Model statement examples

Model statements are best understood through examples. Here are a number of model statements which could be used in an analysis where

Persons comprise facet 1,

Items comprise facet 2,

Judges comprise facet 3.

 

More information: details of Models= and Matching data with measurement models.

 

Model= 23,?,?,M

When person 23 ("23" for facet 1) is rated on any item ("?" for facet 2) by any judge ("?" for facet 3), treat the datum as missing ("M"). This has the effect of deleting person 23.

 

Model= ?,1,?,D

For any person ("?") rated on item 1 ("1") by any judge ("?"), treat the "0" and "1" data as dichotomous ("D"), i.e.,
log() = Bn - D1 - Cj for item i=1

 

Model= ?,2,?,D3

For any person ("?") rated on item 2 ("2") by any judge ("?") dichotomize the data ("D3"), treating 0,1,2 as 0, and 3 and above as 1, i.e.,
log() = Bn - D2 - Cj with data recoding for item i=2

 

Model= ?,2,?,R

For any person ("?") rated on item 2 ("2) by any judge ("?") use a common rating scale (or partial credit) ("R"). Valid ratings are in the range 0 through 9, i.e.,
log() = Bn - D2 - Cj - Fk for i=2, k=1,9

 

Model= ?,2,?,R2

For any person ("?") rated on item 2 ("2) by any judge ("?") use a common rating scale (or partial credit) ("R"). Valid ratings are in the range 0 through 2, i.e.,
log() = Bn - D2 - Cj - Fk for i=2, k=1,2

 

Model= ?,3,#,R

Let each judge ("#") apply his own version of the rating scale ("R"), i.e., a partial credit scale, to every person ("?") on item 3 ("3"), i.e.,
log() = Bn - D3 - Cj - Fjk for i=3, k=1,9

 

Model= ?, ,?,B2

For each person ("?"), ignore the item number (", ,") and let every rating by each judge ("?") be considered two binomial trials ("B2") scored 0 or 1 or 2, i.e.,
log() = Bn - Di - log(k/(3-k)) for k=1,2

 

Model= ?,?,0,P

For each person ("?") observed on each item ("?") which is not judged ("0"), the data are Poisson counts of successes. These are in the theoretical range of 0 to infinity, but in the empirically observed range of 0 to 255, i.e.,
log() = Bn - Di - log(k) for k=1,...

 

Model= ?,?,?,R,2

For any person ("?") rated on any ("?") by any judge ("?") use a common rating scale ("R"), but give each datum a double weight in the estimation, i.e.,
log() = Bn - Di - Cj - Fk for k=1,9

 

Model= ?B,?,?B,D

For any person ("?B") rated on any item ("?") by any judge ("?B"), the data are on a dichotomous scale ("D"), i.e.,
log() = Bn - Di - Cj

 

Then, after that estimation has been completed and all measures and rating-scale structures have been anchored, estimate bias measures for the bias interactions between each person ("?B") and each judge ("?B") across the whole data set for all models specified, i.e.,

log() = {Bn,Di,Cj,Fk,...} + Cnj
where {...} are the final estimates of the previous stage used as anchors and only the Cnj bias terms are now estimated. Cnj terms are appended to all model statements. The modeled expectation of Cnj is zero, but the mean of all estimated Cnj will not be zero due to the non-linear conversions between accumulated raw score residuals and bias measures in logits. Each bias term is a diagnostic specialization which turns a systematic misfit into a measure.

 

Model= ?,-?,?,D

For any person ("?") rated on any item ("-?") by any judge ("?"), the outcome is a dichotomy ("D"). The orientation of the second, item facet is reversed ("-") for data matching this model only, i.e.,
log() = Bn - (-Di) - Cj = Bn + Di - Cj

 

Model= ?, ,?,R

For any person ("?"), irrespective of the item (" "), rated by any judge ("?"), the outcome is a rating ("R"). The item facet is ignored, except that, if the item element number for a matching datum is not specified after Labels=, the datum is treated as missing.

 

Model= ?,X,?,R

For any person ("?"), irrespective of the item ("X"), rated by any judge ("?"), the outcome is a rating ("R"). The item facet is entirely ignored, so that, even if the item element number for a matching datum is not specified after Labels=, the datum is still treated as valid. If a facet is never referenced anywhere, then it may be more convenient to use Entry= rather than "X".


Help for Facets Rasch Measurement Software: www.winsteps.com Author: John Michael Linacre.
 

For more information, contact info@winsteps.com 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 Publications
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
Jan. 5 - Feb. 2, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 10-16, 2018, Wed.-Tues. In-person workshop: Advanced Course in Rasch Measurement Theory and the application of RUMM2030, Perth, Australia (D. Andrich), Announcement
Jan. 17-19, 2018, Wed.-Fri. Rasch Conference: Seventh International Conference on Probabilistic Models for Measurement, Matilda Bay Club, Perth, Australia, Website
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
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
 

Concerned about aches, pains, youthfulness? Mike and Jenny suggest Liquid Biocell