Pairwise follow-up comparisons for a DIF term

Resolves one item's locations over the complete person-factor design and follows up a selected main effect or interaction. Main effects are pairwise marginal differences. Interactions are differences between those differences, providing a logit-scale magnitude for the interaction itself.

Usage

dif_posthoc(
  fit,
  item,
  term,
  factors = NULL,
  within = NULL,
  id = NULL,
  p_adjust = "holm",
  alpha = 0.05,
  flag_logits = 0.5,
  min_n = 20
)

Arguments

fit: A fitted object from rasch or rasch_mfrm. EFRM fits are excluded because resolved comparisons would discard their frame units.
item: Item name or index.
term: A factor name for a main effect, or a character vector of factor names for an interaction. A single colon-separated string is also accepted when the factor names themselves contain no colon.
factors: The complete person-factor design, specified as for dif_contrasts. Other factors are retained when calculating marginal comparisons.
within: Within-person factor names, specified as for dif_contrasts.
id: Person identifiers, specified as for dif_contrasts.
p_adjust: Adjustment over this post-hoc family. The default "holm" controls familywise error; use "BH" only for false-discovery-rate screening. "none" leaves probabilities unadjusted.
alpha: Significance level for adjusted probabilities.
flag_logits: Absolute logit magnitude flagged as practically important.
min_n: Minimum distinct responders required in a resolved design cell. When identifiers repeat, response rows from one person count once within each cell.

Value

An object of class "rasch_dif_posthoc", extending the dif_contrasts result. Its table contains the pairwise marginal differences or interaction contrasts, with logit estimates, standard errors where available, confidence intervals, raw and adjusted probabilities, and statistical and practical flags.

Details

For levels $a,b$ of one factor, the comparison is $$\Delta_{ba}=\bar\delta_b-\bar\delta_a,$$ where the bars average equally over complete cells of the other nominated factors. For a two-factor interaction, levels $a,b$ and $c,d$ give $$\Delta_{ba\mathbin{:}dc}= (\delta_{bd}-\delta_{ad})-(\delta_{bc}-\delta_{ac}).$$ Higher-order interactions use the corresponding tensor-product contrast. Standard errors use the full covariance of the resolved locations.

This is the follow-up to a significant DIF term with more than two levels. It reports effects in Rasch logits, adjusts the chosen family of comparisons, and uses person-level scores with the same equal-cell marginal weights in repeated-measures designs. A planned comparison that cannot be estimated because its levels have no common nuisance-factor cell remains in the multiplicity count, although it is omitted from the result table.

References

Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6(2), 65–70.

Examples

set.seed(1); n <- 800
g <- factor(rep(c("A", "B", "C", "D"), each = n / 4))
sex <- factor(rep(c("female", "male"), length.out = n))
d <- seq(-1.5, 1.5, length.out = 6)
sh <- matrix(0, n, 6); sh[g == "D", 2] <- 0.8
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, group = g, sex = sex),
             factors = c("group", "sex"))
dif_posthoc(fit, "I2", term = "group")
#> DIF follow-up for group (pairwise marginal difference; holm)
#>  item contrast estimate    se statistic p_adj significant practical
#>    I2    B - A   -0.314 0.270    -1.164 0.619                      
#>    I2    C - A    0.028 0.268     0.104 0.917                      
#>    I2    D - A    0.596 0.262     2.276 0.114                     *
#>    I2    C - B    0.342 0.271     1.264 0.619                      
#>    I2    D - B    0.910 0.265     3.437 0.004           *         *
#>    I2    D - C    0.568 0.264     2.155 0.125                     *