Extreme persons (zero or maximum raw score on their observed items) are
excluded from calibration, but they cannot be left out of group
comparisons; Andrich and Marais (2019, ch. 10) therefore describe an
extrapolated measure for them,
continuing the growth of the score-to-score differences so the last
difference is the geometric mean of its neighbours (see
score_table). This helper applies the same rule to the
person table: for each missing-data pattern with extreme persons, the
score-to-measure conversion over that pattern's items is extrapolated at
its ends, and the extreme persons receive the extrapolated location with
the standard error \(1/\sqrt{I(\theta)}\) evaluated there. Non-extreme
persons keep their estimates unchanged. The extrapolation continues the
Warm (weighted likelihood) conversion, matching the package's person
estimates.
Arguments
- fit
A fitted object from
raschwith one common raw-score conversion and a common discrimination. Expanded many-facet and frame response-cell designs do not have such a conversion and are refused.
Value
The fit's person table with two added columns,
theta_extrapolated and se_extrapolated: equal to
theta and se for non-extreme persons, extrapolated for
extreme persons. Patterns with fewer than three interior scores cannot
be extrapolated, or whose interior score locations do not have stable
increasing spacings, keep their Warm values.
Examples
set.seed(1)
d <- seq(-2, 2, length.out = 8)
X <- matrix(rbinom(300 * 8, 1, plogis(outer(rnorm(300, 0, 2), d, "-"))), 300, 8)
colnames(X) <- paste0("I", 1:8)
fit <- rasch(X)
pe <- person_extrapolated(fit)
head(pe[pe$extreme, c("theta", "theta_extrapolated", "se", "se_extrapolated")])
#> theta theta_extrapolated se se_extrapolated
#> -3.686 -3.286 1.677 1.441
#> 3.750 3.363 1.707 1.478
#> 3.750 3.363 1.707 1.478
#> -3.686 -3.286 1.677 1.441
#> 3.750 3.363 1.707 1.478
#> -3.686 -3.286 1.677 1.441