Estimation and Diagnostics for Many-Facet Measurement Models

Native R implementation of many-facet ordered-response measurement models with arbitrary facet counts, rating-scale and partial-credit parameterizations, a bounded generalized partial-credit extension, and both marginal and joint maximum likelihood estimation. The package provides a fit / diagnose / report pipeline covering anchoring, linking, bias and differential-functioning screening, and publication-oriented reporting summaries, with reproducibility manifests for replay. See 'Andrich' (1978) , 'Masters' (1982) , and 'Muraki' (1992) for the underlying ordered-response models.

mfrmr

mfrmr fits unidimensional many-facet ordered-response models in R. It supports rating-scale (RSM) and partial-credit (PCM) models, together with a documented bounded GPCM extension. A facet can represent a rater, item, task, criterion, form, occasion, or another observed role that affects an ordered score.

For GPCM, bounded refers to the documented model and workflow scope; it does not mean finite parameter box constraints. Unsupported combinations and inference states are reported explicitly rather than silently treated as ordinary estimates.

The package extends Rasch-family RSM/PCM work with MML, modern diagnostics, reproducibility, network review, and reporting support. It is not a general FACETS replacement: each fit_mfrm() call uses one response-model family and one observed score scale, and the current public API does not provide mixed response families, multiple independent rating scales, general threshold anchoring, or an imported versioned frozen-calibration bundle for operational scoring. Posterior scoring from an existing fitted object is a separate analysis route.

The recommended workflow is:

long-format data + describe_mfrm_data()
  -> fit_mfrm(method = "MML")
  -> print(fit) / summary(fit)$decision
  -> if ready: summary(profile = "facets")
     if review/blocked: follow summary(fit)$decision$NextAction
  -> native Wright map with uncertainty
  -> focused diagnostics
  -> report and export

The native Wright map is the required first fitted-scale figure in this workflow. A separate FACETS-style renderer is available when a familiar asterisk ruler and labelled category transitions are useful.

The three basic fitted-object methods have deliberately different jobs: print(fit) is a compact triage view, summary(fit) is the canonical structured review surface, and plot(fit, draw = FALSE) returns reusable plot data. The printed Decision and structured summary(fit)$decision are the common first-read for RSM, PCM, and bounded GPCM. All three methods carry the same model/readiness basis; fitted-model plots also retain a scale_contract table so the latent-coordinate and discrimination scales are not inferred from axis labels alone.

Package website: https://ryuya-dot-com.github.io/mfrmr/

Source code: https://github.com/Ryuya-dot-com/mfrmr

Questions and bug reports: https://github.com/Ryuya-dot-com/mfrmr/issues

Installation

Install the CRAN package with:

install.packages("mfrmr")

Install the GitHub version with:

if (!requireNamespace("remotes", quietly = TRUE)) {
  install.packages("remotes")
}

remotes::install_github(
  "Ryuya-dot-com/mfrmr",
  build_vignettes = TRUE
)

Load the package, inspect the six-step beginner route, and list the installed guides:

library(mfrmr)
mfrmr_output_guide("beginner")[, c(
  "Question", "MainFunction", "NextStep"
)]
browseVignettes("mfrmr")

For the shortest end-to-end explanation, open help("mfrmr_workflow_methods", package = "mfrmr") or vignette("mfrmr-workflow", package = "mfrmr"). Use help("mfrmr_visual_diagnostics", package = "mfrmr") when choosing a figure and help("mfrmr_reporting_and_apa", package = "mfrmr") when moving from a reviewed fit to tables and manuscript-draft output.

Data format

fit_mfrm() expects one row per observed rating event. At minimum, the data need:

• one person identifier;
• one or more non-person facet columns;
• one ordered numeric score column.

For example:

head(data.frame(
  Person = c("P01", "P01", "P02", "P02"),
  Rater = c("R1", "R2", "R1", "R2"),
  Criterion = c("Content", "Content", "Content", "Content"),
  Score = c(3, 2, 2, 3)
))

Facet identifiers may be character or factor columns. Scores must represent ordered categories. Use NA for missing responses, or document and recode special missing-value codes before fitting. The design need not be fully crossed, but it must contain enough links among persons and facet levels to support the intended comparisons.

Response type and frequencies

The current response likelihood is ordered categorical. Binary scores are the two-category special case, and RSM, PCM, and bounded GPCM cover ordered polytomous scores. Although their category probabilities form a vector that sums to one, they are not unordered nominal-response or multinomial-logit models. Poisson, negative-binomial, and grouped binomial-trial count responses are also outside the current fit_mfrm() scope. Integer counts supplied as Score are interpreted as ordered category codes, not as Poisson or related counts.

A positive numeric weight weights one row's conditional ordered-category likelihood and can represent a defensible row-replication weight. It is not a general collapsed-person frequency table. Under MML, powering responses within one Person's conditional pattern is not equivalent to replicating a complete Person response pattern after marginalization. It also does not change the response family or model dependence among repeated ratings. Non-unit observation-weight fits are excluded from the common MML information-criterion panel. FACETS has separate Bn binomial-trial and P Poisson response models; those are not reproduced by mfrmr's binary ordered-score route.

Each row should represent a distinguishable rating event. Exact duplicate Person-by-facet combinations are retained but trigger a warning and a Data review state because the package does not model within-cell dependence. For a legitimate re-rating or replicated scoring study, include an event or occasion facet that distinguishes the observations before fitting.

For conventional score sentinels such as 99, -1, N, or ., set missing_codes = TRUE. This convenience policy recodes the score column only; it preserves person and facet identifiers because short labels such as N can be legitimate IDs. Supplying an explicit character vector instead applies that user-declared code set across the selected model columns, so inspect the returned missing_recoding record before fitting or reporting exclusions.

The main workflow below uses a compact synthetic dataset with a connected two-rater assignment, moderately unequal rater workloads, and six planned criterion-level omissions represented by absent long-format rows, not NA or sentinel scores. Its groups contain 24 persons each; three omissions per group leave 141 observed rows in Group A and 141 in Group B:

library(mfrmr)

dat <- load_mfrmr_data("example_operational")
data("mfrmr_example_operational_design", package = "mfrmr")
head(dat)
table(dat$Score)
list_mfrmr_data(details = TRUE)[, c("Key", "PrimaryUse", "Design", "CountBasis")]

All bundled examples are synthetic. example_operational is the applied teaching dataset, not an empirical reference dataset. Use example_core only when an idealized complete crossing is useful for a fast example, and use example_bias for demonstrations with deliberately planted DFF/bias effects.

Complete MML workflow

1. Check the data and intended score scale

Before fitting, state the complete rubric support and inspect retained, missing, and zero-count categories:

data_review <- describe_mfrm_data(
  data = dat,
  person = "Person",
  facets = c("Rater", "Criterion"),
  score = "Score",
  rating_min = 1,
  rating_max = 4,
  expected_design = mfrmr_example_operational_design
)
data_summary <- summary(data_review)
data_summary$structural_missingness
data_summary$design_connectivity

The assignment roster contains no scores. It tells describe_mfrm_data() which Person x Rater x Criterion cells were planned. The review therefore reports the six expected-but-unobserved cells separately from ordinary column NA counts, while confirming that both observed Person-facet graphs remain connected. Without expected_design, structural missingness is reported as not assessed because an absent row may simply mean that the cell was never assigned.

rating_min and rating_max retain unobserved boundary categories in the data-support review. A boundary gap remains review evidence for the separate element-boundary contract; it is not by itself an unsupported free-step contrast. If an intended intermediate category is unobserved, use keep_original = TRUE in both describe_mfrm_data() and fit_mfrm(). In a polytomous fitted ladder, that retained internal gap creates an exact adjacent-step recession direction, so fitting stops before optimization. Otherwise non-consecutive observed scores such as 1, 2, 4, 5 are mapped to a contiguous internal scale; always review the reported score map before interpreting steps.

2. Fit the model

For a new analysis, start with marginal maximum likelihood:

fit <- fit_mfrm(
  data = dat,
  person = "Person",
  facets = c("Rater", "Criterion"),
  score = "Score",
  rating_min = 1,
  rating_max = 4,
  method = "MML",
  model = "RSM"
)

MML integrates over the person distribution and returns posterior person summaries. The default uses 31 quadrature points. Record that setting and examine quadrature sensitivity when the application requires it. Eligible fits below 15 points retain raw AIC/BIC/SABIC for screening, and fits at 15--30 points retain them for review, but automatic deltas, criterion weights, preferred-model labels, evidence ratios, and LRT are disabled below 31 points. Use 31--60 points as a comparison starting grid and 61 or more as a denser sensitivity grid. A close or consequential comparison still requires a prespecified common-grid sensitivity check; q>=31 alone is not evidence that integration error is negligible.

After fitting a bounded GPCM-MML object as fit_gpcm, run the comparison explicitly rather than making summary() refit the model in the background:

q_review <- gpcm_mml_quadrature_sensitivity(
  fit_gpcm,
  data = dat,
  quad_points = c(31, 41)
)
summary(q_review)
apa_table(q_review)

The review reports changes in marginal likelihood per Person, relative slopes, raw local-curvature SEs, population SD, and fitted probabilities. It does not assign a universal stable/unstable cutoff, make raw slope SEs inferentially eligible, or change the fit-readiness decision.

Use model = "PCM", step_facet = "Criterion" when category steps differ across that facet. Choose the model from the scoring design and measurement rationale, not from a single fit statistic.

3. Read the fit-only summary

The default summary is deliberately lightweight:

fit_summary <- summary(
  fit,
  profile = "fit",
  detail = "brief"
)

fit_summary$decision
fit_summary$overview
fit_summary$status
fit_summary$readiness
fit_summary$data_review
fit_summary$settings_overview
fit_summary$facet_overview
fit_summary$person_overview
fit_summary$step_overview

Read fit_summary$decision first. It translates the stored readiness contract into four practical questions: did the fit gates pass, has formal precision support been evaluated, what evidence prevents formal use, and what should be done next. A fit-only summary deliberately returns FormalInference = "No" even when InferenceReady = TRUE, because convergence and estimability do not by themselves validate standard errors, confidence intervals, or reliability. Evaluate that separate contract with diagnostics:

diag <- diagnose_mfrm(fit, residual_pca = "none")
summary(fit, diagnostics = diag)$decision
# Equivalent precision-aware decision:
summary(diag)$decision

The decision is a presentation of existing evidence, not a new statistical test or an automatic model-selection rule. FormalInference = "No" still permits explicitly labelled diagnostic inspection, but not formal SE/CI, reliability, or significance claims. It does not mean that changing optimizer settings until the answer becomes "Yes" is appropriate. Follow NextAction and retain the original reason in reports.

Then review convergence and estimation settings. When optimizer code zero is reached before the common terminal-gradient check passes, fit_mfrm() makes a bounded sequence of warm-started polishing attempts when the requested setting is at least as strict as the public default (reltol <= 1e-9). It retains the best non-worsening stage under the recorded selection rule. The requested and selected-stage settings, every attempted stage, terminal gradients, parameter changes, and evaluation counts remain in fit$opt$optimizer_polish. For L-BFGS-B, the native factr and pgtol controls are also recorded; do not interpret EffectiveReltol as a native L-BFGS-B argument.

Treat maxit as a computational ceiling, not a convergence criterion or a control to tune until preferred estimates appear. The package default is maxit = 400; smaller values in executable examples exist only to shorten checks. Prespecify the estimator and controls before inspecting results. If a fit ends with ConvergenceStatus = "iteration_limit", do not interpret or compare its estimates. Refit the same data, model, method, anchors, optimizer, tolerance, and quadrature rule using the next ceiling in a prespecified sequence. Use a result only after FitReadiness = ready, InferenceReady = TRUE, and Numerical = pass; do not select among runs by coefficient size, fit statistics, significance, or agreement with an expected answer. Material differences between separately ready runs indicate numerical instability that requires review.

InferenceReady is deliberately a conservative fit-level first screen, not a publication decision. It is TRUE only when Input, Estimability, Category, Boundary, and Numerical components all pass. Then inspect the separate Design, Stability, Diagnostics, and Reporting workflow rows in fit_summary$readiness. A fit object saved before this versioned record existed is labelled legacy_unknown; an older InferenceReady = TRUE value does not make its summaries, results, or plots interpretation-ready. Refit it under the current version to establish current readiness. Before optimization, mfrmr now checks the estimator-specific constrained RSM/PCM free-coordinate design. Exact rank deficiency stops with a structured mfrmr_estimability_error; optimization cannot turn it into a usable fit. A disconnected design that is full rank only under its declared constraints, an MML panel linked through a common latent-population assumption rather than shared Persons, or a boundary- constant facet level remains a reporting hold or review even when the optimizer gradient is small. Inspect fit$data_review$estimability for the rank, nullity, parameter blocks, and check scope. In an otherwise supported fit, a Reporting status such as ready_for_diagnostics_and_reporting_follow_up means that fitting succeeded and the next diagnostic stage is pending; it does not mean that optimization failed or that the result is already manuscript-ready. Plots can still be generated for diagnosis, but their returned data carry interpretation_status = "review_only", their subtitle is marked REVIEW ONLY, the drawn title carries the same banner, and the plotting call warns before substantive or cross-subset interpretation. The remaining tables describe the fitted scale; they do not create universal acceptance thresholds.

4. Request the comprehensive FACETS-organized summary

Use the facets profile for the main review:

facets_summary <- summary(
  fit,
  profile = "facets",
  detail = "brief"
)

facets_summary
facets_summary$status
facets_summary$section_status
facets_summary$required_visual

res <- facets_summary$results
res$readiness
res$plot_map[, c(
  "Type", "Available", "InterpretationStatus", "InterpretationReady"
)]

This profile organizes model information, measures, uncertainty, fit evidence, precision, category/step information, and plot routes in a reading order that will be familiar to FACETS users. It computes the documented diagnostics when they are needed and returns the resulting mfrm_results object in facets_summary$results.

The profile name describes organization, not software execution:

• FACETS is not called;
• all estimates remain mfrmr estimates;
• sections that require a study-specific contrast, such as DIF or DFF, are not inferred automatically;
• residual PCA and multi-wave linking or drift analyses remain explicit follow-up decisions.

Pass a matching diagnose_mfrm() object through diagnostics = diag to reuse work already completed. Use compute = "never" for a no-computation review; dependent sections are then marked as not computed.

Person identifiers are omitted from the brief console view. Request detailed person output only when the analysis purpose and data-handling plan require it.

5. Draw the required native Wright map

The native renderer is the primary targeting figure because it keeps uncertainty visible:

plot(
  res,
  type = "wright",
  renderer = "native",
  show_ci = TRUE,
  preset = "publication"
)

Read the vertical axis as the shared logit scale:

• the person distribution shows where the sample lies;
• facet levels show severity, difficulty, or the active signed orientation;
• step locations show the fitted category structure;
• intervals show uncertainty where an appropriate SE is available;
• gaps between the person distribution and the modeled locations may indicate weak targeting in that region.

Person and non-person uncertainty can have different statistical bases. For example, an MML person interval is based on posterior uncertainty, whereas a non-person interval may use observed-information uncertainty. Keep the reported SE method with any table or figure interpretation.

The package defaults to a negative orientation for ordinary non-person facets: higher measures indicate greater severity or difficulty. Facets named in positive_facets have the reverse scoring direction. State the active orientation in the figure caption.

Set draw = FALSE to obtain the fitted coordinates for a custom ggplot2, Quarto, or accessibility-aware figure.

top_n = Inf retains and labels every fitted coordinate. The native text layer keeps the fitted points fixed, moves only colliding labels, and connects them with leader lines; label_points records both coordinates. Step thresholds share a vertical ladder and are labelled with both the score transition and the fitted logit. For genuinely dense maps, use the finite top_n compact view or a larger output device rather than silently omitting interior labels.

When the fit review diagnoses boundary-separated facet levels and no explicit wright_range is supplied, the native and FACETS-style renderers use the same robust central range. Boundary levels appear at the appropriate ruler end with triangles, while OriginalEstimate, CI_Lower, and CI_Upper retain the untruncated values. DisplayEstimate, DisplayCI_Lower, DisplayCI_Upper, and the CIClipped* / CISuppressed fields describe only what was drawn. This prevents a huge separation interval from compressing the interpretable center or being mistaken for a complete visible interval.

6. Add the optional FACETS-style Wright map

Use study-specific rubric labels rather than anonymous category numbers:

rubric_labels <- c(
  "1" = "Beginning",
  "2" = "Developing",
  "3" = "Proficient",
  "4" = "Advanced"
)

plot(
  res,
  type = "wright",
  renderer = "facets",
  category_labels = rubric_labels,
  rows_per_logit = 2,
  show_ci = FALSE,
  preset = "publication"
)

The FACETS-style renderer provides:

• one common logit ruler;
• a person-frequency column drawn with *;
• signed facet headers and facet-level labels;
• horizontal step lines;
• adjacent-score labels such as 1 Beginning -> 2 Developing;
• expected-score midpoint markers;
• an explicit * = n person(s) legend.

Set persons_per_star when the same star density must be used across several figures. Otherwise, the renderer chooses a compact value and prints it below the map.

The step display is designed to make the rating scale readable:

• a solid horizontal line is an estimated adjacent-category step location;
• its label names the lower and upper observed score categories and prints the fitted logit value in brackets;
• its height is the step location on the shared logit scale;
• a shorter dotted line is an expected-score midpoint crossing, not an additional model parameter.

For RSM, the step pattern is shared by the relevant observations. For PCM, read the step column within its curve or step-facet group. Disordered or closely spaced steps are prompts to inspect category use, sample support, and the scoring design; they are not automatic instructions to collapse categories.

Use the actual rubric wording from the instrument. The names of category_labels must match the original scores. A two-column data frame with columns Score and Label is also accepted.

With draw = FALSE, the returned facets_style component exposes category_labels, step_ruler, score_transitions, and settings tables. For line-printer reconstruction, RulerValue records the nearest discrete ruler row; DrawValue records the exact coordinate used for step and midpoint lines in the current renderer.

For a closer FACETS visual comparison, leave show_ci = FALSE. Setting show_ci = TRUE adds mfrmr uncertainty whiskers to the asterisk ruler. That hybrid is useful analytically, but it is intentionally an extension of the FACETS-style layout; its footer identifies the interval level and the dot at each whisker marks the corresponding fitted facet location.

Boundary-separated levels otherwise make an estimate-derived ruler very wide. The automatic boundary-aware range described above is used by default; set an explicit, reported range such as wright_range = c(-4, 4) when the application requires a prespecified display scale. Out-of-range levels remain visible in parentheses at the ruler ends. With show_ci = TRUE, endpoint triangles and the footer identify intervals that extend beyond or are omitted from the displayed ruler; exact values remain in the returned data.

Visual correspondence is not numerical equivalence

The FACETS renderer reproduces the main reading grammar of a FACETS Table 6-style variable map. It does not reproduce a FACETS run.

A defensible numerical comparison requires the same response records, score coding, model, estimator, identification constraints, anchors, facet orientation, extreme-score handling, and convergence criteria. FACETS commonly uses JMLE, whereas the starter mfrmr workflow above uses MML with EAP person summaries when its population-model assumptions are suitable. Those choices target related but different calculations.

When a JMLE-oriented comparison is required, refit with method = "JML" and still document every remaining setting. Matching the estimator family alone does not establish equivalence.

For an exported FACETS fit table, use read_facets_fit_table() followed by facets_fit_review(fit, diagnostics = res$diagnostics, facets_fit = ...). This reads supplied output; it does not launch or automate FACETS.

7. Review the Infit pathway, including persons

The fit pathway uses Infit on the horizontal axis and measure on the vertical axis:

plot(
  res,
  type = "fit_pathway",
  fit_stat = "Infit",
  fit_scale = "mnsq",
  include_person = TRUE,
  top_n_person = 12,
  person_labels = "none",
  facet_labels = "flagged",
  show_ci = TRUE,
  preset = "publication"
)

The vertical axis remains the fitted logit measure. The horizontal reference at Infit MnSq = 1 represents model expectation; the outer lines are review guides. Selected persons use a different point shape from non-person facet levels. Completing this follow-up can change the Reporting readiness row while leaving the already-passed Numerical row unchanged.

top_n_person limits the displayed person layer so a large study remains readable. The selected persons are those with the largest fit distances; non-person rows remain available. Use person_subset for a prespecified case list, or top_n_person = Inf only when displaying every person serves a clear purpose.

Fit statistics are evidence for review, not automatic exclusion rules. Investigate response patterns, design cells, score support, and practical consequences before changing data or operational decisions.

The separate type = "pathway" route displays expected scores and dominant-category regions across theta; type = "fit_pathway" displays Infit or Outfit against the fitted measure.

8. Build a report and export the results

Start with the brief result summary:

results_summary <- summary(res, view = "brief")
results_summary$overview
results_summary$triage
results_summary$next_actions
results_summary$plot_map

Build a report-oriented object from the same fitted results:

report <- mfrm_report(
  res,
  style = "qc"
)

summary(report, view = "reader")
report$first_screen
report$report_index

mfrm_report() organizes existing evidence. It does not refit the model or turn diagnostic thresholds into a validity decision.

Export a reader-oriented, controlled analysis archive:

exported <- export_mfrm_results(
  res,
  output_dir = "mfrmr-results",
  prefix = "analysis01",
  preset = "starter"
)

exported$summary
exported$written_files

The starter preset includes the result summary, report tables, replay code, manifest, native Wright map, and focused plot routes. Existing files are not overwritten unless overwrite = TRUE is requested explicitly.

This preset is a controlled analysis archive, not a deidentified or automatically shareable deliverable. It includes a complete .rds result object, and its tables, HTML, plots, replay code, and manifest can retain direct person identifiers, person-level estimates, original labels, or local paths. Review and transform every file under the study's data-handling policy before sharing it. After making that assessment, acknowledge_sensitive = TRUE can suppress the export warning; it does not remove or pseudonymize any data.

A practical reading order

For most studies, review the output in this order:

1. Confirm the data roles, score range, row retention, and model.
2. Confirm convergence and the estimation settings.
3. Inspect the native Wright map with uncertainty.
4. Review targeting, facet measures, person summaries, and category steps.
5. Inspect Infit/Outfit and the person-inclusive Infit pathway.
6. Add residual, bias/DIF, linking, or interaction analyses only when the design and research question require them.
7. Review report caveats before exporting or drafting substantive claims.

Do not reduce this sequence to a single pass/fail index. Fit, precision, targeting, category function, fairness, and validity answer different questions.

FACETS users

The closest translation of common FACETS concepts is:

For an existing FACETS-oriented script, run_mfrm_facets() provides a one-call wrapper around package fitting and diagnostics. For new work, the explicit fit_mfrm() workflow is easier to review and is recommended.

Use these guides for the full migration details:

• Migrating from FACETS to mfrmr
• Visual diagnostics

The installed references/FACETS_manual_mapping.md maps concepts and output routes. It is not evidence that FACETS was executed.

ConQuest MML comparison

mfrmr can prepare and review a narrow external-table comparison for an MML latent-regression case. The supported overlap is:

• RSM or PCM;
• binary responses;
• exactly one non-person facet, treated as the item facet;
• a unidimensional latent-regression MML fit;
• one numeric person covariate in addition to the intercept;
• complete rectangular person-by-item response data.

Within that scope, comparison targets include the population regression slope, residual variance, centered item estimates, and case-level EAP estimates.

The handoff is explicit: mfrmr prepares the analysis files, the user runs ConQuest separately, and mfrmr then normalizes the requested exports.

# fit_lr must satisfy the documented overlap conditions.
bundle <- build_conquest_overlap_bundle(
  fit = fit_lr,
  output_dir = "conquest-overlap"
)

# Run the generated .cqc file in ConQuest separately, then normalize its
# parameter, regression, covariance, and case-EAP CSV files.
conquest_tables <- normalize_conquest_overlap_exports(
  bundle,
  parameter_file = "conquest-overlap/conquest_overlap_conquest_parameters.csv",
  regression_file = "conquest-overlap/conquest_overlap_conquest_reg_coefficients.csv",
  covariance_file = "conquest-overlap/conquest_overlap_conquest_covariance.csv",
  case_file = "conquest-overlap/conquest_overlap_conquest_cases_eap.csv",
  conquest_version = "5.47.5",
  conquest_edition = "demo/free",
  run_date = Sys.Date()
)

conquest_review <- review_conquest_overlap(
  bundle,
  conquest_tables
)

summary(conquest_review)
conquest_review$attention_items

mfrmr does not execute or control ConQuest, and it does not parse arbitrary raw ConQuest reports. The user runs ConQuest separately; mfrmr can normalize the native comparison CSV exports requested by its generated command. The review reports coordinate-level differences; it does not declare general software equivalence from a single dataset or tolerance.

The generated ConQuest command uses the fitted mfrmr quadrature-point count; the bundle records both values. Record the actual ConQuest version, edition, and run date during normalization so the external comparison remains reproducible.

This public bundle route does not cover multidimensional models, arbitrary imported design matrices, bounded GPCM latent regression, JML latent regression, or the full ConQuest plausible-values workflow. Separately, the item-only bounded-GPCM parameterization can be compared only after the response kernel, slope grouping, threshold coordinates, latent-scale identification, retained rows, and category map have been matched. A result in that restricted overlap does not extend automatically to a multifacet ConQuest generalized-item design.

The ConQuest overlap bundle is also a controlled analysis bundle. Its long and wide response files contain person identifiers and responses; the person-data file contains identifiers and the covariate; and both mfrmr and ConQuest case-EAP files contain identifiers and person-level estimates. The helper warns when writing these files and creates *_privacy_notice.csv. Store the bundle in an approved restricted location and pseudonymize or redact it as required before sharing.

Model and interpretation boundaries

For bounded GPCM, inspect the capability table before choosing a downstream helper:

gpcm_capability_matrix()
vignette("mfrmr-gpcm-scope", package = "mfrmr")

Free-slope GPCM fits can be estimation-converged while parameter-level inference remains review-only. Read print(fit), summary(fit)$decision, and the slope table's ParameterStatus and PrimaryEstimate before interpreting the finite optimizer trace in OptimizerEstimate. Optimizer*SE and Optimizer*CI are diagnostic quantities; ordinary slope SEs and confidence intervals remain unavailable until the parameter-specific readiness checks pass. The GPCM scope vignette explains each status and the appropriate next action.

For MML, the default gpcm_mml_identification = "free_population" estimates an intercept-only population distribution while relative slopes satisfy a geometric-mean-one constraint. The corresponding fixed-latent-SD optimizer coordinate is retained in FixedLatentSDOptimizerEstimate. Use gpcm_mml_identification = "fixed_standard_normal" only when a deliberately matched legacy or external comparison requires that identification.

The bounded GPCM is an aligned single-owner relative-slope GPCM:

$$ \log\frac{P(Y_o=k)}{P(Y_o=k-1)} = \alpha_{g(o)}{\eta_o-\tau_{g(o),k}}, \qquad \prod_g\alpha_g=1. $$

Exactly one facet owns both slopes and steps, because slope_facet == step_facet. Setting all slopes to one recovers the equal-discrimination PCM kernel. This is narrower than the generalized MFRM of Uto and Ueno (2020), whose task and rater slopes enter multiplicatively as alpha_i * alpha_r and whose step owner is stated separately. The current criterion-owned and rater-owned fits are therefore separate restricted many-facet GPCM strata, not interchangeable fits of the full Uto--Ueno model.

The selected facet receives one slope per level, not one common slope for the whole fit. For example, slope_facet = "Criterion" estimates a relative slope for every criterion; slope_facet = "Rater" estimates one for every rater. The other facets retain additive location effects but no slope block. Those effects are still inside the complete adjacent-category predictor multiplied by the selected slope; the current kernel is not a loading-only model with unscaled facet intercepts. Criterion and rater slopes cannot be estimated simultaneously in this model.

plot(fit_gpcm, type = "ccc") and category_curves_report(fit_gpcm) retain the estimated slope for each step-facet level. These are reference-profile curves, however: additive facet main effects and fitted interactions are fixed at zero. The native plot facets multiple curve groups instead of overlaying unlabelled traces, and both native and ggplot displays state the reference profile condition. Inspect CurveBasis, PredictorOffset, and settings$curve_basis before interpreting a curve as if it represented a particular observed Person-by-facet cell.

For unpenalized JML, all-minimum or all-maximum Person patterns can have an unbounded primary ability estimate. A finite adjusted display, when supplied, is kept separate from the likelihood-based primary status. The same principle applies to any GPCM slope whose boundary status has not been resolved: a finite optimizer iterate is not automatically a finite maximum suitable for ordinary inference.

PCM and bounded GPCM can be reviewed on the same data with compare_mfrm(fit_pcm, fit_gpcm), build_weighting_review(fit_pcm, fit_gpcm), or build_model_choice_review(..., run_weighting_review = TRUE). Selectable information-criterion ranking requires comparable, inference-ready MML fits on a common quadrature grid with at least 31 points. Although PCM is the all-unit-slope reduction of the aligned GPCM kernel, the current automatic nesting contract withholds the PCM-versus-GPCM chi-square LRT and records PCM_in_GPCM_ic_only instead.

The practical comparison is available without reconstructing the model matrices manually. After fitting the same data as fit_pcm and fit_gpcm (see the GPCM scope vignette), use:

choice <- build_model_choice_review(PCM = fit_pcm, GPCM = fit_gpcm)
choice$model_roles[, c(
  "Model", "StepCoordinates", "FreeStepParameters",
  "SlopeCoordinates", "FreeSlopeParameters",
  "FitReadiness", "FormalInference", "Interpretation"
)]

The coordinate columns count reported values; the free-parameter columns also apply the fitted constraints. build_weighting_review() keeps JML and MML evidence separate. Comparable, inference-ready MML fits can contribute information criteria, whereas an unpenalized JML likelihood difference is not turned into an automatic PCM-versus-GPCM choice.

Cross-software slope values are not automatically matched estimands. FACETS does not jointly fit Muraki's free-slope polytomous GPCM. FACETS' reported element discrimination is a post-fit diagnostic computed after the Rasch measures and does not feed back into the other estimates; it must not be treated as a free-GPCM slope estimate from mfrmr. TAM can estimate GPCM slopes through its 2PL/GPCM MML route, but its many-facet fitting route does not estimate those slopes. The current immer estimation routes provide PCM- design and hierarchical-rater references rather than a matched free-GPCM fit. Consequently, FACETS and immer are appropriate only for documented equal-discrimination overlaps or deliberately different-model sensitivity checks. A TAM GPCM comparison is numerical only after the response kernel, slope grouping, threshold parameterization, latent-scale identification, retained rows, category map, and covariance information have been matched.

For strict MML diagnostics, keep the two evidence bases distinct:

diag_both <- diagnose_mfrm(
  fit,
  residual_pca = "none",
  diagnostic_mode = "both"
)

summary(diag_both)$diagnostic_basis

The legacy route evaluates residual-oriented summaries using person estimates. The strict marginal route uses latent-integrated expected values. They are complementary screens and should not be collapsed into one decision rule.

Documentation

The package includes the following vignettes:

• End-to-end workflow
• MML estimation and marginal-fit diagnostics
• Migrating from FACETS
• Visual diagnostics
• Reporting and APA-oriented output
• Linking and DFF
• Bounded GPCM scope

Open a guide with vignette("mfrmr-workflow", package = "mfrmr") or list them with browseVignettes("mfrmr"). A printable API overview is installed at cheatsheet/mfrmr-cheatsheet.pdf. Function-level help starts with ?fit_mfrm, ?summary.mfrm_fit, and ?plot.mfrm_fit.

Citation

Use the package citation supplied with the installed version:

citation("mfrmr")

The underlying ordered-response models are described by Andrich (1978), Masters (1982), and Muraki (1992). See the package help and vignettes for the references relevant to each model and diagnostic route.

License

mfrmr is licensed under the MIT License.

Acknowledgements

mfrmr has benefited from discussion and methodological input from Dr. Atsushi Mizumoto and Dr. Taichi Yamashita.