plink-package {plink}R Documentation

Separate Calibration Linking Methods

Description

This package uses unidimensional item response theory methods to compute linking constants and conduct chain linking of tests for multiple groups under a nonequivalent groups common item design. It allows for mean/mean, mean/sigma, Haebara, and Stocking-Lord calibrations of single-format or mixed-format dichotomous (1PL, 2PL, and 3PL) and polytomous (graded response partial credit/generalized partial credit, nominal, and multiple-choice model) common items.

Details

The primary purpose of this package is to use IRT methods to place scores and item parameters for two or more groups onto a common scale. These methods can be used for horizontal equating or vertical scaling. The linking methodology used in this package is commonly referred to as separate calibration. The package allows for chain linking of multiple-groups with the base scale specified for any group. Unique and common items can can be included and rescaled using any of the linking constants (if desired). Ability estimates can also be included and rescaled. Symmetric or non-symmetric optimizations can be specified, various scoring functions can be used for the Stocking-Lord method, 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 the option to rescale 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.

The package is designed to allow a variety of formats for the item parameters including vectors, lists, matrices, and other objects (irt.pars and sep.pars) available in the package. Item parameters and calibration output can be summarized, and descriptive statistics for the item parameters can be displayed as well.

Running the separate calibration is typically a two-step process. The first step is to format the item parameters for processing with plink. Parameters should be formatted as a single irt.pars object with multiple groups, a set of irt.pars objects, or a set of sep.pars object. Once in this format, response probabilities can be computed using drm, gpcm, grm, mcm, or nrm or linking constants can be computed using plink.

The functions as.irt.pars, sep.pars, and combine.pars can be used to create the irt.pars and sep.pars objects. The function summary can be used to summarize item parameters (including descriptive statistics) and linking constants, and plot can be used to create item/category characteristic curves.

Author(s)

Jonathan Weeks weeksjp@gmail.com

References

Haebara, T. (1980). Equating logistic ability scales by a weighted least squares method. Japanese Psychological Research, /emph{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.


[Package plink version 0.0-2 Index]