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.

What does an anchor do?

Suppose a previous calibration placed Rater R01 at 0.35 logits. A direct anchor tells the new fit to keep that value exactly; the new ratings do not re-estimate it. This requires the same rater identity, model orientation and a defensible stability assumption, not just the same text label.

Keep four ideas separate:

Common ratings: overlapping Persons, tasks or raters connect observed ratings. Their parameter values need not be known or fixed.
Scale identification: a constraint such as a zero mean sets an origin for otherwise interchangeable coordinates. It does not establish invariance.
Direct anchors: Facet, Level, Anchor fixes a location. For example, R01 = 0.35 means exactly 0.35 on the internal logit scale.
Group anchors: Facet, Level, Group, GroupValue fixes a mean. For R01 and R02 in a group with target 0.20, their locations must sum to 0.40; neither location is individually fixed unless also directly anchored. This is an unweighted mean across declared levels, including fixed members.

What the current implementation supports

Non-Person location constraints are available in supported ordinary MML/JML fits. Person direct/group constraints require JML; MML integrates ability and rejects them. This is an implementation boundary, not a claim that fixed-Person MML is mathematically impossible. Two-family GPCM has separate restrictions; see gpcm_capability_matrix().

With centering_scope = "facet" (the ordinary-fit default), centered facets sum to zero across all levels, including direct anchors and group totals. A single ungrouped remainder therefore balances those totals. Use centering_scope = "remainder" to reproduce earlier fits that centered only the levels outside direct/group constraints. Ordinary additive RSM/PCM JML also offers centering_scope = "anchor_origin": direct or group anchors replace their facet's centering, with an unanchored, active noncenter facet. Group targets are repeated arithmetic means, not per-element contributions. The default remains "facet". Read fit_mfrm() before linking a cohort with new raters or tasks; population and noncenter_facet settings also determine the scale. Contradictory constraints stop before estimation.

anchor_to_baseline() transfers selected facet locations, not a whole calibration: thresholds/slopes are re-estimated, and most settings must be supplied again. RSM/PCM MML defaults to a fixed standard-normal population; anchoring does not automatically estimate a changed ability distribution. Use extract_mfrm_calibration() and score_mfrm_calibration() to score against a complete fixed calibration within that separate workflow's supported scope.

Annual assessments with common recordings

Suppose an English speech contest has new contestants each year, mostly the same judges, and a common three-minute format. Judges also rate the same recorded speeches each year. These recordings can connect annual ratings if their performance meaning and scoring conditions remain comparable. Returning judges or unchanged criterion names alone do not establish that their severity or interpretation stayed constant.

Give the same recording the same performance ID across years. Give a new speech a new performance ID, even if its speaker competed before. Keep judge identity and rating year/session separately: the question is how a judge's severity changes, not whether that judge is the same person. Contestant-group differences are distinct from individual growth.

Two analysis strategies have different assumptions:

Joint calibration: share an unknown performance measure for each common recording across years and estimate judge-year effects. The recording values need not be known or passed to anchors. Shared unknown measures still require an identified model and common scale.
Fixed-reference calibration: fix previously calibrated recording measures when fitting a later year, while estimating its judges' effects. When recordings occupy the Person role, those direct anchors require JML in the current implementation. The receiving fit treats their values as exact; their source estimation error is excluded.

Do not fix the returning judges' severities merely because they return. Also, centering the panel to the same mean separately each year can remove the panel-wide change being studied. Annual rater effects, criterion/step invariance and population assumptions must be specified together. Separate fixed-standard-normal MML fits do not estimate changing cohort means.

Current helper output answers narrower questions. In an anchored result, $drift compares retained fixed non-Person values with their supplied values; zero differences do not show stability. In detect_anchor_drift(), $drift_table$Drift subtracts LinkOffset. If judges are the linking set, a common shift in all their estimates is removed; the remainder cannot establish that the panel was stable. Nor does LinkOffset alone identify a real panel change, since it can also reflect different coordinates.

Preserve individual ratings before discussion or disclosure of reference scores, training phase, and video/live mode. Check coverage across performance levels and criteria, memory of familiar scores, shared assignments and dependence among repeated ratings. Training agreement alone does not demonstrate stable operational scoring. A complete common-recording workflow and formal year-difference intervals are not yet verified in mfrmr; conditional anchor SEs do not supply cross-year covariance or source-anchor uncertainty. The companion linking vignette develops this design example and explains what the existing returned tables can establish.

Two schools connected by common recordings

Suppose School A has 30 students and five raters, School B has 40 students and three raters, and both use three tasks. If each rater scores only their own school's students, common tasks alone do not separate a school-specific shift in student ability from an equal shift in its panel's severity. Having all eight raters independently score the same three recordings can supply that missing link. In a joint calibration, the common performances share IDs and unknown measures; their scores need not be known anchors. Unique local student IDs and distinct rater IDs prevent accidental overlap. Record the task actually performed in each recording; do not replicate a single recording across tasks that were never observed. Define whether the measured unit is a student across tasks or a particular performance.

This supports a model-based common scale under the linking assumptions, not automatic interchangeability of school raw scores or a causal school effect. Three recordings are three shared performances, not 24 independent linking performances merely because eight raters assess each. Their ability range, category coverage and stability across panels matter. Review whether judgments were independent, reference scores were disclosed, or recording versus live presentation changes severity. A connected graph is necessary evidence to inspect, not proof of identification, precision or invariance.

Specify each rater-by-school comparison separately. A rater's A-minus-B effect relative to the entire panel is different from the difference between two raters' A-minus-B effects. With incomplete school coverage, the second comparison can be identified even when the first is not. State the reference raters and their weights; dropping an unobserved rater changes a whole-panel comparison. Under PCM, also state the step owner: a location contrast alone need not describe every adjacent-category response contrast when the compared raters own different step ladders.

Preserve a recording's school of origin when another school rates it. Shared neutral recordings can connect the scale without supplying the missing A-versus-B observations for each rater. A common latent-population assumption can supply information absent from an unrestricted-Person comparison; allowing school-specific population means can restore that ambiguity. These are different assumptions, not evidence that MML always resolves an unidentified JML comparison. Use describe_mfrm_data() with comparisons to review explicitly weighted RSM/PCM interaction contrasts before fitting. Its conditional-map results and MML limitations remain separate from marginal identification and from residual/refit DFF effects. Its IdentificationBasis column distinguishes a target identified in the unrestricted-Person response model from one whose conditional identification requires the declared population restrictions. Neither makes MML distribution-free or proves global marginal identification. CML instead records identification from conditional support at the observed totals. analyze_dff() can retain that review as comparison_review after checking the retained responses and origin labels; it does not automatically certify the identification of its own residual/refit contrasts. For a matching joint interaction fit, pass the review to interaction_effect_table() or summary(fit, comparison_review = review). These return descriptive weighted interaction estimates after full conditional-rank, model/data alignment and retained-point numerical checks. Unavailable rows retain reasons and separate optimizer traces. Positive MML conditional ranks still do not certify global marginal identification; no partial fit is run by extraction. For target-only identification, explicitly use fit_mfrm(fit_scope = "comparisons", comparison_review = review) with the review's model arguments. Its separate comparison result preserves the observed likelihood and invariant targets, checks JML recession and numerical adequacy, and retains unidentified/failed targets as missing. MML conclusions remain conditional/local; JML/MML comparison fits supply no formal uncertainty. Declaring method = "CML" in the review enables conditional-information SEs and pointwise 95 percent Wald intervals for identified RSM/PCM contrasts. mfrm_facet_intervals(fit) reuses these saved comparisons for interval plots and APA tables, retaining unidentified rows without estimates. Its level argument changes the normal critical value without refitting. Identification uses conditional support at the actual Person totals, and finite-MLE and information checks determine availability. Unidentified targets remain missing. This route needs no ability distribution and estimates no population SD; its asymptotic intervals do not establish finite-sample coverage or a calibrated DFF classification. See fit_mfrm() and the linking vignette.

For matching full RSM/PCM MML fits, mfrm_facet_intervals() with comparison_review adds model-based interaction intervals after joint information and finer-grid checks. scale = "standardized" divides by the same fit's estimated intercept-only normal population SD, with the full joint delta method. That common-population assumption differs from ~Group; the latter supports native intervals but its residual SD is not treated as marginal population SD. Numerical eligibility does not certify global marginal identification or finite-sample coverage.

GPCM comparisons also require the slope owner and ability scale. A positive location difference does not ensure that the expected-score difference has the same sign across ability: unequal slopes can produce crossing response curves. Specify the ability range and compare category probabilities or expected scores with the actual step ladders. One-family slopes have geometric mean one; under default MML the population standard deviation supplies the common discrimination scale. Fixing both that standard deviation and the slope geometric mean to one imposes a narrower model.

With two slope families, distinguish each observed effective slope product from its individual facet components. Disconnected facet crossings can preserve observed products while reversing a component comparison; the current fit route rejects that design. Predicting an unobserved crossing depends on the multiplicative slope model. A full-rank product map alone does not certify the full marginal response model, and a local numerical rank check is not a global identification or precision guarantee. The supported two-family route uses fixed-standard-normal MML with exactly two measurement facets; it does not supply a rater-by-school interaction model.

Prefer the joint route when no externally established reference values are available. Fixing previously estimated recording values in the Person role instead uses the JML-only anchor route and excludes their source uncertainty. Do not force each school's rater panel to have the same mean to manufacture a link, or add School as a free additive response facet alongside unrestricted student effects without checking identification. A population school-mean contrast needs its own population model and handling of common recordings outside those cohorts; it is not an ordinary comparison of EAP means. The existing common-recording workflow has not yet been verified end to end for this school design or its school-difference uncertainty.

Can I obtain intervals when I use anchors?

For ordinary unit-weight RSM/PCM MML with fixed standard-normal ability and fixed-grid integration, mfrm_facet_intervals() can return model-information or cluster-sandwich intervals for free facet locations and contrasts, subject to its checks. These intervals condition on the supplied anchors. A fixed location has SE zero and no inferential bounds; its source uncertainty has not been estimated by the receiving fit.

Estimating the population mean and variance with anchors is a different configuration. Its point estimates are supported, but the native population and location interval helpers currently exclude anchors and constraint groups. An EstimabilityState of "not_evaluated" denotes an incomplete identification check, not failed optimization or proof of nonidentifiability. Inspect fit$readiness$fit for numerical status and fit$data_review$estimability$nonlinear_local_estimability for the separate local-rank result. Passing that local check alone does not authorize intervals or anchor export for reuse. Do not choose a fixed population solely to obtain intervals when its assumptions are inappropriate.

One-family GPCM MML has a separate slope/curve route: confint.mfrm_fit() with parm = "slopes" and mfrm_curve_intervals() can condition on fixed anchors when their own checks pass. Anchored native-location/profile-slope intervals and portable GPCM extraction remain unavailable. An available interval does not certify the separate integration checks required by predict_mfrm_units().

Reusing an analysis saved before the centering change

Read the original result: readRDS() preserves its coefficients and constraints. summary(fit, compute = "never")$settings_overview and specifications_report() identify the centering convention. A native fit without convention metadata uses the legacy "remainder" interpretation.
Repeat the original analysis: build_mfrm_replay_script() embeds its anchors and retains that convention. Running the script refits the model; it does not merely read a saved result.
Adopt whole-facet centering: refit from the original responses with centering_scope = "facet" and the intended anchor, population, rubric, uncentered-facet and owner settings. Do not edit fit$config or recenter an output table to convert the fit. Keep the old and new analyses separately.
Refresh derived output: recompute interval objects from the unchanged fit for revised fixed-contrast derivatives or anchor explanations. Rerun affected analyze_dff() subgroup analyses to retain target/Person anchors; this does require subgroup refitting. Loading old interval/DFF objects does not update them.
Keep a frozen calibration: load_mfrm_calibration() preserves its original labels and values. Re-extract from the source fit, satisfying the current validation requirements, for explicit centering labels. If only the fit survives without the required RSM/PCM MML quadrature review, obtaining that review needs the original data and additional grid fits. If only the calibration file survives, do not infer a missing convention or relabel it; keep its original scoring interpretation. Changing its calibration requires the source analysis and a new validated, frozen artifact.

The linking vignette provides a runnable migration example. Source-anchor uncertainty remains excluded; a new label or file format adds no uncertainty calculation. Older MML analyses containing Person anchors need substantive review: those values were ignored, whereas current fitting rejects them. Merely selecting the legacy centering mode does not repair such an analysis.

Comparing anchors with TAM and ConQuest

The same anchor number does not necessarily fix the same comparison. Check the response model, parameter coding and remaining constraints before transferring values between programs. A parameter index can change when the model or retained facet levels change; match the actual design and labels, not just the row number in an earlier output.

TAM's xsi.fixed fixes indexed coefficients of its response design, which need not be standalone facet locations. ConQuest's anchor_parameters (anchor_xsi) serves that role. Population regression and covariance have separate controls: TAM's beta.fixed/variance.fixed and ConQuest's anchor_beta/anchor_sigma. Slopes also require their own coding; neither an mfrmr location table nor an arbitrary list of external coefficients represents a complete calibration.

For a concrete RSM example, fix one of four raters at 0.70 and leave the others outside group constraints. Whole-facet centering makes the other three raters sum to -0.70: R01 is about 0.933 above their mean. This matches the rater constraint in TAM's tam.mml.mfr(formulaA = ~ item + rater + step, constraint = "cases") and ConQuest's model task+rater+step with lconstraints=cases. Those settings also leave task locations uncentered; use the corresponding noncenter_facet and match the population explicitly. mfrmr's legacy "remainder" mode instead makes the other raters sum to zero, putting R01 0.70 above their mean. Changing labels cannot reconcile these restrictions. Group means likewise require matching linear constraints, not copying them as individual fixed values.

Match the population mean/variance, scoring, estimator and integration accuracy as well. Equal numbers of integration nodes need not mean equal rules or accuracy. ConQuest documents anchor_theta as ignored under MML; mfrmr instead rejects Person anchors there. TAM's tam.jml() documents theta.fixed for version = 1. Common Persons and fixed Person abilities remain distinct concepts in all these comparisons.

Agreement of point estimates does not establish agreement of SEs. Compare uncertainty for the same free parameter or contrast, using the appropriate covariance transformation. In ordinary fixed-anchor estimation, uncertainty is conditional on the supplied values; a zero or missing SE for an anchor does not account for its source calibration error. See the companion vignette for a comparison table and the official manuals below.

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(x).
"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(x, type = "heatmap"), and plot(x, type = "summary").

Keep anchor roles separate

A common-element or common-rating link is observed overlap in the design.
anchors are direct equality constraints on selected parameter values.
group_anchors constrain declared group means and require an externally defensible target or equal-mean assumption.
make_anchor_table() exports candidate direct constraints mechanically; by default it requires a current inference-ready source fit, but it does not select invariant elements. readiness_policy = "review" is for review-only extraction, not anchor reuse.

Constraint-based coordinate transfer does not create empirical overlap. Before reuse, also verify consistent model/score/orientation/population conventions, cross-run element identity, and the relevant assignment connectedness. review_mfrm_anchors() checks syntax and receiving-data support, not those substantive assumptions.

Common persons, rotating assignments, and random assignments

These are ways to collect ratings, not instructions to fix a parameter. For example, asking all eight raters to score the same four performances creates common-person links. Their abilities can still be estimated; do not pass them to anchors unless known values really are intended.

Existing build_mfrm_sim_spec() choices let you inspect these structures:

Common persons: assignment = "sparse_linked" with sparse_controls = list(link_persons = 4, link_raters_per_person = 8). Set n_rater = 8 and specify the ordinary raters_per_person separately. The counts illustrate syntax, not a recommended number of linking persons.
Overlapping rotation: assignment = "rotating" with raters_per_person = 2 assigns successive subsets of raters.
Random subsets: assignment = "sparse_linked" with sparse_controls = list(link_persons = 0, assignment_mode = "random"). This does not guarantee connectedness or equal workloads for every draw.
Task-specific or externally planned assignments: assignment = "skeleton" accepts an explicit Person-by-facet template. The ordinary rotating generator assigns the chosen raters across all generated criteria; it is not a general implementation of task-nested spiral designs.

Generate ratings with simulate_mfrm_data() and inspect them with describe_mfrm_data(). Use the linking vignette for runnable examples. A generator can represent a design without qualifying an estimator for it. Compare both the amount and placement of overlap, and what happens when a critical common person or rater is unavailable. Keep rating costs equal when the question is which allocation uses a fixed budget better.

Design the link, not only the anchor count

There is no universal adequate anchor count or percentage. Linking quality also depends on where overlap occurs, whether links are distributed or rely on one critical bridge, the rating workload and coverage, and model–data fit within the linking set. Inspect both Rater-centered and Person/task- centered assignment graphs when the design is sparse. The package's five-element LinkSupportAdequate screen is therefore a local warning, not a design recommendation or proof of a common scale.

Fixed anchor values also carry uncertainty from their source calibration. Current anchor, drift, and chain summaries do not propagate all source-fit, offset, or cross-fit covariance. Compare substantively defensible anchor sets and report sensitivity when conclusions depend on the selected set. The bounded fixed-SD RSM/PCM anchor-origin route now offers explicit independent-source covariance propagation through mfrm_facet_intervals() and mfrm_population_intervals(). This does not change drift or chain summaries, correct noninvariant anchors, or handle dependent samples.

Reading the theoretical background

Uto (2021, pp. 1442–1444) explains fixed common-rater/task linking. Its simulation fixes generated common parameters and removes a redundant rater identification constraint; its Bayesian estimation and constraints differ from mfrmr. It does not validate every centering convention above or provide uncertainty propagation for anchors estimated in a previous mfrmr fit.

Robitzsch (2024, pp. 1181–1182, 1187–1188) studies bias and linking error from random uniform DIF in fixed-item 2PL calibration. It separates this issue from sampling Persons and does not provide a variance estimator for the fitted population parameters. It motivates checking anchor invariance, not treating current mfrmr SEs as including every source of linking error. For the distinction between an origin constraint and a fixed external value, see the FACETS centering and element documentation cited below; its constraint convention is not identical to mfrmr's.

Drift and chain inference boundary

detect_anchor_drift() and build_equating_chain() currently estimate one pooled offset across all selected common elements and facets. Their element-level SE ratios omit estimated-offset uncertainty and cross-fit covariance, and chain output does not propagate uncertainty across adjacent links. Offset_SD is residual spread, not an offset SE. Treat flags, support counts, and cumulative offsets as review screens; when a common shift across facet blocks is not defensible, analyze one coherent linking facet at a time. ScreeningFallback indicates that preliminary screening retained nothing and the offset instead used all finite differences. N_Contributing counts the rows actually entering the final average, which can differ from N_Retained. Neither count certifies invariant anchors. Missing offsets/spread are explained by OffsetStatus, OffsetReason and, for chains, OffsetSDStatus. A single retained element has undefined residual sample SD, not zero uncertainty. Drift FlagBasis distinguishes the magnitude-only screen from a screen with an available SE ratio.

Which helper answers which task

subset_connectivity_report(): Summarizes connected subsets, bottleneck facets, and design-matrix coverage.
make_anchor_table(): Extracts candidate direct-anchor values from a fit without certifying them for reuse.
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(): Describes group residual differences or linked subgroup facet estimates. Linked refit point contrasts remain screening-only because their uncertainty is conditional on baseline anchors.
mantel_haenszel_table(): Compares binary responses between two groups within declared matching strata, with one response per Person and target. Common odds-ratio inference does not certify matching validity or support pooled repeated ratings.
ordinal_logistic_table(): Compares ordered responses using nested cumulative logistic models for independent Persons. Separates uniform, nonuniform and joint group tests from a proportional-odds diagnostic; retains numerical failures and common-range effect contrasts.

Practical linking rules

Check connectedness before interpreting subgroup or wave differences.
Use mfrm_network_analysis() for assignment/co-observation connectedness. Agreement, severity-direction, and halo networks describe score relations; they do not establish an empirical link or a common measurement scale.
Residual differences do not isolate differential functioning and have no tests or binary classifications. Even with an adequate link, refit SEs condition on baseline anchors and omit their uncertainty and cross-refit covariance; formal inference remains unavailable.
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.
Linked refit contrasts remain descriptive; neither method assigns ETS A/B/C labels or supports a formal differential-functioning decision.
Read a DFF figure with plot_data(p, "pairs"): summary plots retain all source comparisons with a PlotStatus, including those omitted by top_n or lacking a contrast. Both views retain method settings and, for residual results, the response-matching cases table. Positive residual and refit contrasts have different meanings; see plot.mfrm_dif.
For sparse binary cells, exact MH conditions on the stratum margins; intervals may be wide and p-values discrete. This does not correct invalid matching or dependence. Ordinal-logistic LR tests remain asymptotic: successful numerical convergence does not establish small-sample validity.
MH or ordinal-logistic comparisons require explicit matching, and residual DFF's $cases records the actual requested-response matches. Inspect exclusions before comparing methods. Residual N counts rows; NPersons counts distinct Persons, without establishing independence. All methods require comparable rating plans and an appropriate unit of independence. A raw total across different plans or multiple rows from the same Person does not establish these conditions. See analyze_dff() and the companion vignette for differences in targets and response-model assumptions. Its "Compare an explicitly shared response roster" example aligns group direction, retains method-specific case counts and exclusions, and saves complete residual/MH/logistic results together. It uses a common binary item roster; it does not support pooling repeated Person-target ratings.
Treat drift flags as prompts for review, not automatic evidence that an anchor must be removed.
In drift/link-review results, LinkSupportAdequate = FALSE warns that at least one linking facet retained fewer than 5 common elements after screening. Refit DFF uses a different screen: by default at least five anchored levels in total across the non-target linking facets in each subgroup. Inspect ScaleLinkStatus, LinkingThreshold, LinkingAnchoredLevels1/LinkingAnchoredLevels2, and LinkingDetail1/LinkingDetail2. Neither screen proves invariance or supplies a universally adequate anchor count.
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(x).
Group comparison route: subset_connectivity_report() -> analyze_dff() -> dif_report() -> plot(x, type = "heatmap") / plot(x, type = "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").

References

TAM documentation: MML estimation and fixed parameters and JML and fixed Person parameters.

ACER ConQuest manual: Command reference, especially import (anchor parameter types) and set (location and scale constraints). Defaults and supported options depend on the program version.

FACETS documentation: Centering facets and Elements and anchors.

Linacre, J. M. (2012). Facets Tutorial 4: Anchoring, p. 9, discusses rater drift and the assumption involved in fixing a group mean across sessions. It does not establish the common-recording workflow described here or its uncertainty performance.

Eckes, T. (2023). Introduction to Many-Facet Rasch Measurement, Section 9.1, pp. 151–155, Table 9.1. Peter Lang. ISBN 978-3-631-90305-6.

Myford, C. M., & Wolfe, E. W. (2000). Strengthening the ties that bind: Improving the linking network in sparsely connected rating designs. ETS Research Report Series, 2000(1). doi:10.1002/j.2333-8504.2000.tb01832.x

Uto, M. (2021). Accuracy of performance-test linking based on a many-facet Rasch model. Behavior Research Methods, 53(4), 1440–1454. doi:10.3758/s13428-020-01498-x

Wind, S. A., & Jones, E. (2018). The stabilizing influences of linking set size and model–data fit in sparse rater-mediated assessment networks. Educational and Psychological Measurement, 78(4), 679–707. doi:10.1177/0013164417703733

Robitzsch, A. (2024). Bias and linking error in fixed item parameter calibration. AppliedMath, 4(3), 1181–1191. doi:10.3390/appliedmath4030063

Examples

# Long-running workflow; run explicitly when needed.
# example("mfrmr_linking_and_dff", run.dontrun = TRUE)
if (FALSE) { # \dontrun{
ratings <- load_mfrmr_data("example_core")
people <- unique(ratings$Person)
baseline_data <- ratings[ratings$Person %in% people[1:24], , drop = FALSE]
new_data <- ratings[ratings$Person %in% people[25:48], , drop = FALSE]
baseline <- fit_mfrm(
  baseline_data, "Person", c("Rater", "Criterion"), "Score",
  method = "MML", rating_min = 1, rating_max = 4,
  category_policy = "preserve"
)
anchors <- make_anchor_table(baseline, facets = "Criterion")
review <- review_mfrm_anchors(
  new_data, "Person", c("Rater", "Criterion"), "Score", anchors = anchors,
  rating_min = 1, rating_max = 4, category_policy = "preserve"
)
review$issue_counts
linked <- anchor_to_baseline(
  new_data, baseline, "Person", c("Rater", "Criterion"), "Score",
  anchor_facets = "Criterion", anchor_policy = "error",
  rating_min = 1, rating_max = 4, category_policy = "preserve"
)
linked$fit$facets$others
# Fixed-anchor differences are zero by construction, not evidence of stability.
linked$drift[, c("Facet", "Level", "Drift")]

} # }