Equate two test calibrations through their common items

Compares the item locations of a fit with those of a second fit (or a reference table such as an item bank), matched by item name. A scale shift between the two origins is estimated by the precision-weighted mean difference, and each common item is then tested against the shifted identity line; flagged items show drift and weaken the equating link.

Usage

equate_tests(fit, reference, shift = c("mean", "none"))

Arguments

fit: A fitted object from rasch.
reference: A second rasch fit, or a data frame with columns item, location, and optionally se.
shift: "mean" (default) allows a scale shift between the two analyses; "none" compares raw locations, appropriate when both analyses are already on a shared (anchored) scale.

Value

A list with the comparison table (locations, standard errors, difference, t, raw and BH-adjusted p, drift flag), the estimated shift, the location correlation, the root mean square difference after shifting (rmsd), and the number of common items n.

Examples

set.seed(1); d <- seq(-1.5, 1.5, length.out = 8)
mk <- function() {
  X <- matrix(rbinom(400 * 8, 1, plogis(outer(rnorm(400), d, "-"))), 400, 8)
  colnames(X) <- paste0("I", 1:8); rasch(X)
}
eq <- equate_tests(mk(), mk())
eq$table
#>   item location_1      se_1 location_2      se_2  difference adj_difference
#> 1   I1 -1.4780195 0.1246379 -1.5760281 0.1292289  0.09800863     0.10727215
#> 2   I2 -1.1006867 0.1168127 -1.1398494 0.1155055  0.03916271     0.04842624
#> 3   I3 -0.8227470 0.1123970 -0.5314218 0.1083620 -0.29132523    -0.28206171
#> 4   I4 -0.2085726 0.1093047 -0.2287656 0.1063021  0.02019291     0.02945643
#> 5   I5  0.1917743 0.1077741  0.3229450 0.1053953 -0.13117072    -0.12190720
#> 6   I6  0.7088231 0.1124051  0.5366178 0.1097245  0.17220529     0.18146881
#> 7   I7  1.1279739 0.1189861  1.1874751 0.1180524 -0.05950128    -0.05023776
#> 8   I8  1.5814546 0.1284329  1.4290269 0.1263670  0.15242768     0.16169120
#>            t          p     p_adj drift
#> 1  0.5817100 0.56076205 0.8432425 FALSE
#> 2  0.2951436 0.76788421 0.8432425 FALSE
#> 3 -1.8293214 0.06735147 0.5388118 FALSE
#> 4  0.1977476 0.84324253 0.8432425 FALSE
#> 5 -0.8312417 0.40583712 0.8116742 FALSE
#> 6  1.1696652 0.24213573 0.8116742 FALSE
#> 7 -0.2969011 0.76654200 0.8432425 FALSE
#> 8  0.8735713 0.38235177 0.8116742 FALSE