R packages - Apr 2009 - Major revision of plink for separate calibration IRT-based linking

An updated version of the package plink has been uploaded to CRAN. This is a
major revision that now includes multidimensional models and methods.

plink is a package for conducting unidimensional and multidimensional
IRT-based test linking using separate calibration methods for multiple
groups for single-format or mixed-format common items. The package supports
sixteen IRT models and eleven calibration methods.

Dichotomous Models:
1PL, 2PL, 3PL, M1PL, M2PL, M3PL

Polytomous Models:
-Graded response model, MD graded response model
-Partial credit model, MD partial credit model
-Generalized partial credit model, MD generalized partial credit model
-Nominal response model, MD nominal response model
-Multiple-choice model, MD multiple-choice model

Unidimensional Calibration Methods:
-Mean/Mean
-Mean/Sigma
-Haebara
-Stocking-Lord

Multidimensional Calibration Methods:
-Reckase-Martineau (least squares with oblique procrustes rotation)
-MD Haebara
-MD Stocking-Lord
--For the later two methods there are three dilation approaches
  - Oshima-Davey-Lee (oblique rotation)
  - Li-Lissitz (orthogonal procrustes rotation with a single dilation
parameter)
  - Min (orthogonal procrustes rotation with multiple dilation parameters)

Any combination of dichotomous and polytomous items can be supplied with
intermingled unique and common items for as many items and groups as system
memory allows. Linking constants are computed and returned for all the
calibration methods, and (if desired) ability and/or item parameters can be
rescaled and returned using any of the estimated linking constants.

Any of the included groups can be specified as the base scale, the
characteristic curve methods can use symmetric or non-symmetric
optimization, various scoring functions can be supplied for the
Stocking-Lord methods, and there is great flexibility in specifying thetas
and theta weights to be integrated over in the characteristic curve methods.

In addition to computing linking constants and rescaling ability and item
parameters, the methods in the package can be used to compute item/category
response probabilities and create plots of item/category characteristic
curves/surfaces. Particular attention has been given to the creation of
multidimensional plots (they include wireframe plots, contour plots and
vector plots).

The package is designed to allow for a variety of formats for the item
parameters including vectors, lists, matrices, and other objects available
in the package (irt.pars and sep.pars). Item parameters and calibration
output can be summarized, and descriptive statistics for the item parameters
can be displayed as well. There is also functionality for importing item
and/or ability parameters from BILOG, PARSCALE, and TESTFACT (functionality
for MULTILOG will be added in a later version).

Getting Started:
Running the separate calibration is generally a two-step process. The first
step is to format the item parameters for processing with the function
'plink'. In the simplest scenario, parameters should be formatted using
the
function 'as.irt.pars'. This essentially creates a blueprint of the item
parameters, response models, response categories, and common items across
all linked tests. Once this object has been created, the function
'plink' is
used to estimate the linking constants and rescale item and/or ability
parameters.

In addition to the estimation of linking constants, response probabilities
can be computed using the functions 'drm', 'gpcm',
'grm', 'mcm', or 'nrm'
(for both unidimensional and multidimensional models).

I am currently working on a step-by-step walk through of the package, but
for now the current documentation contains extensive details and examples.
The best documentation to start with is help(as.irt.pars) and help(plink).

I have gone through a lot of debugging and validation, so there should be
few, if any bugs. Many of the examples (and the associated output) can be
found in published articles or books. The output from all of the
unidimensional calibration methods have been checked against other available
linking software, and to the extent possible, the multidimensional linking
methods have also been checked against available software.


Jonathan Weeks
Doctoral Candidate
School of Education
University of Colorado, Boulder <weeksjp at gmail.com>

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