Rasch Analysis & Winsteps

Winsteps is Windows-based software which assists with many applications of the Rasch model, particularly in the areas of educational testing, attitude surveys and rating scale analysis. There is more information at: www.winsteps.com


Rasch analysis is a method for obtaining objective, fundamental, additive measures (qualified by standard errors and quality-control fit statistics) from stochastic observations of ordered category responses. Georg Rasch, a Danish mathematician, formulated this approach in 1953 to analyze responses to a series of reading tests (Rasch G, Probabilistic Models for Some Intelligence and Attainment Tests, Chicago: MESA Press, 1992, with instructive Foreword and Afterword by B.D. Wright). Rasch is pronounced like the English word rash in Danish, and like the English sound raa-sch in German. The German pronunciation, raa-sch, is used to avoid misunderstandings.


The person and item total raw scores are used to estimate additive measures. Under Rasch model conditions, these measures are item-free (item-distribution-free) and person-free (person-distribution-free). So that the measures are statistically equivalent for the items regardless of which persons (from the same population) are analyzed, and for the items regardless of which items (from the same population) are analyzed. Analysis of the data at the response-level indicates to what extent these ideals are realized within any particular data set.


The Rasch models implemented in Winsteps include the Georg Rasch dichotomous, Andrich "rating scale", Masters "partial credit", Bradley-Terry "paired comparison", Glas "success model", Linacre "failure model" and most combinations of these models. Other models such as binomial trials and Poisson can also be analyzed by anchoring (fixing) the response structure to accord with the response model. (If you have a particular need, please let us know as Winsteps is continually being enhanced.)


The estimation method is JMLE, "Joint Maximum Likelihood Estimation", with initial starting values provided by PROX, "Normal Approximation Algorithm".


The Rasch Family of Models


The necessary and sufficient transformation of ordered qualitative observations into additive measures is a Rasch model. Rasch models are logit-linear models, which can also be expressed as log-linear models. Typical Rasch models operationalized with Winsteps are:


The dichotomous model:

loge(Pni1 / Pni0 ) = Bn - Di


The polytomous "Rating Scale" model:

log(Pnij/ Pni(j-1) ) = Bn - Di - Fj


The polytomous "Partial Credit" model:

log(Pnij/ Pni(j-1) ) = Bn - Di - Fij = Bn - Dij


The polytomous "Grouped response-structure" model:

log(Pnij/ Pni(j-1) ) = Bn - Dig - Fgj



Pnij is the probability that person n encountering item i is observed in category j,

Bn is the "ability" measure of person n,

Di is the "difficulty" measure of item i, the point where the highest and lowest categories of the item are equally probable.

Fj is the "calibration" measure of category j relative to category j-1, the point where categories j-1 and j are equally probable relative to the measure of the item. No constraints are placed on the possible values of Fj.


Also models with the form of "Continuation Ratio" models, such as the "Success" model and the "Failure" model.


For methods of estimation, see RSA, pp. 72-77.


Work-flow with Winsteps


Control + Data file or Control file and Data file(s)

User-interaction Winsteps Anchor Files

Report Output File + Output Tables + Graphs + Output Files

Word Processor, Spreadsheet, Statistical Package



Winsteps is designed to construct Rasch measurement from the responses of a set of persons to a set of items. Responses may be recorded as letters or integers and each recorded response may be of one or two characters. Alphanumeric characters, not designated as legitimate responses, are treated as missing data. This causes these observations, but not the corresponding persons or items, to be omitted from the analysis. The responses to an item may be dichotomous ("right"/"wrong", "yes"/"no"), or may be on a rating scale ("good"/ "better"/"best", "disagree"/"neutral"/"agree"), or may have "partial credit" or other hierarchical structures. The items may all be grouped together as sharing the one response structure, or may be sub-groups of one or more items which share the same response structure.


Winsteps begins with a central estimate for each person measure, item calibration and response-structure calibration, unless pre-determined, "anchor" values are provided by the analyst. An iterative version of the PROX algorithm is used reach a rough convergence to the observed data pattern. The JMLE method is then iterated to obtain more exact estimates, standard errors and fit statistics.


Output consists of a variety of useful plots, graphs and tables suitable for import into written reports. The statistics can also be written to data files for import into other software. Measures are reported in Logits (log-odds units) unless user-rescaled. Fit statistics are reported as mean-square residuals, which have approximate chi-square distributions. These are also reported t standardized, N(0,1).

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

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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

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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 Winsteps & Facets Events
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
Oct. 12 - Nov. 9, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com



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