rasch: Pairwise Conditional Rasch Measurement Analysis and Diagnostics
Pairwise conditional maximum likelihood estimation of dichotomous
and polytomous Rasch models (partial credit and rating scale) after
Andrich and Luo (2003) and Zwinderman (1995) <doi:10.1177/014662169501900406>,
with standard errors from
a Godambe sandwich estimator. An optional alternative estimator
reparameterises each item's thresholds as Andrich's (1978
<doi:10.1007/BF02293814>, 1985)
orthogonal-polynomial principal components (location, spread, skewness,
and kurtosis; Pedler 1987), exact for items with up to 3 thresholds and a
smoothed reduced-rank model for items with more, useful when some
categories are sparsely populated. Person measures are
Warm's (1989) <doi:10.1007/BF02294627> weighted likelihood estimates, computed per missing-data
pattern. The diagnostic suite follows the conventions set out in
Andrich and Marais (2019) <doi:10.1007/978-981-13-7496-8>: the
log-of-mean-square fit residual with apportioned degrees of freedom
(and its natural form), infit and outfit, the item-trait interaction
chi-square over automatically sized class intervals with its per-interval detail
table, the class-interval ANOVA item-fit F, the person separation index
with and without extremes and the item separation index, Cronbach's
alpha, summary distribution statistics with skewness and kurtosis,
targeting, the score-to-measure table with maximum likelihood and
geometric extreme-score extrapolation options, test information,
threshold and category diagnostics, residual
principal-components dimensionality testing, local dependence by
residual correlation, and differential item functioning by two-way
residual analysis of variance over any number of person factors,
factor-at-a-time (the full two-way table with partial eta-squared
effect sizes) or as a full factorial with interaction precedence,
Tukey HSD post-hoc comparisons on significant group terms and
interaction cells, false-discovery-rate or familywise adjustment, and
DIF magnitudes in logits by resolved-item locations with a
practical-significance criterion. Violations of
independence are quantified, not just flagged: the magnitude of
response dependence between two items by the resolution method of
Andrich and Kreiner (2010) <doi:10.1177/0146621609360202> (polytomous
form Andrich, Humphry and Marais 2012 <doi:10.1177/0146621612441858>), the spread-parameter least-upper-bound screen (Andrich 1985),
and the magnitude of multidimensionality (latent subscale correlation
and common-variance proportion) from Andrich's (2016) two-calculation
reliability comparison. A likelihood-ratio test of the partial credit
against the rating parameterisation is reported both raw, as
conventionally displayed, and with a first-order composite-likelihood calibration
(Kent 1982 <doi:10.1093/biomet/69.1.19>) from the Godambe matrices. Also
included: anchored estimation for test equating (individual threshold
and average item-location anchors), common-item equating tests and
plots, item splitting to resolve invariance violations, tailored
analysis for guessing with the four-step anchored comparison (Andrich,
Marais and Humphry 2012 <doi:10.3102/1076998611411914>), classical test theory companion statistics,
racked and stacked reshaping for repeated measurements, model comparison
by composite-likelihood information criteria whose penalty is the
Godambe effective parameter count (Varin and Vidoni 2005
<doi:10.1093/biomet/92.3.519>; Gao and Song 2010
<doi:10.1198/jasa.2010.tm09414>), absorbing the pairwise over-counting that a nominal AIC or BIC
would ignore, the many-facet
Rasch model (Linacre 1989) for rated long-format data with facet
severities, fit, and optional item-by-facet interactions, subtest
formation for locally dependent items, multiple-choice scoring against
a key with double keying and polytomous option scoring of informative
distractors (Andrich and Styles 2011, with an evidence-based rescoring
proposal), rest-measure distractor analysis and option curves, the Guttman
scalogram with the coefficient of reproducibility, the
Bradley-Terry-Luce model for paired comparisons (Bradley and Terry
1952 <doi:10.1093/biomet/39.3-4.324>; Luce 1959) as the conditional form of the dichotomous Rasch model
(Andrich 1978), estimated by the same conventions with judge-clustered
sandwich errors and judge fit diagnostics, and the first software implementation of
the extended frame of reference model (Humphry 2005; Humphry and Andrich
2008), in which the unit of the latent scale differs across item-set by
person-group frames: group units are estimated by person-free
within-frame pairwise conditioning and set units by error-corrected
person linking, all reported in a common arbitrary unit; its
paired-comparison form estimates judge-panel and object-set units
with the linking identified from cross-set comparisons alone. A modern
'shiny' interface and a one-call exporter for every table and plot are
included.
Implemented from published measurement theory in base R, with no
dependence on other estimation engines.
| Version: |
1.11.7 |
| Imports: |
stats, graphics, grDevices, utils |
| Suggests: |
testthat (≥ 3.0.0), shiny, bslib, DT, bsicons, knitr, rmarkdown, eRm, sirt, psychotools |
| Published: |
2026-07-30 |
| DOI: |
10.32614/CRAN.package.rasch (may not be active yet) |
| Author: |
Josh McGrane [aut, cre] |
| Maintainer: |
Josh McGrane <drjoshmcgrane at gmail.com> |
| BugReports: |
https://github.com/drjoshmcgrane/rasch/issues |
| License: |
MIT + file LICENSE |
| URL: |
https://drjoshmcgrane.github.io/rasch/,
https://github.com/drjoshmcgrane/rasch |
| NeedsCompilation: |
no |
| Materials: |
README, NEWS |
| CRAN checks: |
rasch results |
Documentation:
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