Table 44.1 Global statistics

Global Statistics:

Active KID: 35

Active TAP: 20, weighted: 56

Active datapoints: 699 = 99.9% of Active+Missing datapoints, weighted: 1950

Non-extreme datapoints: 544, weighted: 850

Missing datapoints: 1 = .1% of Active+Missing datapoints

Standardized residuals N(0,1): mean: .07 P.SD: .65

Log-likelihood chi-squared: 391.2940 with approximately 418 d.f., probability = .8214

Global Weighted Root-Mean-Square Residual: .1819 with expected value: .1815

Capped Weighted Binomial Deviance: .0450 for 1915.0 dichotomies with expected value: .0478

 

Global statistics:

Statistics based on the currently-selected data, omitting permanently and temporarily deleted, deselected and dropped items and persons

Active person, weighted

Persons currently active in this analysis. Weighted count only if active persons are weighted.

Active item, weighted

Items currently active in this analysis. Weighted count only if active items are weighted.

Active datapoints, weighted

Observations/responses currently active in this analysis (includes extreme scores).  Weighted count only if active items or persons are weighted.

% of Active+Missing datapoints

If any potentially active data are missing, then percent that are active.

Non-extreme datapoints, weighted

Observations/responses currently active in this analysis (excludes extreme scores). Weighted count if any active persons or items are weighted

Missing datapoints

Observations/responses not active in this analysis, usually because they do not have scored values

Standardized residuals N(0,1):

 mean: P.SD:

Standardized Residuals are modeled to have a unit normal distribution. Gross departures from mean of 0.0 and standard deviation of 1.0 indicate that the data do not conform to the basic Rasch model specification that randomness in the data be normally distributed. and standardized residuals to be close to mean 0.0, P.SD 1.0.

Log-likelihood chi-squared:

 

The chi-square value is approximately = -2 * log-likelihood of the active datapoints. It is based on the currently-reported estimates which may depart noticeably from the "true" maximum likelihood estimates for these datapoints.

with approximately .... d.f. +- ....,

the degrees of freedom are obtained by performing 200 simulations of Rasch-conforming data matching the active datapoints. The estimated d.f. will vary slightly with each output of Table 44, as indicated by +-. Each output of Table 44 includes a fresh computation of the d.f. To keep the reported d.f. constant, specify SISEED= a value 2 or greater.

There is an alternative computation of d.f. in Global fit statistics

probability  = ....

the probability that these data fit the Rasch model globally. There can be considerable local misfit in Tables 6 and 10.

Global (Weighted) Root-Mean-Square Residual (RMSR):

this is √(∑(X-E)²) where the sum is across X, each of the observations, and E, the expectation of each observation according to the Rasch model. Weighting is applied to the data if IWEIGHT= or PWEIGHT= are specified.

with expected value:

the expected value of the RMSR according to the Rasch model. RMSR values smaller than the expected value indicate better fit (or overfit) to the Rasch model.

Capped (Weighted) Binomial Deviance (CBD) = ... for ... dichotomies

this is the average of -[X*LOG10(E) + (1-X)*LOG10(1-E)] for all dichotomous observations where X=0,1 is the observation and E is its Rasch-model expectation. E is limited to the range 0.01 to 0.99. Weighting is applied to the data if IWEIGHT= or PWEIGHT= are specified.

Glickman, Mark E. "Parameter estimation in large dynamic paired comparison experiments." Journal of the Royal Statistical Society: Series C (Applied Statistics) 48.3 (1999): 377-394.

with expected value ...

the expected value of the CBD according to the Rasch model. CBD values smaller than the expected value indicate better fit (or overfit) to the Rasch model.

 

Example: Rating Scale Model (RSM) and Partial Credit Model (PCM) of the same dataset. When the models are nested (as they are with RSM and PCM), then we have:

RSM chi-squared and RSM d.f.

PCM chi-squared (which should be smaller) and PCM d.f. (which will be smaller)

Then the model choice could ne based on: (RSM LL chi-square - PCM LL chi-square)  with (RSM-PCM) d.f., but global fit statistics obtained by analyzing your data with conditional Rasch estimation, CMLE, or log-linear models (e.g., in SPSS) will be more exact than those produced by Winsteps.

 

if global fit statistics are the decisive evidence for choice of analytical model, then Winsteps is not suitable. In the statistical philosophy underlying Winsteps, the decisive evidence for choice of model is "which set of measures is more useful" (a practical decision), not "which set of measures fit the model better" (a statistical decision). For the choice between RSM and PCM, see www.rasch.org/rmt/rmt143k.htm.


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