# easyRasch2

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`easyRasch2` is an R package for Rasch measurement theory
analysis workflows. It is the successor to
[`easyRasch`](https://pgmj.github.io/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](https://pgmj.github.io/easyRasch2/articles/easyRasch2.html) link above contains a short introduction. For broader Rasch-analysis tutorials, see the
[vignette](https://pgmj.github.io/raschrvignette/RaschRvign.html) for the
archived sibling package [`easyRasch`](https://pgmj.github.io/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, and — as its distinguishing feature — replaces rule-of-thumb cutoffs
with sample-specific critical values obtained by parametric bootstrap from the
fitted Rasch/PCM model (Johansson, 2025). 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:

```r
install.packages("easyRasch2")
```

Install the development version from GitHub:

```r
# 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, with optional
  bootstrap *p*-values (`p_value = TRUE`) using Westfall–Young family-wise
  correction (default) or FDR alternatives (Ferreira, 2024).
- **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; optional bootstrap *p*-values
  (`p_value = TRUE`) 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) / `$pairs` (per-pair
  observed-vs-simulated) structure; optional per-pair bootstrap *p*-values
- `RMlocdepGamma()` + `RMlocdepGammaCutoff()` + `RMlocdepGammaPlot()` —
  partial-$\gamma$ local dependence; optional 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()` — posterior-predictive CFA
  fit-index 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-$\gamma$ effect sizes per split, optional
  iterative purification, and `stablelearner`-based stability assessment
- `RMdifGamma()` + `RMdifGammaCutoff()` + `RMdifGammaPlot()` — partial-$\gamma$
  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
- `RMtargeting()` — Wright-map style person-item targeting plot
- `RMscoreSE()` — raw-score → logit transformation table (WLE / EAP)

### 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

```r
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_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>
- 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`](https://github.com/mirka-henninger/raschtreeMH) and
[`effecttree`](https://github.com/mirka-henninger/effecttree) packages for
the effect-size and ETS-classification algorithms.

[Magnus Johansson](https://ki.se/en/people/magnus-johansson-3) 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](https://orcid.org/0000-0003-1669-592X)
- Bluesky: [@pgmj.bsky.social](https://bsky.app/profile/pgmj.bsky.social) 

## License

GPL (>= 3)
