﻿ Between-group and Within-group fit statistics

# Between-group and Within-group fit statistics

Richard Smith (1982, 2009) proposes group-level fit statistics. These statistics indicate more or less consistency across CLASSes. Lack of consistency may indicate  DIF or DPF or some other interaction across CLASSes or inside of CLASSes.

For each item, the persons are segmented into CLASSes using DIF=

Table 30.4 - Between-group fit statistic for person CLASSes:

"This fit statistic is based on the difference between an item's observed score on a subset of persons and the score on that subset as predicted by the item's overall difficulty estimate."

Table 30.5 - Within-group outfit statistic for a person CLASS for an item:

The outfit mean-square statistic for the item computed only across persons in the person CLASS.

Table 30.5 - Within-group infit statistic for an item CLASS for a person:

The infit mean-square statistic for the item computed only across persons in the person CLASS.

For each person, the items are segmented into CLASSes using DPF=

Table 31.4 - Between-group fit statistic for item CLASSes:

"This fit statistic is based on the difference between a person's observed score on a subset of items and the score on that subset as predicted by the person's overall ability estimate."

Table 31.5 - Within-group outfit statistic for an item CLASS for a person:

The outfit mean-square statistic for the person computed only across items in the item CLASS.

Table 31.5 - Within-group infit statistic for an item CLASS for a person:

The infit mean-square statistic for the person computed only across items in the item CLASS.

Smith RM, Hedges LV. Comparison of Likelihood Ratio χ² and Pearsonian χ² Tests of Fit in the Rasch Model. Education Research and Perspectives, 1982; 9(1):44-54

Smith RM, Plackner C. The family approach to assessing fit in Rasch measurement. Journal of Applied Measurement. 2009;10(4):424-37

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

 Forum Rasch Measurement Forum to discuss any Rasch-related topic

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