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.