3 facet Subset reconnection
Here is an example, using Guilford's data, of data that lack sufficient connection to yield unambiguous measure estimates. It reports subsets. In this example, pairs of judges rate subsets of examinees, but without crossing (overlap). Did Betty get the highest score because she was the most able or because her judges were more lenient? The data can't tell us. There is more about this in the discussion of subset connectedness.
Facets specifications and data (in file Subsets.txt):
Title = Ratings of Scientists (edited to illustrate ambiguity in measurement)
Facets = 3 ; three facets: judges, examinees, items
Umean = 50, 10 ; user-scaling = 50 +logit*10
Positive = 1,2,3 ; the examinees have greater creativity with greater score
Non-centered = 1 ; examinees and items are centered on 0, judges are allowed to float
Model = ?,?,?,R9 ; judges, examinees and items produce ratings on "Creativity".
Labels= ; to name the components
1,Judges ; name of first facet
1=Avogadro ; names of elements within facet
2=Brahe ; these must be named, or they are treated as missing
Dvalues = 3, 1-5 ; put in constant value for the 3 facet entry in the data
1,1, 5,5,3,5,3 ; typical paired-rater design
1,2, 9,7,5,8,5 ; raters 1 and 2 rate examinees 1, 2, 3
3,4, 5,3,3,3,1 ; raters 3 and 4 rate examinees 4, 5, 6, 7
In the Iteration Report to the screen:
Consolidating 2 subsets..
2 subsets remain
Warning (6)! There may be 2 disjoint subsets
In the Output file:
Table 6.0.0 Disjoint Subset Element Listing.
Subset number: 1
Facet: 1. Judges 2 Elements: 1 2
Facet: 2. Examinees 3 Elements: 1-3
Subset number: 2
Facet: 1. Judges 2 Elements: 3 4
Facet: 2. Examinees 4 Elements: 4-7
Investigating the ambiguity:
Click on the Output Files Menu pull-down menu
Click on Winsteps control & data file
This enables you to construct data files showing the pattern of responses of one facet against another. Subsetting will show as distinctive patterns.
Here is what it looks like with Examinees as rows, and Judges as columns:
1 Anne ; item-column labels
5 9 3 . . . . 1 Avogadro ; row data + label
6 8 4 . . . . 2 Brahe
. . . 5 9 3 7 3 Cavendish
. . . 5 2 4 3 4 Davey
Click on the Output Files Menu pull-down menu.
Click on Subset group-anchor file.
To resolve subset problems, copy-and-paste after Labels=
Non-center= must reference a facet that is not anchored or group-anchored.
Group anchor this facet:
1,Judges, G ; group-anchoring at Umean = 50
And/or group anchor this facet:
2,Examinees, G ; group-anchoring at Umean = 50
To establish an unambiguous measurement structure,
(a) We can assert that the rater pairs have the same mean severity (i.e., are randomly equivalent) using group-anchoring:
Non-center=2 ; facet 2 is allowed to float, because facet 1 will be group-anchored.
1,Judges, G ; group-anchor
1=Avogadro,50, 1 ; rater 1 is in group 1 with a mean value of 0.
3=Cavendish,50, 2 ; rater 3 is in group 2 with a mean value of 0.
or (b) We can assert that the examinee samples have the same mean ability (i.e., are randomly equivalent):
Non-center=1 ; facet 1 is allowed to float, because facet 2 will be group-anchored.
2,Examinees, G ; group-anchor
1=Anne,50, 1 ; examinee 1 is in group 1 with a mean value of 0
4=David,50, 2 ; examinee 2 is in group 1 with a mean value of 0
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|Rasch Measurement Transactions (free, online)||Rasch Measurement research papers (free, online)||Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch||Applying the Rasch Model 3rd. Ed., Bond & Fox||Best Test Design, Wright & Stone|
|Rating Scale Analysis, Wright & Masters||Introduction to Rasch Measurement, E. Smith & R. Smith||Introduction to Many-Facet Rasch Measurement, Thomas Eckes||Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments, George Engelhard, Jr. & Stefanie Wind||Statistical Analyses for Language Testers, Rita Green|
|Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar||Journal of Applied Measurement||Rasch models for measurement, David Andrich||Constructing Measures, Mark Wilson||Rasch Analysis in the Human Sciences, Boone, Stave, Yale|
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