Log-linear (or Logistic) Regression vs. Logit-linear Rasch | ||
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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 + (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 Publications | ||||
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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 |
Forum | Rasch Measurement Forum to discuss any Rasch-related topic |
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Coming Rasch-related Events | |
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Jan. 25 - March 8, 2023, Wed..-Wed. | On-line course: Introductory Rasch Analysis (M. Horton, RUMM2030), medicinehealth.leeds.ac.uk |
Apr. 11-12, 2023, Tue.-Wed. | International Objective Measurement Workshop (IOMW) 2023, Chicago, IL. iomw.net |
June 23 - July 21, 2023, Fri.-Fri. | On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com |
Aug. 11 - Sept. 8, 2023, Fri.-Fri. | On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com |
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