Estimate item parameters
Description
Estimate IRT item parameters using either ICL, BILOG, or ltm
.
Provides access to the most widely used options in these programs.
Usage
1 2 3 4 
Arguments
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". 
omitsWrong 
If TRUE, all omitted items will be recoded as wrong responses, otherwise they will be treated as missing (default) 
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 
Details
Estimate the parameters of an IRT model defined in the most general case ("3PL") as
P(U_{ij}=1θ_i,a_j,b_j,c_j)=c_j+(1c_j)\frac{\displaystyle\exp(a_j(θ_ib_j))}{1+\displaystyle\exp(a_j(θ_ib_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_ib_j)
rather than a_j(θ_ib_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(1p)+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 4parameter 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.bah.com. Alternative links are provided in the help screen for
this package. 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.
Value
A list with three elements: est
and se
are
matrices containing the parameter estimates and their standard errors, correspondingly.
Each matrix has 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. The third
element, vcm
, is a list of variancecovariance matrices for the item
parameters. Currently, vcm
is only used in function irfPlot
.
When ICL is used as estimation engine, se
and vcm
are NULL as ICL does not
compute standard errors for the item parameter estimates.
Author(s)
Ivailo Partchev
References
Bradley A. Hanson (2002), ICL: IRT Command Language. www.bah.com
Dimitris Rizopoulos (2006). ltm: Latent Trait Models under IRT. cran.rproject.org
M. F. Zimowski, E. Muraki, R. J. Mislevy and R. D. Bock (1996), BILOG–MG. MultipleGroup IRT Analysis and Test Maintenance for Binary Items, SSI Scientific Software International, Chicago, IL. www.ssicentral.com
Examples
1 2  p.1pl < est(Scored, model="1PL", engine="ltm")
p.2pl < est(Scored, model="2PL", engine="ltm")

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