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
Help for Facets Rasch Measurement Software: www.winsteps.com Author: John Michael Linacre.
For more information, contact firstname.lastname@example.org or use the Contact Form
|Facets Rasch measurement software.
Buy for $149. & site licenses.
Freeware student/evaluation download
Winsteps Rasch measurement software. Buy for $149. & site licenses. Freeware student/evaluation download
|State-of-the-art : single-user and site licenses : free student/evaluation versions : download immediately : instructional PDFs : user forum : assistance by email : bugs fixed fast : free update eligibility : backwards compatible : money back if not satisfied|
Rasch, Winsteps, Facets online Tutorials
|Forum||Rasch Measurement Forum to discuss any Rasch-related topic|
Click here to add your email address to the Winsteps and Facets email list for notifications.
Click here to ask a question or make a suggestion about Winsteps and Facets software.
|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|
|Winsteps Tutorials||Facets Tutorials||Rasch Discussion Groups|
|Coming Rasch-related Events|
|April 10-12, 2018, Tues.-Thurs.||Rasch Conference: IOMW, New York, NY, www.iomw.org|
|April 13-17, 2018, Fri.-Tues.||AERA, New York, NY, www.aera.net|
|May 22 - 24, 2018, Tues.-Thur.||EALTA 2018 pre-conference workshop (Introduction to Rasch measurement using WINSTEPS and FACETS, Thomas Eckes & Frank Weiss-Motz), https://ealta2018.testdaf.de|
|May 25 - June 22, 2018, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 27 - 29, 2018, Wed.-Fri.||Measurement at the Crossroads: History, philosophy and sociology of measurement, Paris, France., https://measurement2018.sciencesconf.org|
|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|
|Aug. 10 - Sept. 7, 2018, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
|Sept. 3 - 6, 2018, Mon.-Thurs.||IMEKO World Congress, Belfast, Northern Ireland www.imeko2018.org|
|Oct. 12 - Nov. 9, 2018, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
Our current URL is www.winsteps.com
Winsteps® is a registered trademark
|Mike L.'s Wellness Report: Effective weight loss program? The Mediterranean Diet, especially the M3 version|