plink(x, common, rescale, ability, method, weights.t, weights.f,
startvals, exclude, score = 1, base.grp = 1, symmetric = FALSE,
rescale.com = TRUE, grp.names = NULL, dilation = "oblique",
md.center = FALSE, dim.order = NULL, ...)## S4 method for signature 'list', 'matrix'
plink(x, common, rescale, ability, method, weights.t, weights.f,
startvals, exclude, score, base.grp, symmetric, rescale.com,
grp.names, dilation, md.center, dim.order, ...)
## S4 method for signature 'list', 'data.frame'
plink(x, common, rescale, ability, method, weights.t, weights.f,
startvals, exclude, score, base.grp, symmetric, rescale.com,
grp.names, dilation, md.center, dim.order, ...)
## S4 method for signature 'list', 'list'
plink(x, common, rescale, ability, method, weights.t, weights.f,
startvals, exclude, score, base.grp, symmetric, rescale.com,
grp.names, dilation, md.center, dim.order, ...)
## S4 method for signature 'irt.pars', 'ANY'
plink(x, common, rescale, ability, method, weights.t, weights.f,
startvals, exclude, score, base.grp, symmetric, rescale.com,
grp.names, dilation, md.center, dim.order, ...)
x will not be
transformed to the base scale. To transform the parameters use
"MM","MS","HB","SL","LS" for the Mean/Mean, Mean/Sigma, Haebara,
Stocking-Lord, and least squares linking constants respectively.rescale or the Haebara constants if rescale
is missing."MM","MS","HB","SL","LS" for the Mean/Mean, Mean/Sigma, Haebara,
Stocking-Lord, and least squares linking constants respectively, or if
missing, constants will be estimated for all methods.symmetric=FALSE. See below for more details. score = 1, score responses for the Stocking-Lord
method with zero for the lowest category and k-1 for the highest, k, category
for each item. If score = 2, score responses with one for the
lowest category and k for the highest, k, category for each item. A vector or
list of scoring weights for each response category can be supplied, but this is
only recommended for advanced users.TRUE use symmetric minimization for the characteristic
curve methods. See Kim and Lee (2006) for more informationTRUE rescale the common item parameters using the
estimated linking constants; otherwise, insert the non-transformed common item
parameters into the set of unique transformed item parameters"oblique", an orthogonal Procrustes
approach with a fixed dilation parameter (Li & Lissitz, 2000) "orth.fd", or an
orthogonal Procrustes approach with variable dilations (Min, 2003) "orth.vd"
should be used to estimate the linking constants for the multidimensional methods. Both
orthogonal approaches can be constrained to exclude reflections by using "orth.fdc"
or "orth.vdc".TRUE mean center the slope matrices prior to estimating the
rotation matrix and dilation constantsx contains only
two list elements. If either of the list elements is of class irt.pars, they
can include multiple groups. common is the matrix of common items between
the two groups in x. See details for more information on common.x="list",
common="matrix".x includes two or
more list elements. When x has length two, common (although a single
matrix) should be a list with length one. If x has more than two list elements
common identifies the common items between adjacent list elements. If objects
of class irt.pars are included with multiple groups, common should
identify the common items between the first or last group in the irt.pars object,
depending on its location in x, and the adjacent list element(s) in x.
For example, if x has three elements: an irt.pars object with one group,
an irt.pars object with four groups, and a sep.pars object, common
will be a list with length two. The first element in common is a matrix
identifying the common items between the items in the first irt.pars object
and the first group in the second irt.pars object. The second element in
common should identify the common items between the fourth group in the
second irt.pars object and the items in the sep.pars object.
irt.pars
object with multiple groups.x contains only two elements, common should be a matrix. If x
contains more than two elements, common should be a list. In any of the common
matrices the first column identifies the common items for the first group of two adjacent
list elements in x. The second column in common identifies the corresponding
set of common items from the next list element in x. For example, if x
contains only two list elements, a single set of common items links them together. If
item 4 in group one (row 4 in slot pars) is the same as item 6 in group two, the
first row of common would be (4,6). startvals can be a vector or list of starting values for the slope(s) and intercept(s).
For unidimensional methods, when there are only two groups, this argument should be a vector of
length of two with the first value for the slope and the second value for the intercept or a
character value equal to "MM" or"MS". When there are more than two groups a vector of starting
values or a character value can be supplied (the same numeric values, if a vector is supplied,
will be used for all pairs, or the corresponding MM/MS values for each pair of tests will be
used) or a list of vectors/character values can be supplied with the number of list elements
equal to the number of groups minus one. For the multidimensional methods, the same general
structure applies (a vector or character value for a single group or a vector, character value
or list for multiple groups); however, the length of the vector will vary depending on the
dilation approach used. If dilation is "obliquw", the first m*m values in startvals,
for m dimensions, should correspond to the values in the transformation matrix (starting with
the value in the upper-left corner, then the next value in the column, ..., then the first value
in the next column, etc.). The remaining m values should be for the translation vector. If
dilation is "orth.fd", the first value will be the slope parameter and the remaining m values
will be for the translation vector. If dilation is "orth.vd", the first m values are the
slopes for each dimension and the remaining m values are for the translation vector. weights.t can be a list or a list of lists. The purpose of this object is to specify
the theta values on the To scale to integrate over in the characteristic curve methods
as well as any weights associated with the theta values. See Kim and Lee (2006) or Kolen
and Brennan (2004) for more information of these weights. The function as.weight
can be used to facilitate the creation of this object. If weights.t is missing, the
default--in the unidimensional case--is to use equally spaced theta values ranging from -4 to 4
with an increment of 0.05 and theta weights equal to one for all theta values. In the
multidimensional case, the default is to use 1000 randomly sampled values from a multivariate
normal distribution with correlations equal to 0.6 for all dimensions. The theta weights are
equal to the normal distribution weights at these points. To better understand the elements of weights.t, let us assume for a moment that x
has parameters for only two groups and that we are using non-symmetric linking. In this instance,
weights.t would be a single list with length two. The first element should be a vector
of theta values corresponding to points on the To scale. The second list element should
be a vector of weights corresponding the theta values. If x contains multiple
groups, a single weights.t object can be supplied, and the same set of thetas and weights
will be used for all adjacent groups. However, a separate list of theta values and theta weights
for each adjacent group in x can be supplied. The specification of weights.f is the same as that for weights.t, although the
theta values and weights for this object correspond to theta values on the From scale.
This argument is only used when symmetric=TRUE. If weights.f is missing and
symmetric=TRUE, the same theta values and weights used for weights.t will be
used for weights.f. In general, all of the common items identified in x or common will be used
in estimating linking constants; however, there are instances where there is a need to exclude
certain common items (e.g., NRM or MCM items or items exhibiting parameter drift). Instead of
creating a new matrix or list of matrices for common, the exclude argument can
be used. exclude can be specified as a character vector or a list. In the former case,
a vector of model names (i.e., "drm", "grm", "gpcm", "nrm", "mcm") would be supplied, indicating
that any common item on any test associated with the given model(s) would be excluded from the
set of items used to estimate the linking constants. If the argument is specified as a list,
exclude should have as many elements as groups in x. Each list element can include
model names and/or item numbers corresponding to the common items that should be excluded for
the given group. If no items need to be excluded for a given group, the list element should be
NULL or NA. For example, say we have two groups and we would like to exclude the NRM items and
item 23 from the first group, we would specify exclude as exclude <- list(c("nrm",23),NA).
Notice that the item number corresponding item 23 in group 2 does not need to be specified. The argument dim.order is a k x r matrix for k groups and r unique dimensions across
groups. This object identifies the common dimensions across groups. The elements in the
matrix should correspond to the dimension (i.e., the column in the matrix of slope parameters)
for a given group. For example, say there are four unique dimensions across two groups,
each group only measures three dimensions, and there are only two common dimensions. We might
specify a matrix as follows dim.order <- matrix(c(1:3,NA,NA,1:3),2,4). In words, this means
that dimensions 2 and 3 in the first group correspond to dimensions 1 and 2 in the second
group respectively. If no dim.order is specified, it is assumed that all of the
dimensions are common, or in instances with different numbers of factors, that the first
m dimensions for each group are common and the remaining r-m dimensions for a given group
are unique. For the characteristic curve methods, response probabilities are computed using the functions
drm, grm, gpcm, nrm, and mcm for the associated models
respectively. Various arguments from these functions can be passed to plink. Specifically,
the argument incorrect can be passed to drm and catprob can be passed to
grm. In the functions drm, grm, and gpcm there is an argument D
for the value of a scaling constant. In plink, a single argument D can be passed
that will be applied to all applicable models, or arguments D.drm, D.grm, and
D.gpcm can be specified for each model respectively. If an argument is specified for D
and, say D.drm, the values for D.grm and D.gpcm (if applicable) will be
set equal to D. If only D.drm is specified, the values for D.grm and
D.gpcm (if applicable) will be set to 1.###### Unidimensional Examples ######
# Create irt.pars object with two groups (all dichotomous items),
# rescale the item parameters using the Mean/Sigma linking constants,
# and exclude item 27 from the common item set
pm <- as.poly.mod(36)
x <- as.irt.pars(KB04$pars, KB04$common, cat=list(rep(2,36),rep(2,36)),
poly.mod=list(pm,pm))
out <- plink(x, rescale="MS", base.grp=2, D=1.7, exclude=list(27,NA))
summary(out, descrip=TRUE)
pars.out <- link.pars(out)
# Create object with six groups (all dichotomous items)
pars <- TK07$pars
common <- TK07$common
cat <- list(rep(2,26),rep(2,34),rep(2,37),rep(2,40),rep(2,41),rep(2,43))
pm1 <- as.poly.mod(26)
pm2 <- as.poly.mod(34)
pm3 <- as.poly.mod(37)
pm4 <- as.poly.mod(40)
pm5 <- as.poly.mod(41)
pm6 <- as.poly.mod(43)
pm <- list(pm1, pm2, pm3, pm4, pm5, pm6)
x <- as.irt.pars(pars, common, cat, pm,
grp.names=paste("grade",3:8,sep=""))
out <- plink(x)
summary(out)
constants <- link.con(out) # Extract linking constants
# Create an irt.pars object and a sep.pars object for two groups of
# nominal response model items. Compare non-symmetric and symmetric
# minimization. Note: This example may take a minute or two to run
## Not run: ------------------------------------
# pm <- as.poly.mod(60, "nrm", 1:60)
# pars1 <- as.irt.pars(act.nrm$yr97, cat=rep(5,60), poly.mod=pm)
# pars2 <- sep.pars(act.nrm$yr98, cat=rep(5,60), poly.mod=pm)
# out <- plink(list(pars1, pars2), matrix(1:60,60,2))
# out1 <- plink(list(pars1, pars2), matrix(1:60,60,2), symmetric=TRUE)
# summary(out, descrip=TRUE)
# summary(out1, descrip=TRUE)
## ---------------------------------------------
# Compute linking constants for two groups with multiple-choice model
# item parameters. Rescale theta values and item parameters using
# the Haebara linking constants
# Note: This example may take a minute or two to run
## Not run: ------------------------------------
# theta <- rnorm(100) # In practice, estimated theta values would be used
# pm <- as.poly.mod(60, "mcm", 1:60)
# x <- as.irt.pars(act.mcm, common=matrix(1:60,60,2), cat=list(rep(6,60),
# rep(6,60)), poly.mod=list(pm,pm))
# out <- plink(x, ability=list(theta,theta), rescale="HB")
# pars.out <- link.pars(out)
# ability.out <- link.ability(out)
# summary(out, descrip=TRUE)
## ---------------------------------------------
# Compute linking constants for two groups using mixed-format items and
# a mixed placement of common items. Compare calibrations with the
# inclusion or exclusion of NRM items. This example uses the dgn dataset.
pm1 <- as.poly.mod(55,c("drm","gpcm","nrm"),dgn$items$group1)
pm2 <- as.poly.mod(55,c("drm","gpcm","nrm"),dgn$items$group2)
x <- as.irt.pars(dgn$pars,dgn$common,dgn$cat,list(pm1,pm2))
# Run with the NRM common items included
out <- plink(x)
# Run with the NRM common items excluded
out1 <- plink(x,exclude="nrm")
summary(out)
summary(out1)
# Compute linking constants for six groups using mixed-format items and
# a mixed placement of common items. This example uses the reading dataset.
# See the information on the dataset for an interpretation of the output.
pm1 <- as.poly.mod(41, c("drm", "gpcm"), reading$items[[1]])
pm2 <- as.poly.mod(70, c("drm", "gpcm"), reading$items[[2]])
pm3 <- as.poly.mod(70, c("drm", "gpcm"), reading$items[[3]])
pm4 <- as.poly.mod(70, c("drm", "gpcm"), reading$items[[4]])
pm5 <- as.poly.mod(72, c("drm", "gpcm"), reading$items[[5]])
pm6 <- as.poly.mod(71, c("drm", "gpcm"), reading$items[[6]])
pm <- list(pm1, pm2, pm3, pm4, pm5, pm6)
x <- as.irt.pars(reading$pars, reading$common, reading$cat, pm, base.grp=4)
out <- plink(x)
summary(out)
###### Multidimensional Examples ######
# Reckase Chapter 9
pm <- as.poly.mod(80, "drm", list(1:80))
x <- as.irt.pars(reckase9$pars, reckase9$common,
list(rep(2,80),rep(2,80)), list(pm,pm), dimensions=2)
# Compute constants using the least squares method and
# the orthongal rotation with variable dilation.
# Rescale the item parameters using the LS method
out <- plink(x, dilation="orth.vd", rescale="LS")
summary(out, descrip=TRUE)
# Extract the rescaled item parameters
pars.out <- link.pars(out)
# Compute constants using an oblique Procrustes method
# Display output and descriptives
out <- plink(x, dilation="oblique")
summary(out, descrip=TRUE)
# Compute constants using and orthogonal rotation with
# a fixed dilation parameter
# Rescale the item parameters and ability estimates
# using the "HB" and "LS" methods.
# Display the optimization iterations
ability <- matrix(rnorm(40),20,2)
out <- plink(x, method=c("HB","LS"), dilation="orth.fd",
rescale="HB", ability=list(ability,ability),
control=list(trace=1,rel.tol=0.001))
summary(out)
# Extract rescaled ability estimates
ability.out <- out$ability
# Compute linking constants for two groups using mixed-format items
# modeled with the M3PL and MGPCM. Only compute constants using the
# orth.vd dilation.
pm <- as.poly.mod(60,c("drm","gpcm"), list(c(1:60)[md.mixed$cat==2],
c(1:60)[md.mixed$cat>2]))
x <- as.irt.pars(md.mixed$pars, matrix(1:60,60,2),
list(md.mixed$cat, md.mixed$cat),
list(pm, pm), dimensions=4, grp.names=c("Form.X","Form.Y"))
out <- plink(x,dilation="orth.vd")
summary(out, descrip=TRUE)
# Illustration of construct shift and how to specify common dimensions
pm <- as.poly.mod(80, "drm", list(1:80))
pars <- cbind(round(runif(80),2),reckase9$pars[[1]])
x <- as.irt.pars(list(pars,reckase9$pars[[2]]), reckase9$common,
list(rep(2,80),rep(2,80)), list(pm,pm), dimensions=c(3,2))
dim.order <- matrix(c(1,2,3,NA,1,2),2,3,byrow=TRUE)
out <- plink(x, dilation="oblique", dim.order=dim.order, rescale="LS")
summary(out)
pars.out <- link.pars(out)
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