4 facet Arithmetic Test: Measuring, Anchoring and Describing

Many measurement problems are best tackled with two Facets runs:


1. Measurement of student ability, judge severity, item difficulty, etc.

The actual participant elements that interacted to provide the observations are measured, and then the elements anchored at those measures. This provides a stable frame of reference for further analyses.


2. Descriptive summaries of various effects identified by demographics, judge training, sub-test content, etc.

Participating elements are replaced by their hypothesized components, and further analyses are performed, with care to provide connected, i.e, unambiguous, measurement conditions.


Using R. Mislevy's data set (extracted from the Armed Services Vocational Aptitude Battery - ASVAB), it is hypothesized that 776 students (black females, black males, white females, and white males) each have an arithmetic ability (a fixed effect). The analyst wants to decompose these abilities into gender (sex) and race (ethnicity) effects. First the item difficulties are calibrated and the 776 examinees measured:


Facets specifications and data (in file Measure.txt):


title = Arithmetic Competency - R. Mislevy

anchorfile = measanc.txt ; an anchored file is written out

facets = 4 ; demographics included in the facets

pt-biserial = y ; point-biserial as a rough fit statistics

vertical = 1N,2A,3A,4* ; for communication

yard = 0, 4 ;

models =

?, , ,?,D ; use this model for measuring items and students

; ?,?,?, ,D ; use this model for demographic summaries - commented out here


positive = 2,3,4 ; all facets except item difficulties are abilities

noncenter = 2,  4 ; noncenter students and one demographic

labels =


1-4 ; 4 arithmetic items











1-776 ; no more information about the students


Data =

1-4,2,2,1,0,0,0,0  ; on the 4 items, white male student 1, failed


1-4,1,1,776,1,1,1,1 ; on the 4 items, black female student 776, succeeded



Dvalues = 1, 1-4  ; place 1-4 in first data facet location of all data records


 2,2,1,0,0,0,0 ; on the 4 items, white male student 1, failed


 1,1,776,1,1,1,1 ; on the 4 items, black female student 776, succeeded


Then the descriptive phase is performed to estimate the demographic effects. This is set up by editing the anchor file produced in the measurement phase, and changing the model statement:


Facets specifications and data (in file Measanc.txt, also in file Meas2anc.txt):


title = Arithmetic Competency - R. Mislevy

; anchorfile = measanc.txt

facets = 4

pt-biserial = y

vertical = 1N,2A,3A,4*

yard = 0, 4

positive =   2,3,4 ; facets 1, 2, 3 this time

noncenter=   2,4 ; facet , Race, 2 floats


;?,,,?,RS1,1, (D) ; comment out the measurement model

 ?,?,?,,RS1,1, (D) ; use the summarizing model


Rating (or partial credit) scale=RS1,D ; use the measurement run rating scale

 0=,0,A, ; Rasch-Andrich thresholds in the description run



1,Arithmetic,A ; these are anchored at their Rasch-Andrich thresholds






2,Race,A ; the A is inoperative, because there are no logit values








4,Students,A ; this facet is ignored this run

1,1,-2.537946 ; these anchored measures are ignored this run



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
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