Weighting the data
There are 3 methods of weighting:
These multiply to give a combined weight to each observation.
The true reliability of the measures is from the unweighted analysis. Weighting introduces an arbitrariness into the analysis. One solution is to adjust the weights to maintain the unweighted reliability = Ru. The reliability of the weighted analysis, using an initial set of weights, = Rw. We can then scale the weights using the Spearman-Brown Prophecy Formula: S = Ru * (1-Rw) / ((1-Ru)*Rw)). Multiply the initial set of weights by S. Then the weighted and unweighted reliabilities should be the same.
Weighting sub-tests: Example: Two Cases: A and B. Four aspects: Taste, Touch, Sound, Sight.
Case A Taste weight twice as important as the rest.
Case B Sound weight twice as important as the rest.
?, 1, 1, MyScale, 2 ; Case A Taste weighted 2
?, 2, 3, MyScale, 2 ; Case B Sound weighted 2
?, ?, ?, MyScale, 1 ; everything else weighted 1
Rating scale = MyScale, R9, General ; this rating scale is the same for all models
If you want to keep the "reliabilities" and standard errors meaningful then adjust the weights:
Original total weights = 2 cases x 4 aspects = 8
New total weights = 2 + 2 + 6 = 10
Weight adjustment to maintain total weight is 8/10.
So adjusted weighting is:
?, 1, 1, MyScale, 1.6 ; Case A Taste
?, 2, 3, MyScale, 1.6 ; Case B Sound
?, ?, ?, MyScale, 0.8 ; everything else
Replication of a data point: can be specified by R (or another replication character) and the number of replications, for instance:
R3,2,23,6,4 means that the value of 4 was observed in this context 3 times.
Fractional replication permits flexible observation-weighting:
R3.5,2,23,6,4 means that the value of 4 was observed in this context 3.5 times.
Weighting observations: We want to give some incorrect answers a smaller penalty than other incorrect answers. There are two ways to do this:
1) in the data:
3 facets + correct
3 facets + incorrect
3 facets + half-weight incorrect
R0.5, 2,3,4, 0
2) with a Models= specification
; 3 facets + dummy indicator facet + correct/incorrect
?,?,?,1,D,1 ; full weight
?,?,?,2,D,0.5 ; half weight
4, Weighting, A
1 = Full weight, 0
2 = Half weight, 0
3 facets + indicator +correct
2,3,4, 1, 1
3 facets + indicator + incorrect
2,3,4, 1, 0
3 facets + indicator +half-weight incorrect
2,3,4, 2, 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|
|in Spanish:||Análisis de Rasch para todos, Agustín Tristán||Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez|
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|Jan. 5 - Feb. 2, 2018, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
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|Jan. 22-24, 2018, Mon-Wed.||In-person workshop: Rasch Measurement for Everybody en español (A. Tristan, Winsteps), San Luis Potosi, Mexico. www.ieia.com.mx|
|April 10-12, 2018, Tues.-Thurs.||Rasch Conference: IOMW, New York, NY, www.iomw.org|
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|June 29 - July 27, 2018, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|July 25 - July 27, 2018, Wed.-Fri.||Pacific-Rim Objective Measurement Symposium (PROMS), (Preconference workshops July 23-24, 2018) Fudan University, Shanghai, China "Applying Rasch Measurement in Language Assessment and across the Human Sciences" www.promsociety.org|
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