Jkpp: Run a jackknife

In PP: Person Parameter Estimation

Run a jackknife

Description

This function uses a jackknife approach to compute person parameters. The jackknife ability measure is based on primarily estimated models (PP_4pl(), PP_gpcm() or PPall()) - so the function is applied on the estimation objects, and jackknifed ability measures are returned.

Usage

JKpp(estobj, ...)

## S3 method for class 'ppeo'
JKpp(
  estobj,
  cmeth = "mean",
  maxsteps = NULL,
  exac = NULL,
  fullmat = FALSE,
  ...
)

## S3 method for class 'jk'
print(x, digits = 4, ...)

## S3 method for class 'jk'
summary(object, nrowmax = 15, digits = 4, ...)

## S3 method for class 'ppass'
JKpp(estobj, ...)

Arguments

estobj	An object which originates from using PP_gpcm(), PP_4pl() or PPall().
...	More input.
cmeth	Choose the centering method, to summarize the pseudovalues of a person to one single ability estimate. There are three valid entries: "mean", "median" and "AMT" (see Details for further description).
maxsteps	The maximum number of Newton steps per leave-one-out sample. If NULL (default), the value of estobj is used.
exac	How accurate are the leave-one-out estimates supposed to be? If NULL (default), the value of estobj is used.
fullmat	Default = FALSE. If TRUE, the function returns the whole jackknife matrix of leave-one-out estimates, which is the basis for the jackknife estimator.
x, object	An object of class jk, the result of JKpp().
digits	Number of significant digits to print.
nrowmax	summary(): how many persons to show. Default = 15.

Details

For each person, every answered item is left out once and the ability is estimated again from the remaining items, with the same estimation type, prior and range as in estobj (MLE, WLE, MAP and robust estimates start at the full estimate; EAP estimates use the posterior grid of the full estimate). Items a person did not answer are not left out: with L answered items and the leave-one-out estimates \hat\theta_{(-j)}, the pseudovalues are L\hat\theta - (L-1)\hat\theta_{(-j)}. The jackknife estimate is their mean, median or AMT (cmeth), the standard error is \sqrt{\sum_j (ps_j - \bar{ps})^2 / (L(L-1))} (Wainer & Wright, 1980).

A leave-one-out sample may have no finite estimate, e.g. with type = "mle" when the only wrong answer is left out. Such samples (and samples at the bound of range or not converged) are left out of the person's jackknife, counted in the column excluded, and a warning is given; WLE avoids this in most cases. A person whose full estimate has no solution (status "extreme", "no_response", "boundary" or "not_converged" in estobj$estimates) or who has fewer than two usable leave-one-out samples (status "too_few_items") gets NA.

Up to version 0.6.4 the standard error mixed the leave-one-out estimates with the formula for the pseudovalues and was too small by a factor of about L-1, all items counted as answered, and leave-one-out samples without a finite estimate were dropped silently.

AMT-robustified jackknife: When choosing cmeth = "AMT", the pseudovalues are combined as in scheme 4 of Wainer & Wright (1980): they are split into the pseudovalues of the right and of the wrong answers (polytomous items: answers at or above the expected score at \hat\theta and below it), each group is summarised by Andrews' sine M-estimator (AMT), one of the winners in the Princeton Robustness Study (Andrews et al., 1972), and the two values are averaged with the group sizes as weights. Within a group, T solves \sum_j \psi((ps_j - T)/s) = 0 with \psi(x) = \sin(x/2.1) for |x| \le 2.1\pi and 0 otherwise, where s is the median absolute deviation of the group's pseudovalues from their median; pseudovalues further than 2.1 \pi s from T get no weight. Up to version 0.6.4 the AMT had a sign error, no scale and maximised the sum of the sines.

Value

An object of class jk, a list with

estimates	A data.frame with one row per person (in the order of respm): estimate and SE of the jackknife, L the number of answered items, excluded the number of leave-one-out samples without a finite estimate and status ("ok", "too_few_items" or the status of the full estimate).
resjk	The matrix of estimate and SE, as in earlier versions.
type, cmeth, call	The estimation type of estobj, the centering method and the call.
jk_mat	Only with fullmat = TRUE: the persons x items matrix of leave-one-out estimates, NA for items not answered and excluded samples.

Author(s)

Manuel Reif

References

Wainer, H., & Wright, B. D. (1980). Robust estimation of ability in the Rasch model. Psychometrika, 45(3), 373-391.

Andrews, D. F., Bickel, P. J., Hampel, F. R., Huber, P. J., Rogers, W. H., & Tukey, J. W. (1972). Robust estimates of location: Survey and advances. Princeton University Press.

See Also

PP_gpcm, PP_4pl, PPall

Examples

set.seed(1623)
b  <- seq(-3, 3, length = 12)
sl <- round(runif(12, 0.5, 1.5), 2)
x  <- sim_4pl(beta = b, alpha = sl, lowerA = 0, upperA = 1, theta = rnorm(20, sd = 1.5))

res <- PP_4pl(respm = x, thres = b, slopes = sl, type = "wle")
jk <- JKpp(res)
summary(jk)
# WLE and jackknife side by side
head(cbind(res$estimates[, c("estimate", "SE")], jk = jk$estimates[, c("estimate", "SE")]))

# robust centering: the AMT of Wainer & Wright (1980)
head(JKpp(res, cmeth = "AMT")$estimates)

# partial credit model, EAP
thres <- rbind(0, c(-1, -0.5, 0, 0.4), c(0.5, 0.8, 1, 1.5))
xg <- sim_gpcm(thres = thres, alpha = 1, theta = rnorm(20))
JKpp(PP_gpcm(respm = xg, thres = thres, type = "eap"))

PP documentation built on Oct. 15, 2026, 1:06 a.m.