Estimating Rasch Models with Stata
Conditional (fixed-effects) Logistic Regression

For short tests of i=1,L dichotomous items taken by n=1,N subjects, we can easily obtain conditional-maximum-likelihood estimates of the item difficulty parameters, D_i, of the Rasch model using the logit fixed-effects estimator in the clogit and xtlogit, fe commands of Stata. Data may be unbalanced.

These commands require that all responses (usually coded, 0/1) are stored in separate observations, while a group-variable is used to identify the observations that belong to the same subject. The reshape command may be useful to convert data into this format.

We describe the Rasch model to Stata as a "conditional logit model" with L covariates x(nik), k=1,L, so that x(nik) = -1 if i=k, and 0 otherwise. The regression coefficient of x(..k) becomes D_k. In order to set the origin of the Rasch measurement scale, Stata will automatically withdraw the first predictor variable D₁ and fix it at zero. Alternatively, and better, is to withdraw the most stable of the D_i yourself.

Here is the procedure for obtaining item calibrations:

(1) if necessary, transform the data into long-format
reshape item*, n(subject_id) j(ItemID)

(2) create explanatory variables for the D_i
for num 1/L : gen D = -(X==ItemID)

(3) estimate the D_i parameters
clogit item D*, group(subject_id)
or
xtlogit item D*, n(subject_id) fe

Example: The responses of 120 subjects to 10 math problems are coded as 1 (correct) and 0 (incorrect) - see Subject Score Distribution Table. I want to know whether the 10 problems maintain their difficulties, regardless of the subjects' abilities.

Apply clogit - the box above shows selected output.

To examine item difficulty invariance, we compare the item calibrations obtained from the full sample with those obtained from the low-performing (scores<=5) and high-performing (scores>=5) subjects. The box below shows selected results.

We are pleased to see that for low scorers, the items are exhibiting statistical invariance according to the hausman test. Nevertheless, items 7, 9 and 10 (the harder items) are somewhat problematic, meriting further investigation. For high scorers, it appears that almost all items have become about 1 logit more difficult. In fact, it is item 1 that has become about 1 logit easier. Item 1 is the easiest item and is most off target for the high scorers. This illustrates the need to choose the fixed (i.e., withdrawn) item carefully in order to avoid confusion in interpreting results. After an adjustment is made for item 1, the item difficulties are seen to be statistically invariant also for the high scorers.

If the wording of the items is known, then producing an item map of the construct based on these item difficulty calibrations is straightforward via the Stata graphical plotting command graph.

Once item difficulties have been computed, the subject measures may be estimated (via maximum-likelihood, conditional on the estimates of the item parameter) via logit (combined with byvar).

With the Stata command xtlogit, re, it is easy to estimate the Rasch model in which the person-parameters are treated as random effects, conditional on person-level variables.

For complete details of this analysis, see www.stata.com/support/faqs/stat/rasch.html

Jeroen Weesie
Department of Sociology/ICS
Utrecht University

Estimating Rasch Models with Stata: Conditional (fixed-effects) Logistic Regression, Weesie J. … Rasch Measurement Transactions, 2000, 13:4 p. 724

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

Forum

Rasch 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.

The URL of this page is www.rasch.org/rmt/rmt134g.htm

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