equate-methods {plink} | R Documentation |
This function conducts IRT true score and observed score equating for unidimensional
single-format or mixed-format item parameters for two or more groups. This function
supports all item response models available in plink
with the exception of
the multiple-choice model.
equate(x, method="TSE", true.scores, ts.low, base.grp=1, score=1, startval, weights1, weights2, syn.weights, ...) ## S4 method for signature 'list' equate(x, method, true.scores, ts.low, base.grp, score, startval, weights1, weights2, syn.weights, ...) ## S4 method for signature 'irt.pars', 'ANY' equate(x, method, true.scores, ts.low, base.grp, score, startval, weights1, weights2, syn.weights, ...)
x |
an object of class irt.pars with two or more groups
or the output from plink containing rescaled item parameters. |
method |
character vector identifying the equating method(s) to use.
Values can include "TSE" and "OSE" . |
true.scores |
numeric vector of true score values to be equated |
ts.low |
logical value. If TRUE, interpolate values for the equated true scores in the range of observed scores from one to the value below the lowest estimated true score (a rounded sum of guessing parameters) |
base.grp |
integer identifying the group for the base scale |
score |
if score = 1, score responses for the true-score equating
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. |
startval |
integer starting value for the first value of true.score |
weights1 |
list containing information about the theta values and weights to be used in the observed score equating for population 1. See below for more details. |
weights2 |
list containing information about the theta values and weights to be used in the observed score equating for population 2. See below for more details. |
syn.weights |
vector of length two or a list containing vectors of length two
with synthetic population weights to be used for each pair of tests for populations
1 and 2 respectively. If missing, weights of 0.5 will be used for both populations
for all groups. If syn.weights is a list, there should be k-1 elements for
k groups. |
... |
further arguments passed to or from other methods. See below for details. |
weights1
can be a list or a list of lists. The purpose of this object is to specify
the theta values for population 1 to integrate over in the observed score equating as well as
any weights associated with the theta values. The function as.weight
can be used to facilitate the creation of this object. If weights1
is missing, the
default is to use equally spaced theta values ranging from -4 to 4 with an increment of 0.05
and normal density weights for all groups.
To better understand the elements of weights1
, let us assume for a moment that x
has parameters for only two groups. In this instance, weights1
would be a single list
with length two. The first element should be a vector of theta values corresponding to points
on the base scale. The second list element should be a vector of weights corresponding the
theta values. If x
contains more than two groups, a single weights1
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 weights for each adjacent group in x
can be
supplied.
The specification of weights2
is the same as that for weights1
, although the
theta values and weights for this object correspond to theta values for population 2.
This argument is only used when the synthetic weight associated with population 2 is greater
than zero. If weights2
is missing, the same theta values and weights used for
weights1
will be used for weights2
.
For both equating methods, response probabilities are computed using the functions drm
,
grm
, gpcm
, and nrm
for the associated models respectively. Various
arguments from these functions can be passed to equate
. 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.
Returns a matrix of equated true scores or a list of equated observed scores with associated marginal distributions or a list combining these two objects
Jonathan P. Weeks weeksjp@gmail.com
Kolen, M. J. (1981). Comparison of traditional and item response theory methods for equating tests. Journal of Educational Measurement, 18(1), 1-11.
Kolen, M. J. & Brennan, R. L. (2004) Test Equating, Scaling, and Linking (2nd ed.). New York: Springer
# IRT true score and observed score examples from # Kolen & Brennan (2004, ch. 6) pm <- as.poly.mod(36) x <- as.irt.pars(KB04$pars, KB04$common, exclude=list(27,NA), cat=list(rep(2,36),rep(2,36)), poly.mod=list(pm,pm)) out <- plink(x, rescale="MS", base.grp=2, D=1.7) # Create the quadrature points and weights wt <- as.weight( theta=c(-5.2086,-4.163,-3.1175,-2.072,-1.0269,0.0184, 1.0635,2.109,3.1546,4.2001), weight=c(0.000101,0.00276,0.03021,0.142,0.3149,0.3158, 0.1542,0.03596,0.003925,0.000186)) # Conduct the equating equate(out,method=c("TSE","OSE"),weights1=wt, synth.weights=c(1,0),D=1.7) # Conduct true score equating for specific true scores equate(out, true.scores=7:15, ts.low=FALSE, D=1.7) # Observed score equating for mixed-format tests 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$cat,list(pm1,pm2)) out <- plink(x, rescale="HB") OSE <- equate(out, method="OSE", score=2) # Display the equated scores OSE[[1]] # Multiple group equating pars <- TK07$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, rescale="SL") # True score equating equate(out) # True score equating with the base group changed to 3 equate(out, base.grp=3) # Observed score equating (These data are for non-equivalent groups, but # this example is included to illustrate the multigroup capabilities) OSE <- equate(out, method="OSE", base.grp=3) # Display the equated scores for each group OSE[[1]]