README.md

In easyRasch2: Psychometric Analysis with Rasch Measurement Theory

easyRasch2

easyRasch2 is an R package for Rasch measurement theory analysis workflows. It is the successor to easyRasch, offering a lightweight and consistent structure with proper namespacing and minimal dependencies.

A central design choice is simulation-based critical values for various fit statistics. Rather than relying on rule-of-thumb cutoffs, most diagnostics are paired with a parametric-bootstrap function that generates an empirical null distribution from the fitted Rasch / PCM model and the observed sample (Johansson, 2025, 2026).

The Get Started link above contains a short introduction. For broader Rasch-analysis tutorials, see the vignette for the archived sibling package easyRasch.

Statement of need

A complete Rasch analysis requires many separate procedures: item fit, local dependence, dimensionality, differential item functioning, reliability, targeting, and more. In R these are spread across packages with differing data formats, argument conventions, and output objects, which raises the barrier to entry and can make analyses hard to reproduce. A further problem is that fit statistics (item fit MSQ, Yen's $Q_3$ residuals, the first residual-PCA contrast, CFA fit indices) are usually judged against fixed rule-of-thumb cutoffs that are known to depend on sample size, number of items and other factors such as targeting, and the number of response categories.

easyRasch2 targets applied researchers and students validating rating scales and tests in health, education, and psychology using modern psychometric methods. It provides a single, consistently named interface across the whole workflow with publication-ready output. Its distinguishing feature is that it replaces rule-of-thumb cutoffs with sample-specific critical values obtained by parametric bootstrap from the fitted Rasch/PCM model (Johansson, 2025, 2026). Item fit and local dependence flag on a multiplicity-corrected bootstrap p-value. Several methods, including the polytomous Martin-Löf test with Monte Carlo p-values (Christensen & Kreiner, 2007) and the bootstrap item-restscore test, are not available in other R packages.

Installation

Install from CRAN:

install.packages("easyRasch2")

Install the development version from GitHub:

# install.packages("remotes") # if needed
remotes::install_github("pgmj/easyRasch2")

Key design principles

• Estimation: a single engine across the package — Conditional Maximum Likelihood (CML) item parameters via psychotools and Warm's Weighted Likelihood Estimation (WLE) for person parameters. eRm is used for Andersen's LR test (RMdifLR()); mirt (MML) is available as an optional engine (estimator = "MML" in RMlocdepQ3() and RMitemParameters()) and for the plausible values behind the RMU reliability metric.
• Inference: simulation-based cutoffs throughout. Item fit and local dependence flag on multiplicity-corrected bootstrap p-values whenever the full cutoff object is supplied, using Westfall–Young family-wise correction (default) or FDR alternatives (Ferreira, 2024; Johansson, 2026). Pass p_value = FALSE to flag against the simulated interval instead, which tests every item or pair at once and so sets a family-wise error rate of 1 - width^m implicitly.
• Output: knitr::kable() for tables (Quarto-friendly), ggplot2 for figures, and "dataframe" output options for downstream use. Every caption reports the estimation sample size and missing-data policy.
• Naming: Functions use the RM prefix (e.g., RMlocdepQ3()).

Functions by domain

Item fit

• RMitemInfit() — conditional infit MSQ, flagged on multiplicity-corrected bootstrap p-values with family-wise (Westfall–Young) or FDR multiple-comparison correction
• RMitemInfitCutoff() + RMitemInfitPlot() — simulation-based cutoffs and plot
• RMitemInfitMI() + RMitemInfitCutoffMI() — multiple-imputation variants
• RMitemRestscore() — item-restscore with Goodman-Kruskal's $\gamma$ (gamma)
• RMitemRestscoreBoot() — non-parametric bootstrap of item-restscore fit
• RMitemICCPlot() - conditional item characteristic curves

Local dependence

• RMlocdepQ3() + RMlocdepQ3Cutoff() + RMlocdepQ3Plot() — Yen's $Q_3$ residual correlations (CML/WLE by default, estimator = "MML" optional); table and plot share a $matrix ($Q_3$ heatmap) / $pairs (per-pair observed-vs-simulated) structure; per-pair bootstrap p-values
• RMlocdepGamma() + RMlocdepGammaCutoff() + RMlocdepGammaPlot() — partial-γ local dependence; per-pair bootstrap p-values

Dimensionality / unidimensionality

• RMdimResidualPCA() + RMdimResidualPCACutoff() — PCA of standardized residuals, with simulation-based first-contrast cutoff (Chou & Wang, 2010) and an optional bootstrap p-value
• RMdimMartinLof() + RMdimMartinLofResiduals() — Martin-Löf LR test (Christensen & Kreiner, 2007), supports polytomous data with Monte Carlo p-values
• RMdimCFACutoff() + RMdimCFA() + RMdimCFAPlot() — CFA fit-indices and per-item loading checks under PCM unidimensionality (via lavaan WLSMV) with simulation-based cutoffs and optional bootstrap p-values

Differential item functioning

• RMdifLR() — Andersen's likelihood-ratio test (eRm::LRtest)
• RMdifTree() — Rasch / partial-credit trees (psychotree) with Mantel-Haenszel or partial-γ effect sizes per split, optional iterative purification, and stablelearner-based stability assessment
• RMdifGamma() + RMdifGammaCutoff() + RMdifGammaPlot() — partial-γ DIF; optional bootstrap p-values calibrated against the simulated Rasch null
• RMitemICCPlot() - evaluates DIF across class intervals

Item category threshold ordering

• RMitemCatProb() for classic item probability function trace plots.
• RMitemHierarchy() renders a plot sorting items based on difficulty, showing item threshold locations and confidence intervals.

Reliability, targeting, score conversion

• RMreliability() + RMUreliability() — Cronbach's α, PSI, marginal reliability, and Relative Measurement Uncertainty from plausible values
• RMreliabilityCurve() — conditional SEM, test information, or conditional reliability across the latent scale, with the respondent distribution behind it and an optional bootstrap band
• RMtargeting() — Wright-map style person-item targeting plot
• RMscoreSE() — raw-score → logit transformation table (WLE / EAP)

Individual change

• RMpersonChange() — per-respondent change between two occasions, with the null stated explicitly and critical values simulated rather than assumed normal
• RMretestSD() — occasion-to-occasion SD from a test-retest study, the input to RMpersonChange(null = "retest")

Item & person parameters

• RMitemParameters() — item difficulty / threshold locations in long or wide format, with optional standard errors and confidence intervals (CML via psychotools, or MML via mirt for sparse data)
• RMpersonParameters() — per-respondent person locations (WLE or EAP), estimated on each response pattern so partial missingness is handled directly

Person fit

• RMpersonFit() — per-respondent conditional infit / outfit MSQ and the standardized log-likelihood $\ell_z$, with resampling-based p-values rather than unreliable asymptotic nulls (Sinharay, 2016; Müller, 2020)

Data visualization

• RMplotTile() — response-distribution heatmap with optional group faceting
• RMplotBar() & RMplotStackedbar()

Example

library(easyRasch2)
data("pcmdat2", package = "eRm")
options(mc.cores = 4)
set.seed(42)

# Conditional item infit with simulation-based cutoffs
simfit <- RMitemInfitCutoff(pcmdat2, iterations = 400)
# Passing the full cutoff object flags on the Westfall-Young corrected
# p-value. The 95% interval is reported alongside as a description.
RMitemInfit(pcmdat2, cutoff = simfit)

# Test of unidimensionality via posterior-predictive ordinal CFA
cfa_sim <- RMdimCFACutoff(pcmdat2, iterations = 250)   # simulated reference
tabs <- RMdimCFA(pcmdat2, cutoff = cfa_sim)            # observed vs expected
tabs$fit                                                # fit-index table
tabs$loadings                                           # per-item loading table
plots <- RMdimCFAPlot(cfa_sim, data = pcmdat2)          # list of 2 ggplots
plots$loadings                                          # observed vs expected loadings
plots$fit                                               # fit-index distributions

# DIF analysis via Andersen's LR test
grp <- factor(sample(c("A", "B"), nrow(pcmdat2), replace = TRUE))
RMdifLR(pcmdat2, dif_var = grp)

# Rasch-tree DIF with effect-size classification on continuous +
# categorical covariates simultaneously
covs <- data.frame(
  group = grp,
  band  = sample(c("low", "high"), nrow(pcmdat2), replace = TRUE)
)
RMdifTree(pcmdat2, covariates = covs)

References

• Bjorner, J. B., Kreiner, S., Ware, J. E., Damsgaard, M. T., & Bech, P. (1998). Differential item functioning in the Danish translation of the SF-36. Journal of Clinical Epidemiology, 51(11), 1189–1202. https://doi.org/10.1016/S0895-4356(98)00111-5
• Chou, Y.-T., & Wang, W.-C. (2010). Checking dimensionality in item-response models with principal component analysis on standardized residuals. Educational and Psychological Measurement, 70(5), 717–731. https://doi.org/10.1177/0013164410379322
• Christensen, K. B., & Kreiner, S. (2007). A Monte Carlo approach to unidimensionality testing in polytomous Rasch models. Applied Psychological Measurement, 31(1), 20–30. https://doi.org/10.1177/0146621605286204
• Christensen, K. B., Makransky, G., & Horton, M. (2017). Critical values for Yen's Q3: Identification of local dependence in the Rasch model using residual correlations. Applied Psychological Measurement, 41(3), 178–194. https://doi.org/10.1177/0146621616677520
• Ferreira, J. A. (2024). Methods of testing a 'small' or 'moderate' number of hypotheses simultaneously: An account focusing on the control of the probability of at least one incorrect rejection and of the false discovery rate. Journal of Statistical Theory and Practice, 19(6). https://doi.org/10.1007/s42519-024-00412-4
• Henninger, M., Debelak, R., & Strobl, C. (2023). A new stopping criterion for Rasch trees based on the Mantel-Haenszel effect size measure for DIF. Educational and Psychological Measurement, 83, 181–212. https://doi.org/10.1177/00131644221077135
• Henninger, M., Radek, J., Debelak, R., & Strobl, C. (2025). Partial credit trees meet the partial gamma coefficient for quantifying DIF and DSF in polytomous items. Behaviormetrika, 52, 221–257. https://doi.org/10.1007/s41237-024-00252-3
• Johansson, M. (2025). Detecting item misfit in Rasch models. Educational Methods & Psychometrics, 3(18). https://doi.org/10.61186/emp.2025.5
• Johansson, M. (2026). Simulation-based cutoffs for conditional item fit in Rasch models: Iterations, multiplicity correction, and decision stability. PsyArXiv. https://doi.org/10.31234/osf.io/7pqz4_v2
• Kreiner, S. (2011). A note on item-restscore association in Rasch models. Applied Psychological Measurement, 35(7), 557–561. https://doi.org/10.1177/0146621611410227
• Müller, M. (2020). Item fit statistics for Rasch analysis: Can we trust them? Journal of Statistical Distributions and Applications, 7(1), 5. https://doi.org/10.1186/s40488-020-00108-7
• Philipp, M., Rusch, T., Hornik, K., & Strobl, C. (2018). Measuring the stability of results from supervised statistical learning. Journal of Computational and Graphical Statistics, 27, 685–700. https://doi.org/10.1080/10618600.2018.1473779
• Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1–36. https://doi.org/10.18637/jss.v048.i02
• Sinharay, S. (2016). Assessment of person fit using resampling-based approaches. Journal of Educational Measurement, 53(1), 63–85. https://doi.org/10.1111/jedm.12101
• Strobl, C., Kopf, J., & Zeileis, A. (2015). Rasch trees: A new method for detecting DIF in the Rasch model. Psychometrika, 80, 289–316. https://doi.org/10.1007/s11336-013-9388-3

Credits

As mentioned earlier, this is based on my easyRasch package, and I am using Claude Opus/Fable to rewrite functions to this more properly formatted package. While it uses my earlier code, most of the code in this package is produced by the LLM and tested and bug fixed by me.

RMdifTree() adapts MIT-licensed code from Mirka Henninger and Jan Radek's raschtreeMH and effecttree packages for the effect-size and ETS-classification algorithms.

Magnus Johansson is a licensed psychologist with a PhD in behavior analysis. He works as a research specialist focused on psychometrics and statistics at Karolinska Institutet, Department of Clinical Neuroscience, Center for Psychiatry Research.

• ORCID: 0000-0003-1669-592X
• Bluesky: @pgmj.bsky.social

License

GPL (>= 3)

easyRasch2 documentation built on Sept. 13, 2026, 1:07 a.m.