| JKpp {PP} | R Documentation |
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 'fourpl'
JKpp(
estobj,
cmeth = "mean",
maxsteps = 500,
exac = 0.001,
fullmat = FALSE,
ctrl = list(),
...
)
## S3 method for class 'gpcm'
JKpp(
estobj,
cmeth = "mean",
maxsteps = 500,
exac = 0.001,
fullmat = FALSE,
ctrl = list(),
...
)
## S3 method for class 'gpcm4pl'
JKpp(
estobj,
cmeth = "mean",
maxsteps = 500,
exac = 0.001,
fullmat = FALSE,
ctrl = list(),
...
)
## S3 method for class 'jk'
print(x, ...)
## S3 method for class 'jk'
summary(object, nrowmax = 15, ...)
Arguments
estobj |
An object which originates from using |
... |
More input. |
cmeth |
Choose the centering method, to summarize the n jackknife results to one single ability estimate. There are three valid entries: "mean", "median" and "AMT" (see Details for further description). |
maxsteps |
The maximum number of steps the NR Algorithm will take. |
exac |
How accurate are the estimates supposed to be? Default is 0.001. |
fullmat |
Default = FALSE. If TRUE, the function returns the whole jackknife matrix, which is the basis for the jackknife estimator. |
ctrl |
More controls |
x |
an object of class |
object |
An object of class |
nrowmax |
When printing the matrix of estimates - how many rows should be shown? Default = 15. |
Details
Please use the Jackknife Standard-Error output with caution! It is implemented as suggested in Wainer and Wright (1980), but the results seem a bit strange, because the JK-SE is supposed to overestimate the SE compared to the MLE-SE. Actually, in all examples an underestimation of the SE was observed compared to the MLE/WLE-SE!
AMT-robustified jackknife: When choosing cmeth = AMT, the jackknife ability subsample estimates and the original supplied ability estimate are combined to a single jackknife-ability value by the Sine M-estimator. The AMT (or Sine M-estimator) is one of the winners in the Princeton Robustness Study of 1972. To get a better idea how the estimation process works, take a closer look to the paper which is mentioned below (Wainer & Wright, 1980).
Author(s)
Manuel Reif
References
Wainer, H., & Wright, B. D. (1980). Robust estimation of ability in the Rasch model. Psychometrika, 45(3), 373-391.
See Also
Examples
################# Jackknife ###################################################
### 4 PL model ######
### data creation ##########
set.seed(1623)
# intercepts
diffpar <- seq(-3,3,length=12)
# slope parameters
sl <- round(runif(12,0.5,1.5),2)
la <- round(runif(12,0,0.25),2)
ua <- round(runif(12,0.8,1),2)
# response matrix
abpar <- rnorm(10,0,1.7)
awm <- sim_4pl(beta = diffpar,alpha = sl,lowerA = la,upperA=ua,theta = abpar)
## 1PL model #####
# MLE
res1plmle <- PP_4pl(respm = awm,thres = diffpar,type = "mle")
# WLE
res1plwle <- PP_4pl(respm = awm,thres = diffpar,type = "wle")
# MAP estimation
res1plmap <- PP_4pl(respm = awm,thres = diffpar,type = "map")
# EAP estimation
res1pleap <- PP_4pl(respm = awm,thres = diffpar,type = "eap")
# robust estimation
res1plrob <- PP_4pl(respm = awm,thres = diffpar,type = "robust")
## centering method = mean
res_jk1 <- JKpp(res1plmle)
res_jk2 <- JKpp(res1plwle)
res_jk3 <- JKpp(res1plmap)
res_jk4 <- JKpp(res1plrob)
res_jk5 <- JKpp(res1pleap)
summary(res_jk1)
## centering method = median
res_jk1a <- JKpp(res1plmle,cmeth = "median")
res_jk2a <- JKpp(res1plwle,cmeth = "median")
res_jk3a <- JKpp(res1plmap,cmeth = "median")
summary(res_jk2a)
## centering method = AMT
res_jk1b <- JKpp(res1plmle,cmeth = "AMT")
res_jk2b <- JKpp(res1plwle,cmeth = "AMT")
res_jk3b <- JKpp(res1plmap,cmeth = "AMT")
summary(res_jk3b)
## 2PL model #####
# MLE
res2plmle <- PP_4pl(respm = awm,thres = diffpar, slopes = sl,type = "mle")
# WLE
res2plwle <- PP_4pl(respm = awm,thres = diffpar, slopes = sl,type = "wle")
# MAP estimation
res2plmap <- PP_4pl(respm = awm,thres = diffpar, slopes = sl,type = "map")
# EAP estimation
res2pleap <- PP_4pl(respm = awm,thres = diffpar,slopes = sl,type = "eap")
# robust estimation
res2plrob <- PP_4pl(respm = awm,thres = diffpar,slopes = sl,type = "robust")
res_jk6 <- JKpp(res2plmle)
res_jk7 <- JKpp(res2plwle)
res_jk8 <- JKpp(res2plmap)
res_jk9 <- JKpp(res2pleap)
res_jk10 <- JKpp(res2plrob)
### GPCM model ######
# some threshold parameters
THRES <- matrix(c(-2,-1.23,1.11,3.48,1
,2,-1,-0.2,0.5,1.3,-0.8,1.5),nrow=2)
# slopes
sl <- c(0.5,1,1.5,1.1,1,0.98)
awmatrix <- matrix(c(1,0,2,0,1,1,1,0,0,1,2,0,0,0,0,0,0,0,0,1,
1,2,2,1,1,1,1,0,0,1),byrow=TRUE,nrow=5)
### PCM model ######
# MLE
respcmlmle <- PP_gpcm(respm = awmatrix,thres = THRES,
slopes = rep(1,ncol(THRES)),type = "mle")
# WLE
respcmwle <- PP_gpcm(respm = awmatrix,thres = THRES,
slopes = rep(1,ncol(THRES)),type = "wle")
# MAP estimation
respcmmap <- PP_gpcm(respm = awmatrix,thres = THRES,
slopes = rep(1,ncol(THRES)),type = "map")
res_jk11 <- JKpp(respcmlmle)
res_jk12 <- JKpp(respcmwle)
res_jk13 <- JKpp(respcmmap)
### GPCM/4-PL mixed model ######
THRES <- matrix(c(-2,-1.23,1.11,3.48,1
,2,-1,-0.2,0.5,1.3,-0.8,1.5),nrow=2)
sl <- c(0.5,1,1.5,1.1,1,0.98)
THRESx <- THRES
THRESx[2,1:3] <- NA
# for the 4PL item the estimated parameters are submitted,
# for the GPCM items the lower asymptote = 0
# and the upper asymptote = 1.
la <- c(0.02,0.1,0,0,0,0)
ua <- c(0.97,0.91,1,1,1,1)
awmatrix <- matrix(c(1,0,1,0,1,1,1,0,0,1
,2,0,0,0,1,0,0,0,0,1
,0,2,2,1,1,1,1,0,0,1),byrow=TRUE,nrow=5)
# create model2est
# this function tries to help finding the appropriate
# model by inspecting the THRESx.
model2est <- findmodel(THRESx)
# MLE estimation
respmixed_mle <- PPall(respm = awmatrix,
thres = THRESx,
slopes = sl,
lowerA = la,
upperA=ua,
type = "mle",
model2est=model2est)
# WLE estimation
respmixed_wle <- PPall(respm = awmatrix,
thres = THRESx,
slopes = sl,
lowerA = la,
upperA=ua,
type = "wle",
model2est=model2est)
res_jk114 <- JKpp(respmixed_mle)
res_jk115 <- JKpp(respmixed_wle)