Log-linear (or Logistic) Regression vs. Logit-linear Rasch

Estimation Log-linear Rasch (CMLE) Logit-linear Rasch (JMLE)
Data matrix Contingency table: one cell per response string and demographic combination:
4 dichotomies + 2 genders: 2x2x2x2x2 = 32 cells (see TGK)
3 4-category items: 4x4x4 = 64 (Agresti)		 Response strings for all subjects. Persons coded with demographic variables.
Missing data Must be imputed or subject omitted Merely lessens precision
Basic element Frequency of persons in cell: e.g., (TGK)
F{X1010M} for response string "1010", Male		 Observation: Xni
Model Loge(F{X1010}) =
1*E1 + 0*E2 + 1*E3 + 0*E4 + š(1+0+1+0) (see TGK)		 loge(Pni1/Pni0) = Bn + Ei
Interaction terms Yes, but no longer Rasch model Yes, post-hoc to explain residuals
Constraints To eliminate terms, and establish local origin. To establish local origin
Estimation bias Negligible - equivalent to Conditional Maximum Likelihood (CMLE) Rasch Up to 2, corrected by (L-1)/L
Global fit Decisive as to acceptability of model. Uninformative
Items
Maximum items 13, i.e., 213 cells >3,000
Item calibrations Yes, but relative to the anchored item Yes, with mean calibration of zero or anchor item(s).
Item S.E. Test-dependent, because relative to anchored item. Anchored item has S.E.=0 As test-independent as possible. S.E.s reported for all items.
Item fit diagnosis Unexpected cell frequencies, summarized by tests of local independence (see TGK) Unexpected response patterns, summarized by sums of residuals
Persons
Maximum persons Unlimited, because accumulated in cells >20,000
Person measures Only obtained by secondary analysis Yes, modeled
Person S.E. Obtained by secondary analysis Yes, modeled
Person fit diagnosis Unexpected cell frequencies:
Agresti: 8 strings of "322", but 2.9 expected		 Unexpected response patterns:
in Agresti data: pattern "122".
Unexpected responses No Yes, by residual size
Best for
Item calibration <=13 items with local S.E.s >=5 items with general S.E.s
Person measurement No Yes
Misfit diagnosis No Yes
Software Standard statistical: SAS, SPSS Custom: BIGSTEPS, QUEST

John Michael Linacre

Agresti: Agresti A (1993) Computing conditional maximum likelihood estimates for generalized Rasch models using simple log-linear models with diagonals parameters. Scandinavian Journal of Statistics 20(1) 63-71.

TGK: TenVergert E, Gillespie M, & Kingma J (1993) Testing the assumptions and interpreting the results of the Rasch model using log-linear procedures in SPSS. Behavior Research Methods, Instruments & Computers 25(3) 350-359.

Log-linear (logistic) regression vs. Logit-linear Rasch. Linacre J.M. … Rasch Measurement Transactions, 1997, 11:3 p. 586.



Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn. George Engelhard, Jr. & Jue Wang Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes Statistical Analyses for Language Testers (Facets), Rita Green Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind Rasch Measurement: Applications, Khine Winsteps Tutorials - free
Facets Tutorials - free		 Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan
Other Rasch-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse Rasch Measurement Theory Analysis in R, Wind, Hua Applying the Rasch Model in Social Sciences Using R, Lamprianou El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Rasch Models for Measurement, David Andrich Constructing Measures, Mark Wilson Best Test Design - free, Wright & Stone
Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias Diseño de Mejores Pruebas - free, Spanish Best Test Design A Course in Rasch Measurement Theory, Andrich, Marais Rasch Models in Health, Christensen, Kreiner, Mesba Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen

To be emailed about new material on www.rasch.org
please enter your email address here:

I want to Subscribe: & click below
I want to Unsubscribe: & click below

Please set your SPAM filter to accept emails from Rasch.org

Rasch Measurement Transactions welcomes your comments:

Your email address (if you want us to reply):

If Rasch.org does not reply, please post your message on the Rasch Forum
 

ForumRasch Measurement Forum to discuss any Rasch-related topic

Go to Top of Page
Go to index of all Rasch Measurement Transactions
AERA members: Join the Rasch Measurement SIG and receive the printed version of RMT
Some back issues of RMT are available as bound volumes
Subscribe to Journal of Applied Measurement

Go to Institute for Objective Measurement Home Page. The Rasch Measurement SIG (AERA) thanks the Institute for Objective Measurement for inviting the publication of Rasch Measurement Transactions on the Institute's website, www.rasch.org.

Coming Rasch-related Events
Apr. 21 - 22, 2025, Mon.-Tue. International Objective Measurement Workshop (IOMW) - Boulder, CO, www.iomw.net
Jan. 17 - Feb. 21, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Feb. - June, 2025 On-line course: Introduction to Classical Test and Rasch Measurement Theories (D. Andrich, I. Marais, RUMM2030), University of Western Australia
Feb. - June, 2025 On-line course: Advanced Course in Rasch Measurement Theory (D. Andrich, I. Marais, RUMM2030), University of Western Australia
May 16 - June 20, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 20 - July 18, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Further Topics (E. Smith, Facets), www.statistics.com
Oct. 3 - Nov. 7, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com

 

The URL of this page is www.rasch.org/rmt/rmt113r.htm

Website: www.rasch.org/rmt/contents.htm