---
title: "GPCM scope and current limitations"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{GPCM scope and current limitations}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
is_cran_check <- !isTRUE(as.logical(Sys.getenv("NOT_CRAN", "false")))
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 7,
  fig.height = 5,
  eval = !is_cran_check
)
```

`mfrmr` includes a bounded implementation of the Generalized Partial Credit
Model (GPCM; Muraki 1992). The bounded estimator is available under the
documented constraints, while several
downstream reporting helpers remain restricted because score-side semantics
under free discrimination differ from the Rasch-family case. This vignette
documents which helpers are available, which are not, and what to use as a
substitute when a helper is restricted.

## Before fitting: model-choice triage

Do not choose `GPCM` only because it is the most flexible model in the menu.
Start with the score interpretation.

| Model | Use when | Main risk if over-used |
|---|---|---|
| `RSM` | The rating scale is intended to share one category-threshold structure across the step facet. | Real threshold differences can be hidden in residual diagnostics. |
| `PCM` | Thresholds may differ by item, criterion, task, or another designated step facet, but rating events should still contribute equally after conditioning on the modeled facets. | It can absorb threshold heterogeneity without asking whether some levels are more discriminating. |
| bounded `GPCM` | The analysis explicitly allows discrimination-based reweighting and treats slopes as part of the substantive sensitivity question. | Better statistical fit can be mistaken for a better operational scoring rule. |

This ordering matters for reporting. `RSM` and `PCM` are the package's
equal-weighting reference route; bounded `GPCM` is a slope-aware extension.
If equal contribution of items, criteria, or raters is part of the validity
argument, a better-fitting bounded `GPCM` should be reported as sensitivity
evidence rather than as an automatic replacement.

## Report wording templates

Use wording that matches the model actually fitted:

- `RSM`: "We fit a many-facet rating-scale Rasch model, treating category
  thresholds as common across the step facet."
- `PCM`: "We fit a many-facet partial-credit Rasch model, allowing thresholds
  to vary by the designated step facet while retaining equal discrimination."
- bounded `GPCM`: "We fit a bounded generalized partial-credit many-facet model
  as a slope-aware sensitivity analysis; interpretation focused on whether
  discrimination-based reweighting changed the substantive conclusions."

Avoid wording that says bounded `GPCM` "improves the score" solely because it
improves log-likelihood, `AIC`, or `BIC`. The model can fit better while changing
the scoring contract.

## Checking the support boundary

`gpcm_capability_matrix()` is the canonical reference. It returns one row
per helper family with a `Status` column drawn from `supported`,
`supported_with_caveat`, `blocked`, and `deferred`. Read `Boundary` for the
interpretive limit and `RecommendedRoute` for the route to use next. The
default print is deliberately compact; subset by status to inspect a focused
set of rows.

```{r capability-supported}
library(mfrmr)
gpcm_capability_matrix("supported")[, c("Area", "Status")]
```

```{r capability-with-caveat}
gpcm_capability_matrix("supported_with_caveat")[, c("Area", "Status")]
```

```{r capability-blocked}
gpcm_capability_matrix("blocked")[, c("Area", "Status", "RecommendedRoute")]
```

```{r capability-deferred}
gpcm_capability_matrix("deferred")[, c("Area", "Status", "Boundary", "RecommendedRoute")]
```

The matrix is intentionally conservative. A row stays in `blocked` or
`deferred` even when some individual computation is already available, because the
scope statement includes the interpretation needed for a complete public
workflow rather than only checking whether code executes.

## Source-grounded recovery interpretation

The bounded `GPCM` route follows Muraki's generalized partial credit model
and its information-function extension. The package-specific `slope_regime`
labels are narrower than that model theory: they summarize the centered
log-slope spread of the simulation generator so recovery evidence can be
read against a declared stress condition. They are not model-fit tests and
they are not literature-derived adequacy cut points.

For simulation reporting, read direct recovery checks in an ADEMP-style order:
the data-generating mechanism first, then the estimands and performance
measures, and only then the row-level recovery diagnostics. In practice, this
means:

1. Build or extract an explicit `mfrm_sim_spec`.
2. Run `evaluate_mfrm_recovery()` for the direct parameter-recovery question.
3. Run `assess_mfrm_recovery()` with practical RMSE/bias limits.
4. Read `summary(recovery_review)`, then
   `recovery_review$condition_reporting_notes` and
   `recovery_review$condition_review`, then
   `recovery_review$diagnostic_reporting_notes` and
   `recovery_review$diagnostic_review` when optional diagnostics were retained,
   then
   `plot(recovery_review, type = "status")`, then
   `plot(recovery_review, type = "metrics", metric = "rmse")`.

## Supported routes and verification evidence

The following bounded-`GPCM` routes are documented and verified within the
stated constraints:

- **Fitting and core summaries** via `fit_mfrm(model = "GPCM", step_facet =
  ...)`. The documented default keeps `slope_facet == step_facet`, with the
  direct `MML` engine.
- **Posterior scoring and information** via `predict_mfrm_units()`,
  `sample_mfrm_plausible_values()`, `compute_information()`, and
  `plot_information()`.
- **Curve and category views** via `plot(fit, type = c("wright",
  "pathway", "ccc", "ccc_surface"))`, `category_structure_report()`, and
  `category_curves_report()`.
- **Slope-aware simulation specifications** via `build_mfrm_sim_spec()`
  and `simulate_mfrm_data()`.
- **Direct recovery checks** via `evaluate_mfrm_recovery()` and
  `assess_mfrm_recovery()`, including fitted bounded-GPCM slope recovery on the
  log-slope scale.

## What works with caveats

The following are exposed for `GPCM` but should be read as exploratory
screens rather than as Rasch-style invariance evidence:

- `diagnose_mfrm()` and the residual and unexpected-response stack:
  `unexpected_response_table()`, `displacement_table()`,
  `measurable_summary_table()`, `rating_scale_table()`,
  `interrater_agreement_table()`, `facet_quality_dashboard()`,
  `plot_qc_dashboard()`, `plot_marginal_fit()`,
  `plot_marginal_pairwise()`.
- `reporting_checklist()` and `precision_review_report()` route to the
  supported direct tables and plots. The broader APA/QC/export family is
  available as caveated sensitivity-reporting output with explicit
  `gpcm_boundary` rows.
- `build_misfit_casebook()` inherits the exploratory screening framing of
  its underlying sources.
- `estimate_bias()` now provides bounded-GPCM conditional screening rows with
  slope-aware information and profile-likelihood columns. Treat these rows as
  screening evidence for follow-up, not as standalone confirmatory fairness
  tests. `unexpected_after_bias_table()` provides a descriptive in-sample
  before/after flag comparison; a lower flag count does not show that bias has
  been removed.
- `estimation_iteration_report()` provides a slope-aware reconstructed
  optimization trajectory. It is a diagnostic replay, not the exact optimizer
  history or an additional convergence test.
- `analyze_dff()`, `analyze_dif()`, `dif_interaction_table()`,
  `dif_report()`, `plot_dif_heatmap()`, and `plot_dif_summary()` provide
  bounded-GPCM DFF/DIF screening and reporting surfaces with explicit
  `gpcm_boundary` rows.
- `build_apa_outputs()`, `build_visual_summaries()`, `run_qc_pipeline()`,
  `build_mfrm_manifest()`, `build_mfrm_replay_script()`,
  `export_mfrm_bundle()`, package-native scorefile export, and
  `build_linking_review()` return caveated bounded-`GPCM` reporting or
  exploratory-review objects with explicit `gpcm_boundary` rows. The
  package-native scorefile can include native structural delta-method
  expected-score SEs and score-side delta SEs selected by `score_se_method`
  when the required MML diagnostics are available, but those SEs are not
  FACETS-equivalent score-side uncertainty.
- `evaluate_mfrm_design()`, `predict_mfrm_population()`,
  `evaluate_mfrm_diagnostic_screening()`, and
  `evaluate_mfrm_signal_detection()` are available as caveated role-based
  repeated simulation/refit routes. Treat their outputs as design-level or
  screening sensitivity evidence, not as operational scoring, calibrated
  inferential testing, or arbitrary-facet planning validation.

The dashboard marks the fair-average panel unavailable under `GPCM`; use
`fair_average_table()` directly for the slope-aware element-conditional table
and `fair_average_table(fair_se = TRUE)` when you need structural
fair-average SEs for non-person rows.

## What is intentionally restricted

The slope-aware `fair_average_table()` route and package-native scorefile route
are available under `GPCM`, including native expected-score uncertainty and
score-side delta SEs where the required MML diagnostics support them. Full
FACETS-style score-side compatibility remains restricted because free
discrimination changes the relationship between the latent measure and
operational score-side summaries. Specifically:

- `facets_output_contract_review()` still depends on FACETS-style
  compatibility semantics that are not generalized to free discrimination.
- posterior-predictive checks and MCMC estimation are not available in mfrmr;
  use external Bayesian software when those analyses are required.
- Caveated reporting, export, linking, design-forecast, and screening helpers
  must keep their `gpcm_boundary` wording visible and must not imply
  FACETS-equivalent score-side uncertainty, operational scoring, calibrated
  screening gates, or arbitrary-facet planning validation.

## Recommended substitutes

When a restricted helper is needed for a `GPCM` report, the practical paths
are:

- Refit with `model = "PCM"` if the discrimination-free assumption is
  defensible for the data and a full FACETS score-side review is required;
  `compare_mfrm()` quantifies the loss in fit.
- Keep the report on the `GPCM` fit itself but draft the manuscript section
  manually around the supported tables: `summary(fit)` for parameters,
  `diagnose_mfrm()` for residual fit, `facet_quality_dashboard()` for the
  per-facet quality summary, and `compute_information()` for precision
  evidence.
- When a Rasch-family baseline comparison is substantively useful, optionally
  generate a second manifest from a parallel `RSM` or `PCM` fit. The two fits
  can be reported side by side, with the `GPCM` fit identified as the
  discrimination-aware counterpart. This is not required to use the caveated
  bounded-`GPCM` manifest/replay/export route.

Restricted helpers use the capability matrix at runtime. An unsupported
bounded-`GPCM` call stops with the relevant limitation and a supported
alternative instead of producing a partial score-side or backend result. Use
`gpcm_capability_matrix()` or `mfrmr_output_guide("gpcm")` before choosing a
downstream route.

## A worked example

The `example_core` dataset includes a small synthetic block that supports a
bounded `GPCM` fit. This example uses compact quadrature and iteration settings
to keep optional local execution short; for final evidence, rerun with the
package default or a higher quadrature setting and a larger recovery design.

```r
library(mfrmr)
toy <- load_mfrmr_data("example_core")

fit_gpcm <- fit_mfrm(
  data = toy,
  person = "Person",
  facets = c("Rater", "Criterion"),
  step_facet = "Criterion",
  score = "Score",
  model = "GPCM",
  method = "MML",
  quad_points = 7,
  maxit = 20
)

summary(fit_gpcm)

diag_gpcm <- diagnose_mfrm(fit_gpcm)
summary(diag_gpcm)

info <- compute_information(fit_gpcm)
plot_information(info)

rec_gpcm <- evaluate_mfrm_recovery(
  sim_spec = build_mfrm_sim_spec(
    n_person = 30,
    n_rater = 3,
    n_criterion = 4,
    raters_per_person = 2,
    model = "GPCM",
    step_facet = "Criterion",
    slope_facet = "Criterion",
    slopes = c(0.8, 1.0, 1.15, 1.05)
  ),
  reps = 10,
  model = "GPCM",
  fit_method = "MML",
  quad_points = 7,
  maxit = 20,
  include_diagnostics = TRUE,
  diagnostic_fit_df_method = "both",
  seed = 1
)
review_gpcm <- assess_mfrm_recovery(
  rec_gpcm,
  max_rmse = c(facet = 0.5, step = 0.5, slope = 0.25),
  max_abs_bias = c(default = 0.25)
)

summary(review_gpcm)$overview
summary(review_gpcm)$reading_order
review_gpcm$condition_reporting_notes[, c(
  "ConditionArea", "ReportingAttention", "ConditionFinding"
)]
review_gpcm$condition_review[, c(
  "Model", "GPCMSlopeRegime", "StressLevel", "ScoreSupportStatus"
)]
review_gpcm$diagnostic_reporting_notes[, c(
  "Facet", "ReportingAttention", "DiagnosticFinding"
)]
summary(review_gpcm)$diagnostic_review
plot(review_gpcm, type = "status")
plot(review_gpcm, type = "metrics", metric = "rmse")

```

The fit, summary, residual diagnostics, information, recovery, fair-average, and
conditional bias-screening helpers all run under `GPCM` with the caveats listed
above. `build_apa_outputs(fit_gpcm)` returns a caveated sensitivity-reporting
object with a `gpcm_boundary`; full FACETS score-side review remains on the
`RSM` / `PCM` route.

## Current boundary

Score-side semantics for free-discrimination polytomous models differ from the
Rasch-family route. Use the current matrix returned by
`gpcm_capability_matrix()` as the workflow contract and
`gpcm_score_side_contract()` for score-side alternatives.