Resolve differential item functioning by iterative item splitting

Splits items with uniform DIF one at a time, beginning with the largest estimated effect, and refits after each split. This order addresses the artificial DIF that a large departure can induce in otherwise invariant items (Andrich and Hagquist 2012, 2015). The DIF in each round is judged by the residual analysis of dif_anova or, with criterion = "wald", by the conditional Wald test of dif_wald, which compares each item's split locations on the calibration anchored by the unsplit items and so needs no class intervals. Each split gives the item a separate location in every factor cell. A PCM also estimates the split copies' thresholds separately; an RSM retains its common rating-scale threshold structure. A location split does not model a group-specific discrimination, so items with non-uniform DIF are left for review rather than being made untestable by a split. The procedure stops when no resolvable uniform DIF remains or the remaining unsplit reference set reaches min_anchors. Items fixed by external anchors are not split.

Usage

resolve_dif(
  fit,
  factors = NULL,
  alpha = 0.05,
  p_adjust = "holm",
  min_n = 20L,
  min_anchors = NULL,
  max_splits = NULL,
  effects = c("main", "factorial"),
  criterion = c("anova", "wald")
)

Arguments

fit

A fitted object from rasch.

factors

Person factors to test, as in dif_anova; defaults to every nominated factor.

alpha

Significance level for the adjusted probabilities.

p_adjust

Multiplicity adjustment for the DIF tests in each round.

min_n

Minimum distinct responders required in every item-by-factor cell before an automatic split is allowed. Repeated response rows from one person count once within a cell. The omnibus DIF test determines whether a split is needed; pairwise follow-ups describe where the difference lies but are not a second significance gate.

min_anchors

Minimum number of original items to leave unsplit as the internal reference set. The procedure stops before this set becomes smaller; pervasive DIF is not artificial DIF. Default max(3, items / 4).

max_splits

Hard cap on the number of splits. Default: the number of items.

effects

"main" fits the factors additively; "factorial" also tests their interactions. The same model is used at every round and in the final DIF assessment.

criterion

"anova" flags and ranks items by the residual analysis of dif_anova (uniform DIF only is split; a significant non-uniform term leaves the item for review). "wald" flags items by the conditional Wald test of dif_wald on each factor's main effect and ranks them by the resolved location shift; it requires effects = "main" and does not test non-uniform DIF.

Value

A list of class "rasch_resolve_dif": the final resolved fit, the splits performed (order, item, factor, base_item, eta2, magnitude in logits), the stopped reason, the residual dif table, and the number of distinct source items that still show DIF in the final fit. n_untested counts the uniform and non-uniform hypotheses the final assessment could not estimate although the design could answer them; those terms are reported as neither DIF nor no DIF, so the remaining-DIF count is a lower bound whenever n_untested is positive. A split copy answered in one level of its splitting factor only is not counted: its term is structurally absent, not lost. A split's magnitude is NA when the complete-design post-hoc comparison that supplies it failed or returned no trustworthy finite estimate; the split still stands, and notes names the item, the factor and the reason. An NA magnitude is an unmeasured difference, not a zero one. n_remaining_dif is NA when no hypothesis was estimable. n_nonuniform counts significant non-uniform item-factor findings and is NA if any answerable non-uniform hypothesis is unavailable, or no hypothesis was estimable. n_untested is always a count. effects records the factor model used and criterion the test. With the Wald criterion eta2 is NA, magnitude is the absolute resolved shift the test compared (the range of the locations for more than two levels), the dif table carries the shift and p_adj of each item still flagged, and n_nonuniform is NA because non-uniform DIF is not tested.

References

Andrich, D., & Hagquist, C. (2012). Real and artificial differential item functioning. Journal of Educational and Behavioral Statistics, 37(3), 387-416.

See also

split_items for a single split, drop_items to remove an item instead, dif_anova and dif_wald for the tests it resolves.

Examples

set.seed(1); n <- 300
d <- seq(-2, 2, length.out = 6); g <- rep(c("a", "b"), each = n / 2)
sh <- matrix(0, n, 6); sh[g == "b", 3] <- 1.5      # one strong DIF item
X <- matrix(rbinom(n * 6, 1, plogis(outer(rnorm(n), d, "-") - sh)), n, 6)
colnames(X) <- paste0("I", 1:6)
fit <- rasch(data.frame(X, grp = g), factors = "grp")
resolve_dif(fit)$splits
#>  order item factor base_item  eta2 magnitude
#>      1   I3    grp        I3 0.108     1.726
resolve_dif(fit, criterion = "wald")$splits
#>  order item factor base_item eta2 magnitude
#>      1   I3    grp        I3          1.726