plink-methods {plink} | R Documentation |
This function conducts separate calibration of IRT single-format or mixed-format item parameters for multiple groups using the Mean/Mean, Mean/Sigma, Haebara, and Stocking-Lord methods. The function includes symmetric and non-symmetric optimization and chain-linked rescaling of item and ability parameters.
plink(x, common, rescale, ability, weights, startvals, score=1, base.grp=1, symmetric=TRUE, grp.names=NULL, mn=c(FALSE,FALSE), ...) ## S4 method for signature 'list', 'matrix' plink(x, common, rescale, ability, weights, startvals, score, base.grp, symmetric, grp.names, mn, ...) ## S4 method for signature 'list', 'data.frame' plink(x, common, rescale, ability, weights, startvals, score, base.grp, symmetric, grp.names, mn, ...) ## S4 method for signature 'list', 'list' plink(x, common, rescale, ability, weights, startvals, score, base.grp, symmetric, grp.names, mn, ...) ## S4 method for signature 'irt.pars', 'ANY' plink(x, common, rescale, ability, weights, startvals, score, base.grp, symmetric, grp.names, mn, ...)
x |
an object of class irt.pars with multiple groups or
a list of irt.pars and/or sep.pars objects. |
common |
matrix or list of common items. See below for more details. |
rescale |
if missing (default), the parameters in x will not be
transformed to the base scale. To transform the parameters use "MM","MS","HB","SL"
for the mean/mean, mean/sigma, Haebara, and Stocking-Lord linking constants
respectively. |
ability |
list of theta values with length equal to the number of groups.
If supplied, these values will be transformed to the base scale using the
constants identified in rescale or the Haebara constants if rescale
is missing. |
weights |
list containing information about the theta values and weights to use for the characteristic curve methods. See below for more details. |
score |
if 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 of
scores for each response category can be supplied, but this is only recommended
for advanced users. |
startvals |
vector of length two of starting values for the slope and
intercept respectively for the characteristic curve methods. The default
values (if startvals is missing) are 1 and 0. |
base.grp |
integer identifying the group for the base scale |
symmetric |
if TRUE use symmetric minimization for the characteristic
curve methods. See Kim and Lee (2006) for more information |
grp.names |
character vector of group names |
mn |
logical vector of length two. If the first element is FALSE , do use
nominal response model and multiple-choice model parameters when estimating
mean/mean and mean/sigma linking constants. If the second element is FALSE ,
do not use NRM and MCM parameters with the Stocking-Lord calibration. |
... |
further arguments passed to or from other methods |
If 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"
.
weights
can be a list or a list of lists. The purpose of this object is to specify
the theta values 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
is missing, the default 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.
To better understand the elements of weights
, let us assume for a moment that x
has parameters for only two groups. In this instance, weights
would be a single
list with length two. The first element should be an n x 2 matrix of theta values
corresponding to group 1 and group 2 respectively. The second list element should be an
n x 2 matrix of weights corresponding the the theta values. If x
contains multiple
groups, a single weights
object can be supplied, and the same set of thetas and weights
will be used for all adjacent groups. However, if Wj
is the weights
object
for adjacent groups j
, weights
can be a list with multiple W
objects
(i.e. a separate list of theta values and theta weights for each adjacent group in x
).
In generally, including a different W
for each adjacent group is unnecessary, but
the most likely scenario for its use is when the intent is to integrate over empirical
theta values instead of equally spaced or random values.
Returns an object of class link
. The labels for the linking constants are
specficied in the following manner "group1/group2", meaning the group1 parameters were transformed
to the group2 test. The base group is indicated by an asterisk.
x
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.Jonathan P. Weeks weeksjp@gmail.com
Haebara, T. (1980). Equating logistic ability scales by a weighted least squares method. Japanese Psychological Research, 22(3), 144-149.
Kim, S. & Lee, W.-C. (2006). An Extension of Four IRT Linking Methods for Mixed-Format Tests. Journal of Educational Measurement, 43(1), 53-76.
Kolen, M. J. & Brennan, R. L. (2004) Test Equating, Scaling, and Linking (2nd ed.). New York: Springer
Loyd, B. H. & Hoover, H. D. (1980). Vertical Equating Using the Rasch Model. Journal of Educational Measurement, 17(3), 179-193.
Marco, G. L. (1977). Item Characteristic Curve Solutions to Three Intractable Testing Problems. Journal of Educational Measurement, 14(2), 139-160.
Stocking, M. L. & Lord, F. M. (1983). Developing a common metric in item response theory. Applied Psychological Measurement, 7(2), 201-210.
# Create irt.pars object with two groups (all dichotomous items) # rescale the item parameters using the Stocking-Lord linking constants 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="SL", base.grp=2) 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 symmetric and non-symmetric minimization # Note: This example may take a minute or two to 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=FALSE) 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 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", symmetric=FALSE) 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)) out <- plink(x) # Run with NRM items included in the calibration out1 <- plink(x,mn=c(TRUE,TRUE)) # Run with NRM items excluded from the calibration summary(out) summary(out1)