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
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
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 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: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. 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

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

www.rasch.org welcomes your comments:

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


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
May 17 - June 21, 2024, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 12 - 14, 2024, Wed.-Fri. 1st Scandinavian Applied Measurement Conference, Kristianstad University, Kristianstad, Sweden http://www.hkr.se/samc2024
June 21 - July 19, 2024, Fri.-Fri. On-line workshop: Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
Aug. 5 - Aug. 6, 2024, Fri.-Fri. 2024 Inaugural Conference of the Society for the Study of Measurement (Berkeley, CA), Call for Proposals
Aug. 9 - Sept. 6, 2024, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Oct. 4 - Nov. 8, 2024, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 17 - Feb. 21, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
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