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
rasch(equal discriminations; not EFRM).
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 and 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
#> 1 -3.686068 -3.285814 1.677222 1.440928
#> 4 3.750309 3.362643 1.706623 1.478043
#> 11 3.750309 3.362643 1.706623 1.478043
#> 14 -3.686068 -3.285814 1.677222 1.440928
#> 15 3.750309 3.362643 1.706623 1.478043
#> 24 -3.686068 -3.285814 1.677222 1.440928