mfrmr Linking and DFF

In mfrmr: Estimation and Diagnostics for Many-Facet Measurement Models

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 7,
  fig.height = 5
)

This vignette covers the package-native route for:

• checking whether a design is connected enough for a common scale
• exporting anchor candidates from an existing fit
• screening differential facet functioning (DFF)
• deciding when subgroup contrasts are descriptive versus formally comparable

For a broader workflow guide, see vignette("mfrmr-workflow", package = "mfrmr"). For the shorter help-page map, see help("mfrmr_linking_and_dff", package = "mfrmr").

Minimal setup

library(mfrmr)

bias_df <- load_mfrmr_data("example_bias")

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 audit_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. Multi-wave anchor review

When you work across administrations, the route usually moves from anchor export to anchored fitting and then to drift review.

d1 <- load_mfrmr_data("study1")
d2 <- load_mfrmr_data("study2")

fit1 <- fit_mfrm(d1, "Person", c("Rater", "Criterion"), "Score",
                 method = "JML", maxit = 25)
fit2 <- fit_mfrm(d2, "Person", c("Rater", "Criterion"), "Score",
                 method = "JML", maxit = 25)

anchored <- anchor_to_baseline(
  d2,
  fit1,
  person = "Person",
  facets = c("Rater", "Criterion"),
  score = "Score"
)

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 audit_mfrm_anchors()
5. analyze_dff()
6. dif_report() and plot_dif_heatmap()
7. 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("detect_anchor_drift", package = "mfrmr")

mfrmr documentation built on March 31, 2026, 1:06 a.m.