mfrmr Linking and DFF Guide

Package-native guide to checking connectedness, building anchor-based links, monitoring drift, and screening differential facet functioning (DFF) in mfrmr.

Start with the linking question

• "Is the design connected enough to support a common scale?" Use subset_connectivity_report() and plot(..., type = "design_matrix").

• "Which elements can I export as anchors from an existing fit?" Use make_anchor_table() and review_mfrm_anchors().

• "How do I anchor a new administration to a baseline?" Use anchor_to_baseline().

• "Have common elements drifted across separately fitted waves?" Use detect_anchor_drift() and plot_anchor_drift().

• "Can I synthesize anchor review, drift, and chain evidence into one review?" Use build_linking_review().

• "Do specific facet levels function differently across groups?" Use analyze_dff(), plot_dif_heatmap(), and plot_dif_summary().

Recommended linking route

1. Fit with fit_mfrm() and diagnose with diagnose_mfrm().

2. Check connectedness with subset_connectivity_report().

3. Build or review anchors with make_anchor_table() and review_mfrm_anchors().

4. Use anchor_to_baseline() when you need to place raw new data onto a baseline scale.

5. Use build_equating_chain() only as a screened linking aid across already fitted waves.

6. Use detect_anchor_drift() for stability monitoring on separately fitted waves.

7. Use build_linking_review() when you need one operational synthesis object rather than separate anchor/drift/chain tables.

8. Run analyze_dff() only after checking connectivity and common-scale evidence.

Which helper answers which task

subset_connectivity_report()

Summarizes connected subsets, bottleneck facets, and design-matrix coverage.

make_anchor_table()

Extracts reusable anchor candidates from a fit.

anchor_to_baseline()

Anchors new raw data to a baseline fit and returns anchored diagnostics plus a consistency check against the baseline scale.

detect_anchor_drift()

Compares fitted waves directly to flag unstable anchor elements.

build_equating_chain()

Accumulates screened pairwise links across a series of administrations or forms.

build_linking_review()

Synthesizes anchor review, drift, and screened-chain evidence into one operational review surface.

analyze_dff()

Screens differential facet functioning with residual or refit methods, using screening-only language unless linking and precision support stronger interpretation.

Practical linking rules

• Check connectedness before interpreting subgroup or wave differences.

• Use DFF outputs as screening results when common-scale linking is weak.

• Always name the facet, facet level, and group pair involved in a DFF contrast. A generic "DIF exists" statement is not interpretable in a many-facet design.

• Residual-method DFF classifications are screening labels. ETS A/B/C labels require refit output whose ClassificationSystem is "ETS".

• Treat drift flags as prompts for review, not automatic evidence that an anchor must be removed.

• Treat LinkSupportAdequate = FALSE as a weak-link warning: at least one linking facet retained fewer than 5 common elements after screening.

• Rebuild anchors from a defensible baseline rather than chaining unstable links by hand.

Typical workflow

• Cross-sectional linkage review: fit_mfrm() -> diagnose_mfrm() -> subset_connectivity_report() -> plot(..., type = "design_matrix").

• Baseline placement review: make_anchor_table() -> anchor_to_baseline() -> diagnose_mfrm().

• Multi-wave drift review: fit each wave separately -> detect_anchor_drift() -> build_linking_review() -> plot_anchor_drift().

• Group comparison route: subset_connectivity_report() -> analyze_dff() -> dif_report() -> plot_dif_heatmap() / plot_dif_summary().

Companion guides

• For visual follow-up, see mfrmr_visual_diagnostics.

• For report/table selection, see mfrmr_reports_and_tables.

• For end-to-end routes, see mfrmr_workflow_methods.

• For a longer walkthrough, see vignette("mfrmr-linking-and-dff", package = "mfrmr").

Examples

if (FALSE) { # \dontrun{
toy <- load_mfrmr_data("example_bias")
fit <- fit_mfrm(
  toy,
  person = "Person",
  facets = c("Rater", "Criterion"),
  score = "Score",
  method = "MML",
  quad_points = 7,
  maxit = 30
)
diag <- diagnose_mfrm(fit, residual_pca = "none", diagnostic_mode = "both")

subsets <- subset_connectivity_report(fit, diagnostics = diag)
subsets$summary[, c("Subset", "Observations", "ObservationPercent")]

dff <- analyze_dff(fit, diag, facet = "Rater", group = "Group", data = toy)
head(dff$dif_table[, c("Level", "Group1", "Group2",
                       "Classification", "ClassificationSystem")])
} # }