dif_interaction_table: Compute interaction table between a facet and a grouping...

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

Compute interaction table between a facet and a grouping variable

Description

Produces a cell-level interaction table showing Obs-Exp differences, standardized residuals, and screening statistics for each facet-level x group-value cell.

Usage

dif_interaction_table(
  fit,
  diagnostics,
  facet,
  group,
  data = NULL,
  min_obs = 10,
  p_adjust = "holm",
  abs_t_warn = 2,
  abs_bias_warn = 0.5
)

Arguments

fit	Output from fit_mfrm().
diagnostics	Output from diagnose_mfrm().
facet	Character scalar naming the facet.
group	Character scalar naming the grouping column.
data	Optional data frame with the group column. If NULL (default), the data stored in fit$prep$data is used, but it must contain the group column.
min_obs	Minimum observations per cell. Cells with fewer than this many observations are flagged as sparse and their test statistics set to NA. Default 10.
p_adjust	P-value adjustment method, passed to stats::p.adjust(). Default "holm".
abs_t_warn	Threshold for flagging cells by absolute t-value. Default 2.
abs_bias_warn	Threshold for flagging cells by absolute Obs-Exp average (in logits). Default 0.5.

Details

This function uses the fitted model's observation-level residuals (from the internal compute_obs_table() function) rather than re-estimating the model. For each facet-level x group-value cell, it computes:

• N: number of observations in the cell

• ObsScore: sum of observed scores

• ExpScore: sum of expected scores

• ObsExpAvg: mean observed-minus-expected difference

• Var_sum: sum of model variances

• StdResidual: (ObsScore - ExpScore) / sqrt(Var_sum)

• t: approximate t-statistic (equal to StdResidual)

• df: N - 1

• p_value: two-tailed p-value from the t-distribution

Value

Object of class mfrm_dif_interaction with:

• table: tibble with per-cell statistics and flags.

• summary: tibble summarizing flagged and sparse cell counts.

• config: list of analysis parameters.

When to use this instead of analyze_dff()

Use dif_interaction_table() when you want cell-level screening for a single facet-by-group table. Use analyze_dff() when you want group-pair contrasts summarized into differential-functioning effect sizes and method-appropriate classifications.

Further guidance

For plot selection and follow-up diagnostics, see mfrmr_visual_diagnostics.

Interpreting output

• ⁠$table⁠: the full interaction table with one row per cell.

• ⁠$summary⁠: overview counts of flagged and sparse cells.

• ⁠$config⁠: analysis configuration parameters.

• Cells with ⁠|t| > abs_t_warn⁠ or ⁠|ObsExpAvg| > abs_bias_warn⁠ are flagged in the flag_t and flag_bias columns.

• Sparse cells (N < min_obs) have sparse = TRUE and NA statistics.

Typical workflow

1. Fit a model with fit_mfrm().

2. Run dif_interaction_table(fit, diag, facet = "Rater", group = "Gender", data = df).

3. Inspect ⁠$table⁠ for flagged cells.

4. Visualize with plot_dif_heatmap().

See Also

analyze_dff(), analyze_dif(), plot_dif_heatmap(), dif_report(), estimate_bias()

Examples

toy <- load_mfrmr_data("example_bias")

fit <- fit_mfrm(toy, "Person", c("Rater", "Criterion"), "Score",
                 method = "JML", model = "RSM", maxit = 25)
diag <- diagnose_mfrm(fit, residual_pca = "none")
int <- dif_interaction_table(fit, diag, facet = "Rater",
                             group = "Group", data = toy, min_obs = 2)
int$summary
head(int$table[, c("Level", "GroupValue", "ObsExpAvg", "flag_bias")])

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