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.