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.

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

Key design principles

• Estimation: Conditional Maximum Likelihood (CML) via eRm, psychotools, and iarm for item parameters; Weighted Likelihood Estimation (WLE) for person parameters; mirt (MML) only where CML alternatives do not exist (e.g., Q3 residual correlations).
• Output: knitr::kable() for tables (Quarto-friendly), ggplot2 for figures, and "dataframe" output options for downstream use.
• Naming: Functions use the RM prefix (e.g., RMlocdepQ3()).

Functions by domain

Item fit

• RMitemInfit() — conditional infit MSQ
• RMitemInfitCutoff() + RMitemInfitCutoffPlot() — simulation-based cutoffs and plot
• RMitemInfitMI() + RMitemInfitCutoffMI() — multiple-imputation variants
• RMitemRestscore() — item-restscore with Goodman-Kruskal’s gamma
• RMitemRestscoreBoot() — non-parametric bootstrap of item-restscore fit
• RMitemICCPlot() - conditional item characteristic curves

Local dependence

• RMlocdepQ3() + RMlocdepQ3Cutoff() — Yen’s Q3 residual correlations
• RMlocdepGamma() + RMlocdepGammaCutoff() + RMlocdepGammaPlot() — partial-gamma local dependence

Dimensionality / unidimensionality

• RMdimResidualPCA() + RMdimResidualPCACutoff() — PCA of standardized residuals, with simulation-based first-contrast cutoff (Chou & Wang, 2010)
• RMdimMartinLof() + RMdimMartinLofResiduals() — Martin-Löf LR test (Christensen & Kreiner, 2007), supports polytomous data
• RMdimCFACutoff() + RMdimCFAPlot() — posterior-predictive CFA fit-index cutoffs under PCM unidimensionality (via lavaan WLSMV)

Differential item functioning

• RMdifLR() — Andersen’s likelihood-ratio test (eRm::LRtest)
• RMdifTree() — Rasch / partial-credit trees (psychotree) with Mantel-Haenszel or partial-gamma effect sizes per split, optional iterative purification, and stablelearner-based stability assessment
• RMdifGamma() + RMdifGammaCutoff() + RMdifGammaPlot() — partial-gamma DIF
• 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, empirical reliability, and Relative Measurement Uncertainty from plausible values
• RMtargeting() — Wright-map style person-item targeting plot
• RMscoreSE() — raw-score → logit transformation table (WLE / EAP)

Data visualization

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

Installation

Install the development version from GitHub:

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

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 = 250)
RMitemInfit(pcmdat2, cutoff = simfit)

# Test of unidimensionality via posterior-predictive ordinal CFA
cfa_res <- RMdimCFACutoff(pcmdat2, iterations = 250)
cfa_res                # kable: observed vs simulated cutoffs
RMdimCFAPlot(cfa_res)     # histogram + observed diamond

# 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
• 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
• 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
• 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 to “transfer” 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 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 at Karolinska Institutet, Department of Clinical Neuroscience, Center for Psychiatry Research.

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

License

GPL (>= 3)