Expected Score ICC, IRF

 

Select by clicking on "Expected Score ICC" or from the Graphs menu. Expected Score ICC plots the model-expected item characteristic curve, also called the Item Response Function, IRF. This shows the Rasch-model prediction for each measure relative to item difficulty Its shape is always ascending monotonic. The dashed lines indicate the Rasch-half-point thresholds correspond to expected values of .5 score points. The intervals on the x-axis demarcated by dashed lines are the zones within which the expected score rounds to each observed category. To remove the dashed lines, double-click on them.

 

The plot is of the "model item characteristic curve (ICC)" , also called the "item response function (IRF)". This is used for inference. If we know the score on the item, we can infer the ability of the person responding. If we know the ability of the person responding, we can infer the expected score on the item.

 

(difficulty of item + person's score on the item on y-axis) -> person's ability on x-axis

 

(person's ability on x-axis - difficulty of item) -> expected score on the item on y-axis

 

Item discrimination: the item is more discriminating where the ICC is steeper, and less discriminating where the ICC is flatter.

 

Buttons are described in Graph window.

 


 

Computation of the IRF

 

For an item with categories k=0,1,2,...,m and Andrich Thresholds Fk, with F0 chosen to be 0, then

 

At location x on the latent variable (relative to the item difficulty), the probability of observing category k is

 

Pk(x) = exponential( k*x - sum(Fh) for h=0 to k) / sump(x)

 

sumpx = sum (exponential( k*x - sum(Fh) for h=0 to k)) for k=0 to m

 

The expected score y at location x is given by

 

y = sum (k*Pk(x)) for k=0 to m

 


 

Computation of the Half-Point Threshold

 

The formula for the half-point threshold is solved iteratively, for category j, the half-point threshold is at  point x (relative to the item difficulty) given by

 

j - 0.5 = sum (k*Pk(x)) for k=0 to m

 

 


Help for Winsteps 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