rnc for robustness_properties

[John P. Morgan]

Dear All,

Below is a proposal for the rnc element robustness_properties. Please criticize 
as needed. Thanks.

JP


DEFINITIONS and EXPLANATION of RNC
----------------------------------

Statistical robustness of a block design is defined as its ability to maintain
desirable statistical properties under loss of individual plots or entire
blocks.  A catastrophic result of such a loss is that the design become
disconnected.  Less catastrophic but of genuine concern are losses in the
information provided by the design, as measured by various optimality criteria.
The two elements of robustness_properties accommodate these two perspectives.

The element robust_connected makes the statement
 "The design is connected under all possible ways in which
             number_lost category_lost
  can be removed" 
If the reported value of number_lost is known to be the largest integer for 
which this statement is true then is_max takes the value "true" and otherwise 
takes the value "unknown."

The element robust_criteria_values reports A, E, D, and MV efficiencies for a
given number (number_lost) of plots or blocks (category_lost) removed from the
design.  The efficiencies can be calculated from two different perspectives.  If
loss_measure="average" then the criterion value used is the average of all its
values over all possible deletions of the type and number prescribed.  If
loss_measure="worst" then the criterion value used is the maximum of all its
values over all possible deletions of the type and number prescribed.



NOTES
-----

1. Balance measures have not been incorporated under robust_criteria_values.  
This
is because designed balance is typically severely affected by plot/block loss
and in ways that need have no relation to treatment structure.

2. The calculations associated with the values reported here can be quite 
expensive.



RNC
---

robustness_properties = element robustness_properties { 
    robust_connected * ,
    robust_criteria_values * 
}

robust_connected = element robust_connected {
    attribute category_lost { "plots" | "blocks" } ,
    attribute number_lost { xsd:positiveInteger } ,
    attribute is_max { "true" | "unknown" }
}

robust_criteria_values = element robust_criteria_values {
    attribute precision { xsd:positiveInteger } ,
    attribute category_lost { "plots" | "blocks" } ,
    attribute number_lost { xsd:positiveInteger } ,
    attribute loss_measure { "average" | "worst" } ,
    element phi_0 {
        # sum of log(z_i)
        robustness_value
    } ?
    &
    element phi_1 {
        # mean of the z_i
        robustness_value
    } ?
    &
    element maximum_pairwise_variances {
        # largest of the v_{ij}
        robustness_value
    } ?
    & 
    element E_1 { 
        # E_1=z_1 is often called "the" E-value
        robustness_value
    } ? 
}

robustness_value = element robustness_value { 
    # self_efficiency =       (value of the criterion for the full design)/
    #                          (value for the reduced design)
    # absolute_efficiency =   (value for best in reduced binary class)/
    #                          (value for the reduced design)
    # calculated_efficiency = (value for best in selected list of designs)/
    #                          (value for the reduced design)
    attribute self_efficiency   { xsd:decimal }  ,
    attribute absolute_efficiency   { xsd:decimal | "not_applicable" | "unknown" 
} ? ,
    attribute calculated_efficiency { xsd:decimal } ?
}