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Accessing the results of observed adjustments and partial adjustments

Consider the following scenario: Suppose that the base tex2html_wrap_inline40230 has been adjusted by the base tex2html_wrap_inline40232 . 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 tex2html_wrap_inline40236 ; and that tex2html_wrap_inline35840 represents the complete adjustment tex2html_wrap_inline40240 . Suppose that we might observe tex2html_wrap_inline41128 , tex2html_wrap_inline41130 , and so too tex2html_wrap_inline41132 (otherwise, data-related results - and thus these options - are not available).

Observed adjusted expectations
   


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

tex2html_wrap_inline33806 tex2html_wrap_inline33806

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 tex2html_wrap_inline40674 , the name of the element and its observed adjusted expectation tex2html_wrap_inline41136 . (See [31][section 4].)

Extended output for an adjustment
For a single adjustment the extended output consists of, for every element tex2html_wrap_inline40674 , the name of the element; its initial expectation tex2html_wrap_inline41140 ; its observed adjusted expectation tex2html_wrap_inline41136 ; and its standardised adjustment tex2html_wrap_inline41144 . (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:

displaymath41116

and the standardised value of the change: tex2html_wrap_inline41152 . (See [48][sections 6.2.3, 13.2.3].)

Bearing
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  b  tex2html_wrap_inline33712 switches on bearing output.

  • BD>option  -b  tex2html_wrap_inline33712 switches off bearing output.

  • BD>show  (b ) tex2html_wrap_inline33712 displays bearing output for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

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 tex2html_wrap_inline40230 :

  • firstly, the bearing for the current adjustment, tex2html_wrap_inline40246 ;
  • secondly, in the case of partial adjustment, the bearing for the partial adjustment, tex2html_wrap_inline41158 ;
  • thirdly, in the case of partial adjustment, the bearing for the initial adjustment, tex2html_wrap_inline41160 .

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, tex2html_wrap_inline37660 , tex2html_wrap_inline41164 , and tex2html_wrap_inline37658 . The first is available as the operand size , and the second is available as the operand rmtr .
  • for the partial adjustment, tex2html_wrap_inline41168 , tex2html_wrap_inline41170 , and tex2html_wrap_inline41172 . The first is available as the operand psize , and the second is available as the operand prmtr .
  • for the previous adjustment, tex2html_wrap_inline41174 , tex2html_wrap_inline41176 , and tex2html_wrap_inline41178 .

 

Standardised bearing
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  b*  tex2html_wrap_inline33712 switches on standardised bearing output.

  • BD>option  -b*  tex2html_wrap_inline33712 switches off standardised bearing output.

  • BD>show  (b* ) tex2html_wrap_inline33712 displays standardised bearing output for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

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 tex2html_wrap_inline40230 , where each element is standardised to have expectation zero and prior variance unity:

  • firstly, the standardised bearing for the current adjustment, tex2html_wrap_inline40246 .
  • secondly, in the case of partial adjustment, the standardised bearing for the partial adjustment, tex2html_wrap_inline41158 .
  • thirdly, in the case of partial adjustment, the standardised bearing for the initial adjustment, tex2html_wrap_inline41160 .

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, tex2html_wrap_inline37660 , tex2html_wrap_inline41164 , and tex2html_wrap_inline37658 . The first is available as the operand size , and the second is available as the operand rmtr .
  • for the partial adjustment, tex2html_wrap_inline41168 , tex2html_wrap_inline41170 , and tex2html_wrap_inline41172 . The first is available as the operand psize , and the second is available as the operand prmtr .
  • for the previous adjustment, tex2html_wrap_inline41174 , tex2html_wrap_inline41176 , and tex2html_wrap_inline41178 .

 

Correlations between bearings and elements
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  becorr  tex2html_wrap_inline33712 switches on bearing-element correlation output.

  • BD>option  -becorr  tex2html_wrap_inline33712 switches off bearing-element correlation output.

  • BD>show  (becorr ) tex2html_wrap_inline33712 displays bearing-element correlation output for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The becorr  option yields the prior correlation between the bearing for the current adjustment, tex2html_wrap_inline40246 , and every element tex2html_wrap_inline40674 . If a partial adjustment has been made, then the prior correlations for the bearings for the previous and partial adjustments, tex2html_wrap_inline41160 and tex2html_wrap_inline41158 , with every element tex2html_wrap_inline40674 are given.  

Correlations between bearings
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  bcorr  tex2html_wrap_inline33712 switches on bearing inter-correlation output.

  • BD>option  -bcorr  tex2html_wrap_inline33712 switches off bearing inter-correlation output.

  • BD>show  (bcorr ) tex2html_wrap_inline33712 displays bearing inter-correlation output for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

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, tex2html_wrap_inline40246 ; the previous adjustment, tex2html_wrap_inline41160 ; and the partial adjustment, tex2html_wrap_inline41158 . 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
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  dv  tex2html_wrap_inline33712 switches on discrepancy vector output.

  • BD>option  -dv  tex2html_wrap_inline33712 switches off discrepancy vector output.

  • BD>show  (dv ) tex2html_wrap_inline33712 displays discrepancy vector output for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

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 tex2html_wrap_inline40230 :

  • firstly, the discrepancy vector for the current adjustment, tex2html_wrap_inline40346 B.
  • secondly, in the case of partial adjustment, the discrepancy vector for the partial adjustment, tex2html_wrap_inline41416 B.
  • thirdly, in the case of partial adjustment, the discrepancy vector for the initial adjustment, tex2html_wrap_inline41418 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, tex2html_wrap_inline41420 , tex2html_wrap_inline41224 , and tex2html_wrap_inline41424 . The first is available as the operand dvsize , and the second is available as the operand rmrank .
  • for the partial adjustment, tex2html_wrap_inline41426 , tex2html_wrap_inline41228 , and tex2html_wrap_inline41430 . The first is available as the operand pdvsize , and the second is available as the operand prmrank .
  • for the previous adjustment, tex2html_wrap_inline41432 , tex2html_wrap_inline41232 , and tex2html_wrap_inline41436 .

 

Standardised discrepancy vector
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  dv*  tex2html_wrap_inline33712 switches on standardised discrepancy vector output.

  • BD>option  -dv*  tex2html_wrap_inline33712 switches off standardised discrepancy vector output.

  • BD>show  (dv* ) tex2html_wrap_inline33712 displays standardised discrepancy vector output for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

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 tex2html_wrap_inline40230 , where each element is standardised to have expectation zero and prior variance unity:

  • firstly, the standardised discrepancy vector for the current adjustment, tex2html_wrap_inline40346 B.
  • secondly, in the case of partial adjustment, the standardised discrepancy vector for the partial adjustment, tex2html_wrap_inline41416 B.
  • thirdly, in the case of partial adjustment, the standardised discrepancy vector for the initial adjustment, tex2html_wrap_inline41418 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, tex2html_wrap_inline41420 , tex2html_wrap_inline41224 , and tex2html_wrap_inline41424 . The first is available as the operand dvsize , and the second is available as the operand rmrank .
  • for the partial adjustment, tex2html_wrap_inline41426 , tex2html_wrap_inline41228 , and tex2html_wrap_inline41430 . The first is available as the operand pdvsize , and the second is available as the operand prmrank .
  • for the previous adjustment, tex2html_wrap_inline41432 , tex2html_wrap_inline41232 , and tex2html_wrap_inline41436 .

 

Correlations between discrepancy vectors and elements
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  dvecorr  tex2html_wrap_inline33712 switches on discrepancy vector-element correlation output.

  • BD>option  -dvecorr  tex2html_wrap_inline33712 switches off discrepancy vector-element correlation output.

  • BD>show  (dvecorr ) tex2html_wrap_inline33712 displays discrepancy vector-element correlation output for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The dvecorr  option yields the prior correlation between the discrepancy vector for the current adjustment, tex2html_wrap_inline40346 B, and every element tex2html_wrap_inline40674 . If a partial adjustment has been made, then the prior correlations for the discrepancy vectors for the previous and partial adjustments, tex2html_wrap_inline41418 B and tex2html_wrap_inline41416 B, with every element tex2html_wrap_inline40674 are given.  

Correlations between discrepancy vectors
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  dvcorr  tex2html_wrap_inline33712 switches on discrepancy vector inter-correlation output.

  • BD>option  -dvcorr  tex2html_wrap_inline33712 switches off discrepancy vector inter-correlation output.

  • BD>show  (dvcorr ) tex2html_wrap_inline33712 displays discrepancy vector inter-correlation output for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

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, tex2html_wrap_inline40346 B; the previous adjustment, tex2html_wrap_inline41418 B; and the partial adjustment, tex2html_wrap_inline41416 B.  

Observed adjusted expectations for canonical directions
   


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  cda  tex2html_wrap_inline33712 switches on standard observed adjusted expectation output for the canonical directions.

  • BD>option  cda+  tex2html_wrap_inline33712 switches on extended observed adjusted expectation output for the canonical directions.

  • BD>option  -cda  tex2html_wrap_inline33712 switches off observed adjusted expectation output for the canonical directions.

  • BD>show  (cda ) tex2html_wrap_inline33712 displays standard observed adjusted expectation output for the current adjustment for the canonical directions.

  • BD>show  (cda+ ) tex2html_wrap_inline33712 displays extended observed adjusted expectation output for the current adjustment for the canonical directions.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The cda  and cda+  options are used to display standard and extended results for the observed adjustments of canonical directions. Suppose that tex2html_wrap_inline34522 is a canonical direction. Then the standard output consists of its name and its observed adjusted expectation, tex2html_wrap_inline41256 . The extended output consists additionally of its initial expectation (always tex2html_wrap_inline41258 by convention); and its standardised adjustment tex2html_wrap_inline41260 . 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
   


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  mcda  tex2html_wrap_inline33712 switches on standard observed adjusted expectation output for the maximal canonical directions.

  • BD>option  mcda+  tex2html_wrap_inline33712 switches on extended observed adjusted expectation output for the maximal canonical directions.

  • BD>option  -mcda  tex2html_wrap_inline33712 switches off observed adjusted expectation output for the maximal canonical directions.

  • BD>show  (mcda ) tex2html_wrap_inline33712 displays standard observed adjusted expectation output for the current adjustment for the maximal canonical directions.

  • BD>show  (mcda+ ) tex2html_wrap_inline33712 displays extended observed adjusted expectation output for the current adjustment for the maximal canonical directions.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The mcda  and mcda+  options are used to display standard and extended results for the observed adjustments of maximal canonical directions. Suppose that tex2html_wrap_inline41262 is a maximal canonical direction. Then the standard output consists of its name and its observed adjusted expectation, tex2html_wrap_inline41264 . The extended output consists additionally of its initial expectation (always tex2html_wrap_inline41266 by convention); and its standardised adjustment tex2html_wrap_inline41268 . The option is ignored when there is no adjustment, and also when lack of exchangeability in tex2html_wrap_inline35840 implies that there are no maximal results available.    

Adjusted means and standard deviations summary
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  msd  tex2html_wrap_inline33712 switches on a summary of the effects of adjustment on individual elements.

  • BD>option  -msd  tex2html_wrap_inline33712 switches off a summary of the effects of adjustment on individual elements.

  • BD>show  (msd ) tex2html_wrap_inline33712 displays a summary of the effects of the current adjustment on individual elements.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The msd  option summarises the output given by the a+  and v+  options for individual elements tex2html_wrap_inline41272 . 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
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  pathsum  tex2html_wrap_inline33712 enables path summaries and disables all other adjustment output options.

  • BD>option  -pathsum  tex2html_wrap_inline33712 disables output of path summaries.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

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 tex2html_wrap_inline40230 is adjusted initially by the base tex2html_wrap_inline41276 , and then partially by the base\ tex2html_wrap_inline41278 , and so forth; and suppose that tex2html_wrap_inline41280 is the union of the bases tex2html_wrap_inline41282 . Suppose that we observe tex2html_wrap_inline41284 to be tex2html_wrap_inline41286 for each tex2html_wrap_inline41288 , and that we write tex2html_wrap_inline41290 for the observed union tex2html_wrap_inline41280 .

Suppose that we have adjusted already by tex2html_wrap_inline41294 . For the tex2html_wrap_inline34732 stepwise partial adjustment, when the base tex2html_wrap_inline41298 is added, the information displayed is

  • the name of the partially adjusting base tex2html_wrap_inline41298 ;
  • for every element tex2html_wrap_inline40674 , the new current observed adjusted expectation for tex2html_wrap_inline35430 , tex2html_wrap_inline41306 ;
  • the size of the partial adjustment, tex2html_wrap_inline41308 ;
  • the expected size of the partial adjustment, tex2html_wrap_inline41310 ;
  • and the tex2html_wrap_inline34732 stepwise path correlation tex2html_wrap_inline41314 .

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

Path correlations
 


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  pc  tex2html_wrap_inline33712 switches on path correlation output.

  • BD>option  -pc  tex2html_wrap_inline33712 switches off path correlation output.

  • BD>show  (pc ) tex2html_wrap_inline33712 displays path correlation output for the current adjustment.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

When the results of a partial adjustment are available, the pc  option yields tex2html_wrap_inline41316 , 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
   


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Usage

  • BD>option  pcda  tex2html_wrap_inline33712 switches on standard observed adjusted expectation output for the partial canonical directions.

  • BD>option  pcda+  tex2html_wrap_inline33712 switches on extended observed adjusted expectation output for the partial canonical directions.

  • BD>option  -pcda  tex2html_wrap_inline33712 switches off observed adjusted expectation output for the partial canonical directions.

  • BD>show  (pcda ) tex2html_wrap_inline33712 displays standard observed adjusted expectation output for the current adjustment for the partial canonical directions.

  • BD>show  (pcda+ ) tex2html_wrap_inline33712 displays extended observed adjusted expectation output for the current adjustment for the partial canonical directions.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

The pcda  and pcda+  options are used to display standard and extended results for the observed adjustments of partial canonical directions. Suppose that tex2html_wrap_inline35844 is a partial canonical direction. Then the standard output consists of its name and its observed adjusted expectation, tex2html_wrap_inline41320 . The extended output consists additionally of its initial expectation (always tex2html_wrap_inline41322 by convention); and its standardised adjustment tex2html_wrap_inline41324 . The option is ignored when there is no partial adjustment.    


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Next: Plotting options Up: Output options Previous: Accessing the results of

David Wooff
Wed Oct 21 15:14:31 BST 1998