mfrmr Linking and DFF

Minimal setup

library(mfrmr)

bias_df <- load_mfrmr_data("example_bias")

# The vignette uses compact quadrature so optional local execution stays fast.
# For final DFF or linking evidence, refit with the package default or a higher
# quadrature setting and record that setting in the analysis log.
fit <- fit_mfrm(
  bias_df,
  person = "Person",
  facets = c("Rater", "Criterion"),
  score = "Score",
  method = "MML",
  model = "RSM",
  quad_points = 7
)

diag <- diagnose_mfrm(fit, residual_pca = "none")

1. Check connectedness first

Use subset_connectivity_report() before interpreting subgroup or cross-form contrasts.

sc <- subset_connectivity_report(fit, diagnostics = diag)

sc$summary[, c("Subset", "Observations", "ObservationPercent")]
plot(sc, type = "design_matrix", preset = "publication")

Interpretation:

• Sparse rows or columns indicate weaker design coverage.
• Weak coverage should lower confidence in subgroup comparisons.

2. Export anchor candidates

make_anchor_table() is the shortest route when you need reusable anchor elements from an existing calibration.

anchors <- make_anchor_table(fit, facets = "Criterion")
head(anchors)

Use review_mfrm_anchors() when you want a stricter review of anchor quality.

3. Residual DFF as a screening layer

Residual DFF is the fast screening route. It is useful for triage, but it is not automatically a logit-scale inferential contrast.

dff_resid <- analyze_dff(
  fit,
  diag,
  facet = "Criterion",
  group = "Group",
  data = bias_df,
  method = "residual"
)

dff_resid$summary
head(
  dff_resid$dif_table[, c("Level", "Group1", "Group2", "Classification", "ClassificationSystem")],
  8
)
plot_dif_heatmap(dff_resid)

Interpretation:

• Treat residual output as screening evidence.
• Check ClassificationSystem to see how the current residual screen was labeled.
• Reserve ScaleLinkStatus and ContrastComparable for refit-based contrasts.

4. Refit DFF when subgroup comparisons are defensible

The refit route can support logit-scale contrasts only when subgroup linking is adequate and the precision layer supports it.

dff_refit <- analyze_dff(
  fit,
  diag,
  facet = "Criterion",
  group = "Group",
  data = bias_df,
  method = "refit"
)

dff_refit$summary
head(
  dff_refit$dif_table[, c("Level", "Group1", "Group2", "Classification", "ContrastComparable")],
  8
)

5. Cell-level follow-up

If the level-wise screen points to a specific facet, follow up with the interaction table and narrative report.

dit <- dif_interaction_table(
  fit,
  diag,
  facet = "Criterion",
  group = "Group",
  data = bias_df
)

head(dit$table)

dr <- dif_report(dff_resid)
cat(dr$narrative)

6. Model-estimated facet interactions

Residual bias and DFF tools screen for unusual cells after fitting the additive model. When the interaction hypothesis is specified in advance, use facet_interactions to estimate the named two-way non-person facet interaction in the model likelihood.

fit_add <- fit_mfrm(
  bias_df,
  person = "Person",
  facets = c("Rater", "Criterion"),
  score = "Score",
  method = "MML",
  model = "RSM",
  quad_points = 7
)

fit_interaction <- fit_mfrm(
  bias_df,
  person = "Person",
  facets = c("Rater", "Criterion"),
  score = "Score",
  method = "MML",
  model = "RSM",
  facet_interactions = "Rater:Criterion",
  quad_points = 7
)

interaction_effect_table(fit_interaction)
compare_mfrm(Additive = fit_add, Interaction = fit_interaction, nested = TRUE)

Interpretation:

• Name the facet pair explicitly before fitting.
• Treat the interaction estimates as fixed-effect deviations from the additive MFRM under zero marginal-sum constraints.
• Inspect sparse interaction cells before reporting substantive claims.
• Keep this route separate from residual screening with estimate_bias().

7. Multi-wave anchor review

When you work across administrations, the route usually moves from a declared common-anchor design to anchored fitting and then to drift review. The block below is schematic: wave1 and wave2 must be administrations for which the listed facet levels have documented cross-wave identity and unchanged meaning.

Do not substitute ej2021_study1 and ej2021_study2 here. They are independent legacy synthetic studies; reused raw labels do not identify common persons, raters, or anchors and do not link their scales.

declared_common_facets <- c("Criterion")

fit1 <- fit_mfrm(
  wave1, "Person", c("Rater", "Criterion"), "Score",
  method = "MML"
)

anchored <- anchor_to_baseline(
  wave2,
  fit1,
  person = "Person",
  facets = c("Rater", "Criterion"),
  score = "Score",
  anchor_facets = declared_common_facets
)

fit2 <- fit_mfrm(
  wave2, "Person", c("Rater", "Criterion"), "Score",
  method = "MML"
)
drift <- detect_anchor_drift(list(Wave1 = fit1, Wave2 = fit2))
plot_anchor_drift(drift, type = "drift", preset = "publication")

Recommended sequence

For a compact linking route:

1. fit_mfrm()
2. diagnose_mfrm()
3. subset_connectivity_report()
4. make_anchor_table() or review_mfrm_anchors()
5. analyze_dff()
6. dif_report() and plot_dif_heatmap()
7. interaction_effect_table() after a confirmatory facet_interactions fit
8. anchor_to_baseline() / detect_anchor_drift() when working across waves

Related help

• help("mfrmr_linking_and_dff", package = "mfrmr")
• help("subset_connectivity_report", package = "mfrmr")
• help("analyze_dff", package = "mfrmr")
• help("interaction_effect_table", package = "mfrmr")
• help("detect_anchor_drift", package = "mfrmr")