Subset connection demonstration

Here is the "Minimal Effort Judging Plan":

Figure A.8. Minimal effort judging plan from www.rasch.org/rn3.htm

In this plan, each person writes 3 essays (A,B,C). For each person, each essay is rated by a different rater, so that each essay is rated only once, resulting in the minimum rater effort. However, all persons, raters and essays are comparable because all ratings form one connected set of data. Here is the procedure to verify the data connection:

 

1.The ratings are processed consecutively.
Example: the ratings in the plan are stored by columns so each of the 12x3 = 36 columns of data is scanned in turn.
 

2.Lists of connected elements are constructed. When the elements of two facets for an observation are the same as the elements of two facets for another observation, the two observations are connected in the same subset and their elements are added to the subset's list.
Example: Persons 3 and 6 are connected because they share Rater 1 and Essay A, as does Person 12. So they are added to subset list 1. Rater 1, Essay B and Persons 13, 15, 28 are added to list 2. Rater 1, Essay C and Persons 14 and 30 are added to list 3.  
 

3.Scanning down the columns of observations in this way, 36 lists of connected elements are constructed. A list may contain the elements for only one observation.
 

4.Pairs of lists are compared and lists with connected elements are combined. When the same elements of two facets appear in two lists, then the lists are combined.
Example: List 1 has Rater 1, Essay B, Persons 3, 6, 12. List 29 has Rater 10, Essay B, Persons 3, 5. Essay B and Person 3 are common to the two lists, so the two lists, and so the two subsets of ratings, are combined. The combined list is Raters 1, 10, Essay B, Person 3, 5, 6, 12.
 

5.Paired comparison of lists continues until no more lists can be connected. The final lists contain the details of the disconnected subsets. An element can be in several disconnected subsets.
Example: for this plan, the 36 lists connect and are combined until there is only one list. The ratings in the data are connected.

 

Here is the Facets specification and data file:

 

Title = "Minimal effort judging plan"

Facets=3

Models=?,?,?,R9

Subsets=Yes

Labels=

1,Person

1-32

*

2, Judge

1-12

*

3, Essay

1=A

2=B

3=C

*

Dvalues=3,1-3 

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