
This function implements the kernel method of test equating as described in Holland and Thayer (1989), and Von Davier et al. (2004). Nonstandard kernels others than the gaussian are available. Associated standard error of equating are also provided.
ker.eq(scores, kert, hx = NULL, hy = NULL, degree, design, Kp = 1, scores2,
degreeXA, degreeYA, J, K, L, wx, wy, w, gapsX, gapsY, gapsA, lumpX, lumpY,
lumpA, alpha, h.adap)
An object of class ker.eq
representing the kernel equating process. Generic functions such as
print
, and summary
have methods to show the results of the equating. The results include
summary statistics, equated values, standard errors of equating, and others.
The function SEED
can be used to obtain standard error of equating differences (SEED) of two
objects of class ker.eq
. The function PREp
can be used on a ker.eq
object to
obtain the percentage relative error measure (see Von Davier et al, 2004).
The possible values of
The equated values of test
The equated values of test
The standard error of equating for equating
The standard error of equating for equating
Note that depending on the specified equating design, not all arguments are necessary as detailed below.
If the "EG" design is specified, a two column matrix containing the raw sample frequencies
coming from the two groups of scores to be equated. It is assumed that the data in the first
and second columns come from tests
If the "SG" design is specified, a matrix containing the (joint) bivariate sample
frequencies for
If the "CB" design is specified, a two column matrix containing the observed scores
of the sample taking test scores2
argument is then used for the scores of the sample taking test Y first followed by test
If either the "NEAT_CB" or "NEAT_PSE" design is selected, a two column matrix containing
the observed scores on test scores2
argument is then used for the observed
scores on test
A character string giving the type of kernel to be used for continuization.
Current options include "gauss
", "logis
", "uniform
", "epan
" and "adap
"
for the gaussian, logistic, uniform, Epanechnikov and Adaptative kernels, respectively
An integer indicating the value of the bandwidth parameter to be used for kernel continuization
of
An integer indicating the value of the bandwidth parameter to be used for kernel continuization
of
A vector indicating the number of power moments to be fitted to the marginal distributions ("EG" design), and/or the number or cross moments to be fitted to the joint distributions (see Details).
A character string indicating the equating design (one of "EG", "SG", "CB", "NEAT_CE", "NEAT_PSE")
A number which acts as a weight for the second term in the combined penalization function used
to obtain h
(see details).
Only used for the "CB", "NEAT_CE" and "NEAT_PSE" designs. See the description of
scores
.
A vector indicating the number of power moments to be fitted to the marginal distributions
Only used for the "NEAT_CE" and "NEAT_PSE" designs (see the description for
degreeXA
)
The number of possible
The number of possible
The number of possible
A number that satisfies
A number that satisfies
A number that satisfies
A list object containing:
index
A vector of indices between
degree
An integer indicating the maximum degree of the moments fitted by the log-linear model.
Only used for the "NEAT" design.
A list object containing:
index
A vector of indices between
degree
An integer indicating the maximum degree of the moments fitted.
Only used for the "NEAT" design.
A list object containing:
index
A vector of indices between
degree
An integer indicating the maximum degree of the moments fitted.
Only used for the "NEAT" design.
An integer to represent the index where an artificial "lump" is created in the marginal distribution of frecuencies for
An integer to represent the index where an artificial "lump" is created in the marginal distribution of frecuencies for
An integer to represent the index where an artificial "lump" is created in the marginal distribution of frecuencies for
Only for Adaptative Kernel. Sensitivity parameter.
Only for Adaptative Kernel. A list(hx, hy) containing bandwidths for Adaptative kernel for each Form.
Jorge Gonzalez jorge.gonzalez@mat.uc.cl
This is a generic function that implements the kernel method of test equating as described in Von Davier et al.
(2004). Given test scores loglin.smooth
). The value of
Gonzalez, J. (2014). SNSequate: Standard and Nonstandard Statistical Models and Methods for Test Equating. Journal of Statistical Software, 59(7), 1-30.
Holland, P. and Thayer, D. (1989). The kernel method of equating score distributions. (Technical Report No 89-84). Princeton, NJ: Educational Testing Service.
Holland, P., King, B. and Thayer, D. (1989). The standard error of equating for the kernel method of equating score distributions (Tech. Rep. No. 89-83). Princeton, NJ: Educational Testing Service.
Von Davier, A., Holland, P., and Thayer, D. (2004). The Kernel Method of Test Equating. New York, NY: Springer-Verlag.
loglin.smooth
, SEED
, PREp
#Kernel equating under the "EG" design
data(Math20EG)
mod<-ker.eq(scores=Math20EG,kert="gauss",hx=NULL,hy=NULL,degree=c(2,3),design="EG")
summary(mod)
#Reproducing Table 7.6 in Von Davier et al, (2004)
scores<-0:20
SEEXy<-mod$SEEXy
SEEYx<-mod$SEEYx
Table7.6<-cbind(scores,SEEXy,SEEYx)
Table7.6
#Other nonstandard kernels. Table 10.3 in Von Davier (2011).
mod.logis<-ker.eq(scores=Math20EG,kert="logis",hx=NULL,hy=NULL,degree=c(2,3),design="EG")
mod.unif<-ker.eq(scores=Math20EG,kert="unif",hx=NULL,hy=NULL,degree=c(2,3),design="EG")
mod.gauss<-ker.eq(scores=Math20EG,kert="gauss",hx=NULL,hy=NULL,degree=c(2,3),design="EG")
XtoY<-cbind(mod.logis$eqYx,mod.unif$eqYx,mod.gauss$eqYx)
YtoX<-cbind(mod.logis$eqXy,mod.unif$eqXy,mod.gauss$eqXy)
Table10.3<-cbind(XtoY,YtoX)
Table10.3
## Examples using Adaptive and Epanechnikov kernels
x_sim = c(1,2,3,4,5,6,7,8,9,10,11,10,9,8,7,6,5,4,3,2,1)
prob_sim = x_sim/sum(x_sim)
set.seed(1)
sim = rmultinom(1, p = prob_sim, size = 1000)
x_asimD = c(1,7,13,18,22,24,25,24,20,18,16,15,13,9,5,3,2.5,1.5,1.5,1,1)
probas_asimD = x_asimD/sum(x_asimD)
set.seed(1)
asim = rmultinom(1, p = probas_asimD, size = 1000)
scores = cbind(asim,sim)
mod.adap = ker.eq(scores,degree=c(2,2),design="EG",kert="adap")
mod.epan = ker.eq(scores,degree=c(2,2),design="EG",kert="epan")
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