Description Usage Arguments Details Value Author(s) References Examples
Estimate IRT item parameters using either ICL, BILOG, or
ltm
. Provides access to the most widely used
options in these programs.
1 2 3 4 |
resp |
A matrix of responses: persons as rows, items as columns, entries are either 0 or 1, no missing data |
model |
The IRT model: "1PL", "2PL", or "3PL". Default is "2PL". |
engine |
One of "icl", "bilog", or "ltm". Default is "icl". |
nqp |
Number of quadrature points. Default is 20. |
est.distr |
T if the probabilities of the latent
distribution are to be estimated, F if a normal
distribution is assumed. Default is F. Ignored when
|
nch |
Number of choices in the original item
formulation. Used to determine the prior for the
asymptote when |
a.prior |
Whether a prior for the item
discriminations is used. Ignored when |
b.prior |
Whether a prior for the item difficulties
is used. Ignored when |
c.prior |
Whether a prior for the asymptotes is
used. Ignored when |
bilog.defaults |
When |
rasch |
When |
run.name |
A (short) string used in the names of all
files read or written by ICL or BILOG. Default is
|
Estimate the parameters of an IRT model defined in the most general case ("3PL") as
P(U_{ij}=1|θ_i,a_j,b_j,c_j)=c_j+(1-c_j)\frac{\displaystyle\exp(a_j(θ_i-b_j))}{1+\displaystyle\exp(a_j(θ_i-b_j))}
where U_{ij} is a binary response given by person i to item j, θ_i is the value of the latent variable ("ability") for person i, a_j is the discrimination parameter for item j, b_j is the difficulty parameter for item j, c_j is the asymptote for item j.
Some authors prefer to represent the model with a logit
1.7a^*_j(θ_i-b_j) rather than
a_j(θ_i-b_j). This option has been removed
from irtoys
as it is not supported by the
remaining functions of the package.
In the 2PL model (model="2PL"
), all asymptotes
c_j are 0. In the 1PL model (model="1PL"
),
all asymptotes c_j are 0 and the discriminations
a_j are equal for all items (and sometimes to 1).
Package irtoys
provides a simple common interface
to the estimation of item parameters with three different
programs. It only accesses the most basic and widely used
options in these programs. Each of the three programs has
a much wider choice of options and cababilities, and
serious users must still learn the corresponding syntax
in order to access the advanced features. Even when
models are fit "by hand", irtoys
may be useful in
plotting results, doing comparisons across programs etc.
Estimation of the more complex IRT models (2PL and 3PL)
for some "difficult" data sets often has to use prior
distributions for the item parameters. irtoys
adopts the default behaviour of BILOG: no priors for
b in any model, priors for a in the 2PL and
3PL models, priors for c in the 3PL model. This can
be overriden by changing the values of a.prior
,
b.prior
, and c.prior
.
If priors are used at all, they will be the same for all
items. Note that both ICL and BILOG can, at some
additional effort, set different priors for any
individual item. At default, the common priors are the
BILOG defaults: normal(0,2)
for b,
lognormal (0, 0.5)
for a, and
beta(20*p+1, 20(1-p)+1)
for c; p is 1
over the number of choices in the original item
formulations, which can be set with the parameter
nch
, and is again assumed the same for all items.
When engine="icl"
and bilog.defaults=F
, any
priors used will be the ICL default ones, and based on
the 4-parameter beta distribution: beta(1.01, 1.01,
-6, 6)
for b, beta(1.75, 3, 0, 3)
for
a, and beta(3.5, 4, 0, 0.5)
for c.
When engine="ltm"
, all commands involving priors
are ignored.
est
only works when some IRT software is
installed. Package ltm
is automatically loaded.
ICL can be downloaded from www.b-a-h.com. BILOG is
commercial software sold by SSI — see
www.ssicentral.com for further detail. On Windows,
make sure that the executable files (icl.exe
for
ICL, blm1.exe
, blm2.exe
, and
blm3.exe
, for BILOG) are located in directories
that are included in the PATH variable.
A list with two elements, est
and se
, for
the parameter estimates and their standard errors,
correspondingly. Each element is a matrix with one row
per item, and three columns: [,1] item discrimination
a, [,2] item difficulty b, and [,3] asymptote
c. For the 1PL and 2PL models, all asymptotes are
equal to 0; for the 1PL, the discriminations are all
equal but not necessarily equal to 1. When ICL is used as
estimation engine, se
is NULL as ICL does not
compute standard errors for the item parameter estimates.
Ivailo Partchev
Bradley A. Hanson (2002), ICL: IRT Command Language. www.b-a-h.com
Dimitris Rizopoulos (2006). ltm: Latent Trait Models under IRT. cran.r-project.org
M. F. Zimowski, E. Muraki, R. J. Mislevy and R. D. Bock (1996), BILOG–MG. Multiple-Group IRT Analysis and Test Maintenance for Binary Items, SSI Scientific Software International, Chicago, IL. www.ssicentral.com
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