Multilevel Rasch Model
Also known as: hierarchical Rasch model, random-effects Rasch model, multilevel IRT Rasch, MRCML model
The multilevel Rasch model extends the standard Rasch model to data with a nested structure — for example, students within classrooms within schools — by embedding person ability parameters inside a hierarchical linear model. It yields item difficulty estimates on a logit scale while simultaneously partitioning person-ability variance across cluster levels and correcting standard errors for non-independence.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
When to use it
Use the multilevel Rasch model when item response data are nested within identifiable clusters and the intraclass correlation at the cluster level is non-negligible (typically ICC > 0.05). Typical settings include large-scale educational assessments with students nested in schools, clinical outcomes with patients nested in hospitals, and organizational surveys with employees nested in teams. The method requires a reasonable number of clusters (at least 20–30 for stable variance-component estimates) and sufficient respondents per cluster. Do not use a standard (single-level) Rasch model when clustering is present, as it underestimates standard errors of item parameters and person ability estimates. Do not use the multilevel Rasch model when data are not genuinely nested or when cluster sizes are extremely small (fewer than 5 respondents per cluster on average).
Strengths & limitations
- Correctly accounts for non-independence of observations within clusters, producing unbiased item-difficulty estimates and valid standard errors.
- Decomposes variance in person ability into within-group and between-group components, revealing the substantive importance of context.
- Supports inclusion of person-level and group-level covariates to explain ability variation at each hierarchical level.
- Retains all the interpretive advantages of the Rasch model — item difficulties on a common logit scale, person-free item calibration — while extending to clustered designs.
- Compatible with polytomous Rasch extensions (partial credit model, rating scale model) for Likert-type items.
- Requires many clusters (at least 20–30) for reliable between-group variance-component estimates; small numbers of clusters yield biased standard errors at the group level.
- Estimation is computationally intensive, especially with three or more levels or large item banks, compared to standard Rasch software.
- Software options are fewer and more specialized than for standard Rasch or multilevel regression; ConQuest and dedicated R packages (TAM, lme4 with IRT extensions) are main options.
- Model complexity can obscure interpretation when many levels or covariates are included simultaneously.
- The assumption of normal random effects at each level may not hold for all populations.
Frequently asked
How is the multilevel Rasch model different from testing differential item functioning (DIF)?
DIF tests whether an item is harder for one identifiable subgroup than another after controlling for ability — it is about item parameters differing across groups. The multilevel Rasch model instead treats group membership as a source of random variation in person ability, partitioning ability variance across levels. The two analyses address different questions and are often used together: fit the multilevel model to obtain unbiased ability estimates, then test DIF on top of that.
How many clusters do I need for stable variance-component estimates?
A commonly cited minimum is 20–30 clusters for the highest level of the hierarchy. With fewer clusters the between-group variance component tau^2 is estimated with poor precision and confidence intervals are wide. Simulation studies suggest that 30 or more clusters with at least 5 respondents each give satisfactory coverage.
Can the multilevel Rasch model handle polytomous items, such as Likert scales?
Yes. The multilevel partial credit model and multilevel rating scale model extend the framework to polytomous items in exactly the same way that those models extend the basic Rasch model. Software such as ConQuest and the R package TAM supports polytomous multilevel estimation.
What software can I use to fit a multilevel Rasch model?
ConQuest (Adams, Wu & Wilson) is the most widely used dedicated software. The R package TAM (Test Analysis Modules) provides MML estimation for a broad class of multilevel IRT models. For Bayesian estimation the mlirt package in R implements the Fox–Glas MCMC approach. lme4 combined with manual logit offsets is an alternative but requires more programming effort.
Should I use the multilevel Rasch model or multilevel confirmatory factor analysis?
Both handle nested data, but they rest on different measurement theories. The Rasch model places persons and items on the same logit scale, assumes a specific item discrimination (all equal to 1), and provides person-free item calibration. Multilevel CFA is more flexible with factor loadings but operates in a covariance-structure framework without the Rasch-specific probabilistic interpretations. Choose Rasch when you want logit-scale measurement and can defend the equal-discrimination assumption; choose CFA when you need freely estimated factor loadings or are working with continuous indicators.
Sources
- Adams, R. J., Wilson, M. & Wu, M. (1997). Multilevel item response models: An approach to errors in variables regression. Journal of Educational and Behavioral Statistics, 22(1), 47–76. DOI: 10.3102/10769986022001047 ↗
- Fox, J.-P. & Glas, C. A. W. (2001). Bayesian estimation of a multilevel IRT model using Gibbs sampling. Psychometrika, 66(2), 271–288. DOI: 10.1007/BF02294839 ↗
How to cite this page
ScholarGate. (2026, June 3). Multilevel Rasch Model. ScholarGate. https://scholargate.app/en/psychometrics/multilevel-rasch-model
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Differential Item FunctioningPsychometrics↔ compare
- Item Response TheoryPsychometrics↔ compare
- Multilevel CFAPsychometrics↔ compare
- Multilevel Measurement InvariancePsychometrics↔ compare
- Rasch ModelPsychometrics↔ compare