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). 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")
)

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.

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. 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.

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, and dif_anova for the test it resolves.

Examples

set.seed(1); n <- 600
d <- seq(-2, 2, length.out = 8); g <- rep(c("a", "b"), each = n / 2)
sh <- matrix(0, n, 8); sh[g == "b", 3] <- 1.2      # one strong DIF item
X <- matrix(rbinom(n * 8, 1, plogis(outer(rnorm(n), d, "-") - sh)), n, 8)
colnames(X) <- paste0("I", 1:8)
fit <- rasch(data.frame(X, grp = g), factors = "grp")
resolve_dif(fit)$splits
#>  order item factor base_item  eta2 magnitude
#>      1   I3    grp        I3 0.054     1.111