Resolve differential item functioning by iterative item splitting

Splits DIF items one at a time, largest effect first, refitting after each split, until no item shows significant DIF (or the anchor set would fall too low). Splitting the item with the largest real DIF first removes the artificial DIF it induces on other items (Andrich & Hagquist 2012, 2015), so the procedure resolves genuine DIF without chasing the artificial DIF that a single simultaneous pass would flag. Each split resolves the item into one copy per group (or per factor-combination cell for an interaction), with independent locations and thresholds, so both uniform and non-uniform DIF are resolved together.

Usage

resolve_dif(
  fit,
  factors = NULL,
  alpha = 0.05,
  p_adjust = "BH",
  min_anchors = NULL,
  max_splits = NULL
)

Arguments

fit

A fitted object from rasch carrying person factors.

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 across items each round.

min_anchors

Minimum number of original items to leave unsplit; the procedure stops before the anchor set falls below this (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.

Value

A list of class "rasch_resolve_dif": the final resolved fit, the splits performed (order, item, factor, partial eta-squared, DIF magnitude in logits), the stopped reason, and the residual dif table for the final fit.

References

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

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       eta2 magnitude
#> 1     1   I3    grp 0.05389885  1.110898