlation output.

• BD>show  (dvcorr ) displays discrepancy vector inter-correlation output for the current adjustment.

When the results of a partial adjustment are available, the dvcorr  option yields the prior correlations between the three kinds of discrepancy vector: the discrepancy vector for the current adjustment, B; the previous adjustment, B; and the partial adjustment, B.  

Observed adjusted expectations for canonical directions

   

Usage

• BD>option  cda  switches on standard observed adjusted expectation output for the canonical directions.

• BD>option  cda+  switches on extended observed adjusted expectation output for the canonical directions.

• BD>option  -cda  switches off observed adjusted expectation output for the canonical directions.

• BD>show  (cda ) displays standard observed adjusted expectation output for the current adjustment for the canonical directions.

• BD>show  (cda+ ) displays extended observed adjusted expectation output for the current adjustment for the canonical directions.

The cda  and cda+  options are used to display standard and extended results for the observed adjustments of canonical directions. Suppose that is a canonical direction. Then the standard output consists of its name and its observed adjusted expectation, . The extended output consists additionally of its initial expectation (always by convention); and its standardised adjustment . Note that the adjusted expectations for the canonical quantities can be obtained using the cde  or cde*  options.   

Observed adjusted expectations for maximal canonical directions

   

Usage

• BD>option  mcda  switches on standard observed adjusted expectation output for the maximal canonical directions.

• BD>option  mcda+  switches on extended observed adjusted expectation output for the maximal canonical directions.

• BD>option  -mcda  switches off observed adjusted expectation output for the maximal canonical directions.

• BD>show  (mcda ) displays standard observed adjusted expectation output for the current adjustment for the maximal canonical directions.

• BD>show  (mcda+ ) displays extended observed adjusted expectation output for the current adjustment for the maximal canonical directions.

The mcda  and mcda+  options are used to display standard and extended results for the observed adjustments of maximal canonical directions. Suppose that is a maximal canonical direction. Then the standard output consists of its name and its observed adjusted expectation, . The extended output consists additionally of its initial expectation (always by convention); and its standardised adjustment . The option is ignored when there is no adjustment, and also when lack of exchangeability in implies that there are no maximal results available.    

Adjusted means and standard deviations summary

 

Usage

• BD>option  msd  switches on a summary of the effects of adjustment on individual elements.

• BD>option  -msd  switches off a summary of the effects of adjustment on individual elements.

• BD>show  (msd ) displays a summary of the effects of the current adjustment on individual elements.

The msd  option summarises the output given by the a+  and v+  options for individual elements . For each such element the output consists of the initial and adjusted expectation; the initial and adjusted standard deviations; and the standardised value of the change in expectation.  

Path summary

 

Usage

• BD>option  pathsum  enables path summaries and disables all other adjustment output options.

• BD>option  -pathsum  disables output of path summaries.

The pathsum  option is rather special because its being set disables all other adjustment output options, and the setting of any other adjustment output option likewise disables the pathsum  option. This is because the two sorts of option are incompatible, giving messy output.

When switched on, the option gives a summary of sequential observed adjustments, and in particular of the path correlations between successive adjustments. Suppose that the base is adjusted initially by the base , and then partially by the base\ , and so forth; and suppose that is the union of the bases . Suppose that we observe to be for each , and that we write for the observed union .

Suppose that we have adjusted already by . For the stepwise partial adjustment, when the base is added, the information displayed is

• the name of the partially adjusting base ;
• for every element , the new current observed adjusted expectation for , ;
• the size of the partial adjustment, ;
• the expected size of the partial adjustment, ;
• and the stepwise path correlation .

(See [31][section 5.6].) The path correlation is undefined for the first such adjustment.  

Path correlations

 

Usage

• BD>option  pc  switches on path correlation output.

• BD>option  -pc  switches off path correlation output.

• BD>show  (pc ) displays path correlation output for the current adjustment.

When the results of a partial adjustment are available, the pc  option yields , the path correlation. In the case of model fitting, this is the prior correlation between the bearings for the previous and partial adjustments, and in the case of model reduction, this is the prior correlation between the bearings for the current and partial adjustments.  

Observed adjusted expectations for partial canonical directions

   

Usage

• BD>option  pcda  switches on standard observed adjusted expectation output for the partial canonical directions.

• BD>option  pcda+  switches on extended observed adjusted expectation output for the partial canonical directions.

• BD>option  -pcda  switches off observed adjusted expectation output for the partial canonical directions.

• BD>show  (pcda ) displays standard observed adjusted expectation output for the current adjustment for the partial canonical directions.

• BD>show  (pcda+ ) displays extended observed adjusted expectation output for the current adjustment for the partial canonical directions.

The pcda  and pcda+  options are used to display standard and extended results for the observed adjustments of partial canonical directions. Suppose that is a partial canonical direction. Then the standard output consists of its name and its observed adjusted expectation, . The extended output consists additionally of its initial expectation (always by convention); and its standardised adjustment . The option is ignored when there is no partial adjustment.