mfrm_d_study: Project G-theory coefficients under alternative D-study...

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

Project G-theory coefficients under alternative D-study designs

Description

mfrm_d_study() applies a practical D-study projection to the variance components from mfrm_generalizability(). It answers questions such as "what happens to G and Phi if we use 2, 3, or 4 raters?" without re-fitting the Rasch/MFRM model.

Usage

mfrm_d_study(
  x,
  design_grid = NULL,
  object_facet = "Person",
  random_facets = NULL,
  residual_scaling = c("highest_order", "single_condition", "none", "sensitivity"),
  ...
)

Arguments

x	Output from mfrm_generalizability() or an mfrm_fit. If an mfrm_fit is supplied, mfrm_generalizability() is called first.
design_grid	Data frame or named list giving planned counts for each random measurement facet. Column names may be the facet names themselves (for example Rater) or n_ plus the facet name (for example n_Rater). When NULL, one row using the observed number of levels is returned.
object_facet, random_facets	Passed to mfrm_generalizability() when x is an mfrm_fit.
residual_scaling	How the collapsed residual variance should be scaled when planned facet counts increase. "highest_order" treats the residual as highest-order person-by-all-conditions/error variance and divides by the product of planned counts. "single_condition" divides by the smallest planned facet count, a conservative sensitivity check when unmodeled person-by-one-facet interactions may dominate. "none" leaves the residual unscaled. "sensitivity" returns all three assumptions for each design row.
...	Additional arguments passed to mfrm_generalizability() when x is an mfrm_fit.

Details

The projection uses the variance decomposition already estimated by mfrm_generalizability(). For a random measurement facet j, main-effect variance contributes sigma2_j / n_j to the absolute-error denominator. The residual term contains unmodeled person-by-facet and higher-order interaction variance in the current simplified G-study, so the selected residual_scaling assumption is reported explicitly. The relative-decision denominator uses only this scaled residual term.

This is a pragmatic D-study planning layer, not a full p x r x i ANOVA decomposition. If person-by-rater or person-by-item interactions are a primary estimand, use residual_scaling = "sensitivity" and treat the output as planning evidence; fit a fully crossed G-theory model externally when those interaction components must be estimated separately.

The G and Phi values returned here belong to the generalizability-theory metric family. They should not be interpreted as coefficient alpha, omega, KR-20, or IRT marginal/separation reliability, even though all of those summaries may be displayed on a 0–1 scale in broader reporting dashboards.

Value

An object of class mfrm_d_study, a data.frame with one row per design scenario and columns for planned facet counts, variance terms, projected G, projected Phi, and interpretation bands.

References

Cronbach, L. J., Gleser, G. C., Nanda, H., & Rajaratnam, N. (1972). The dependability of behavioral measurements: Theory of generalizability for scores and profiles. Wiley.

Brennan, R. L. (2001). Generalizability theory. Springer.

See Also

mfrm_generalizability(), evaluate_mfrm_design(), recommend_mfrm_design(), plot_data()

Examples

toy <- load_mfrmr_data("example_core")
fit <- fit_mfrm(toy, "Person", c("Rater", "Criterion"), "Score",
                method = "JML", maxit = 30)
if (requireNamespace("lme4", quietly = TRUE)) {
  gt <- mfrm_generalizability(fit)
  mfrm_d_study(gt, data.frame(Rater = c(2, 3, 4), Criterion = 4))
}

mfrmr documentation built on June 13, 2026, 1:07 a.m.