Sample approximate plausible values under fitted posterior scoring

Usage

sample_mfrm_plausible_values(
  fit,
  new_data,
  person = NULL,
  facets = NULL,
  score = NULL,
  weight = NULL,
  person_data = NULL,
  person_id = NULL,
  population_policy = c("error", "omit"),
  n_draws = 5,
  interval_level = 0.95,
  scoring_quad_points = 31L,
  readiness_policy = c("error", "review"),
  seed = NULL,
  scoring_prior = NULL
)

Arguments

fit: Output from fit_mfrm() estimated with method = "MML" or method = "JML".
new_data: Long-format data for the future or partially observed units to be scored.
person: Optional person column in new_data. Defaults to the person column recorded in fit.
facets: Optional facet-column mapping for new_data. Supply either an unnamed character vector in the calibrated facet order or a named vector whose names are the calibrated facet names and whose values are the column names in new_data.
score: Optional score column in new_data. Defaults to the score column recorded in fit.
weight: Optional weight column in new_data. Defaults to the weight column recorded in fit, if any.
person_data: Optional one-row-per-person data.frame with the background variables required by a latent-regression fit. Ignored for ordinary fitted-object posterior scoring. Intercept-only latent-regression fits can reconstruct the minimal scored-person table internally. This is the scoring-time table for new_data, not the fit object's replay/export provenance table. For categorical background variables, supply values on the same coding scale used at fit time; the fitted factor levels and contrasts are reused when building the scoring design matrix. Fitted standardization and polynomial/spline bases are also reused; they are not re-estimated from the scoring cohort.
person_id: Optional person-ID column in person_data.
population_policy: How missing background data are handled when fit uses the latent-regression branch. "error" (default) requires complete person-level covariates; "omit" drops scored persons lacking complete covariates and records that omission in population_review.
n_draws: Number of posterior draws per person. Must be a positive integer.
interval_level: Posterior interval level passed to predict_mfrm_units() for the accompanying EAP summary table. The same level selects the empirical draw quantiles reported by summary().
scoring_quad_points: Number of Gauss-Hermite nodes used only for this scoring call. Passed to predict_mfrm_units() and independent of the fit-time quadrature order. Fixed or adaptive integration is inherited from fit.
readiness_policy: Source-fit readiness policy passed to predict_mfrm_units(). Conditional calibration and scoring-integration checks are shared with that function and retained in the returned settings.
seed: Optional seed for reproducible posterior draws.
scoring_prior: Optional normal scoring prior, list(mean = ..., sd = ...), passed to predict_mfrm_units(). NULL retains the fitted scoring prior. Estimates and draws retain both the original and the supplied prior; checks of the fitted calibration and numerical accuracy are unchanged.

Value

An object of class mfrm_plausible_values with components:

values: one row per person per draw
estimates: companion posterior EAP summaries
row_review: row-preparation review
population_review: optional person-level omission review for latent-regression scoring
input_data: cleaned canonical scoring rows retained from new_data
person_data: cleaned or supplied person-level background data used for latent-regression scoring; NULL otherwise
settings: scoring settings
notes: interpretation notes

Details

sample_mfrm_plausible_values() uses predict_mfrm_units() to return draws from each Person's posterior distribution as a standalone object. It is useful when downstream workflows want repeated latent-value imputations rather than just one posterior EAP summary.

In the current mfrmr implementation these are approximate plausible values drawn from the fitted quadrature-grid posterior under the scoring basis implied by fit, unless scoring_prior explicitly supplies another normal prior. With the default prior, for ordinary MML fits this is the fitted marginal calibration; for latent-regression MML fits it is the fitted conditional normal population model for the scored persons; for JML fits it is the fixed facet/step calibration together with a standard normal reference prior on the quadrature grid. They should be interpreted as posterior uncertainty summaries for the scored persons, not as deterministic future truth values and not as a claim of full many-facet plausible-values equivalence with population-model software.

In other words, the JML path here is a practical scoring approximation layered on top of the fitted joint-likelihood calibration, whereas the latent-regression MML path uses the fitted one-dimensional conditional normal population model. Neither path should be described as a full many-facet plausible-values system with all ConQuest-style extensions.

Interpreting output

values contains one row per person per draw.
estimates contains the companion posterior EAP summaries from predict_mfrm_units().
summary() reports draw counts and empirical draw summaries by person. LowerValue and UpperValue use the requested interval_level and are labelled with IntervalLevel and DrawSummaryBasis. They are empirical quantiles of a finite sample of discrete draws, not the continuous posterior limits in the companion estimates table. With few draws they are coarse; one draw has an unavailable empirical SD. Recreate older summaries from the original plausible-values object to update these limits and labels; no refitting or resampling is needed.

What this does not justify

This helper does not update the calibration, estimate new non-person facet levels, or provide exact future true values. It samples from the quadrature- grid posterior implied by the existing fitted-model scoring basis, using fixed or Person-specific adaptive nodes according to the fit's setting. Calibration and population parameters remain fixed. These draws alone do not validate downstream group comparisons or regressions; those analyses require a compatible conditioning model and sampling design.

References

The underlying posterior scoring follows the usual quadrature-based EAP framework of Bock and Aitkin (1981). The interpretation of multiple posterior draws as plausible-value-style summaries follows the general logic discussed by Mislevy (1991), while the current implementation remains a practical fitted-object posterior approximation rather than a full published many-facet plausible-values method. For JML source fits, the quadrature posterior uses a package-level standard normal reference prior for this post hoc scoring layer.

Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46(4), 443-459.
Mislevy, R. J. (1991). Randomization-based inference about latent variables from complex samples. Psychometrika, 56(2), 177-196.

Examples

toy <- load_mfrmr_data("example_core")
keep_people <- unique(toy$Person)[1:18]
toy_fit <- fit_mfrm(
  toy[toy$Person %in% keep_people, , drop = FALSE],
  "Person", c("Rater", "Criterion"), "Score",
  method = "MML",
  quad_points = 5,
  maxit = 30
)
new_units <- data.frame(
  Person = c("NEW01", "NEW01"),
  Rater = unique(toy$Rater)[1],
  Criterion = unique(toy$Criterion)[1:2],
  Score = c(2, 3)
)
pv <- sample_mfrm_plausible_values(toy_fit, new_units, n_draws = 3, seed = 1)
summary(pv)$draw_summary
#> # A tibble: 1 × 23
#>   Person Draws MeanValue SDValue LowerValue UpperValue IntervalLevel
#>   <chr>  <dbl>     <dbl>   <dbl>      <dbl>      <dbl>         <dbl>
#> 1 NEW01      3    -0.373   0.323      -0.56          0          0.95
#> # ℹ 16 more variables: DrawSummaryBasis <chr>, CalibrationMethod <chr>,
#> #   Prior <chr>, PriorMean <dbl>, PriorSD <dbl>, PriorSource <chr>,
#> #   RetainedPrior <chr>, RetainedPriorMean <dbl>, RetainedPriorSD <dbl>,
#> #   WeightedLikelihood <lgl>, UncertaintyBasis <chr>, ScoringAlgorithm <chr>,
#> #   SourceScoringReady <lgl>, ScoreIntegrationReady <lgl>, EstimateUse <chr>,
#> #   DrawBasis <chr>