Reliability metrics for a Rasch model

Computes three reliability indices for a Rasch / partial credit model: the Person Separation Index (PSI) via eRm::SepRel(), empirical reliability via mirt::empirical_rxx(), and Relative Measurement Uncertainty (RMU) via RMUreliability() applied to plausible values from mirt::fscores().

Usage

RMreliability(
  data,
  conf_int = 0.95,
  draws = 1000,
  rmu_iter = 50,
  estim = "WLE",
  boot = FALSE,
  boot_iter = 200,
  parallel = TRUE,
  n_cores = NULL,
  seed = NULL,
  verbose = FALSE,
  theta_range = c(-10, 10),
  output = "kable"
)

Arguments

data: A data.frame or matrix of item responses. Items must be scored starting at 0 (non-negative integers).
conf_int: Numeric in (0, 1). HDCI width for both bootstrap CIs and RMU. Default 0.95.
draws: Integer. Number of plausible-value draws drawn from the mirt model for the RMU calculation. Default 1000. More gives a more stable RMU; computational cost is mostly linear.
rmu_iter: Integer. Number of times RMUreliability() is repeated on the same set of plausible-value draws (each repetition uses a fresh random column split). Estimates are averaged across repetitions to stabilise against split-induced variability. Default 50.
estim: Character. Theta estimator used by mirt::fscores() for the empirical reliability and the plausible-value seed. One of "WLE" (default), "EAP", "MAP", "ML". Plausible draws themselves are produced by Metropolis-Hastings.
boot: Logical. If TRUE, run a non-parametric bootstrap to obtain CIs for PSI and Empirical reliability. Default FALSE.
boot_iter: Integer. Number of bootstrap iterations when boot = TRUE. Default 200.
parallel: Logical. Use parallel processing via mirai for the bootstrap if available. Default TRUE.
n_cores: Integer or NULL. Number of parallel workers. When NULL, getOption("mc.cores") is checked first; if neither is set, bootstrapping falls back to sequential.
seed: Integer or NULL. Master random seed for reproducibility.
verbose: Logical. Print progress messages and a progress bar for the bootstrap. Default FALSE.
theta_range: Numeric length-2 vector. Theta limits passed to mirt::fscores(). Default c(-10, 10).
output: Character. "kable" (default) for a formatted knitr::kable() table, or "dataframe" for the underlying data.frame.

Value

If output = "kable": a knitr_kable object with one row per metric.
If output = "dataframe": a data.frame with columns metric, estimate, lower, upper, notes.

Details

Confidence intervals for PSI and Empirical reliability are obtained by non-parametric bootstrap (refitting both the eRm and mirt models on each resample). The RMU interval is the HDCI of correlations across plausible-value draws, averaged over rmu_iter random splits of the draws.

This is a CRAN-friendly replacement for easyRasch::RIreliability(). The TAM-based plausible-values path has been removed; mirt is the only MML backend.

For dichotomous data (max = 1), mirt::mirt(..., itemtype = "Rasch") and eRm::RM() are fitted. For polytomous data, the same itemtype is used in mirt and eRm::PCM() in eRm.

PSI is computed by eRm::SepRel() on the person-parameter object from eRm::person.parameter(). Note that PSI excludes respondents with extreme (min/max) raw scores by construction.

RMU is from Bignardi, Kievit, & Bürkner (2025), modified here to use mirt plausible values rather than fully Bayesian posterior draws (see Mislevy, 1991, for the plausible-values framework).

Bootstrap iterations that fail to converge in either mirt or eRm are silently dropped.

References

Bignardi, G., Kievit, R., & Bürkner, P. C. (2025). A general method for estimating reliability using Bayesian Measurement Uncertainty. PsyArXiv. doi:10.31234/osf.io/h54k8_v1

Mislevy, R. J. (1991). Randomization-Based Inference about Latent Variables from Complex Samples. Psychometrika, 56(2), 177-196. doi:10.1007/BF02294457

Adams, R. J. (2005). Reliability as a measurement design effect. Studies in Educational Evaluation, 31(2), 162-172. doi:10.1016/j.stueduc.2005.05.008

Examples