Multidimensional test assembly based on Lagrangian relaxation techniques

Research output: Book/ReportReportProfessional

14 Downloads (Pure)

Abstract

In this paper, a mathematical programming approach is presented for the assembly of ability tests measuring multiple traits. The values of the variance functions of the estimators of the traits are minimized, while test specifications are met. The approach is based on Lagrangian relaxation techniques and provides good results for the two dimensional case in a small amount of time. Empirical examples of a test assembly problem from a two dimensional mathematics item pool illustrate the method. In the area of ability measurement, Item Response Theory (IRT) is usually used as a psychometric theory underlying the test assembly process. In this process, three steps can be distinguished. First, an IRT model has to be chosen and the items in the item bank have to be calibrated. From this item bank, many different tests can be assembled. Therefore, the second step consists of specifying the properties of the desired test. One could specify, for example, the test length, the desired amount of information, or the administration time of the test. The third step of the test assembly process is to formulate a model that selects items from the item bank so that test specifications are met. A mathematical programming approach is often used for this step.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversiteit Twente TO/OMD
Number of pages23
Publication statusPublished - 1998

Publication series

NameOMD research report
PublisherUniversity of Twente, Faculty of Educational Science and Technology
No.98-08

Fingerprint

Mathematical programming
Specifications

Keywords

  • METIS-136544
  • IR-104087

Cite this

Veldkamp, B. P. (1998). Multidimensional test assembly based on Lagrangian relaxation techniques. (OMD research report; No. 98-08). Enschede: Universiteit Twente TO/OMD.
Veldkamp, Bernard P. / Multidimensional test assembly based on Lagrangian relaxation techniques. Enschede : Universiteit Twente TO/OMD, 1998. 23 p. (OMD research report; 98-08).
@book{d1897dadcaf34104b72d0ab05e9bfb4b,
title = "Multidimensional test assembly based on Lagrangian relaxation techniques",
abstract = "In this paper, a mathematical programming approach is presented for the assembly of ability tests measuring multiple traits. The values of the variance functions of the estimators of the traits are minimized, while test specifications are met. The approach is based on Lagrangian relaxation techniques and provides good results for the two dimensional case in a small amount of time. Empirical examples of a test assembly problem from a two dimensional mathematics item pool illustrate the method. In the area of ability measurement, Item Response Theory (IRT) is usually used as a psychometric theory underlying the test assembly process. In this process, three steps can be distinguished. First, an IRT model has to be chosen and the items in the item bank have to be calibrated. From this item bank, many different tests can be assembled. Therefore, the second step consists of specifying the properties of the desired test. One could specify, for example, the test length, the desired amount of information, or the administration time of the test. The third step of the test assembly process is to formulate a model that selects items from the item bank so that test specifications are met. A mathematical programming approach is often used for this step.",
keywords = "METIS-136544, IR-104087",
author = "Veldkamp, {Bernard P.}",
year = "1998",
language = "English",
series = "OMD research report",
publisher = "Universiteit Twente TO/OMD",
number = "98-08",

}

Veldkamp, BP 1998, Multidimensional test assembly based on Lagrangian relaxation techniques. OMD research report, no. 98-08, Universiteit Twente TO/OMD, Enschede.

Multidimensional test assembly based on Lagrangian relaxation techniques. / Veldkamp, Bernard P.

Enschede : Universiteit Twente TO/OMD, 1998. 23 p. (OMD research report; No. 98-08).

Research output: Book/ReportReportProfessional

TY - BOOK

T1 - Multidimensional test assembly based on Lagrangian relaxation techniques

AU - Veldkamp, Bernard P.

PY - 1998

Y1 - 1998

N2 - In this paper, a mathematical programming approach is presented for the assembly of ability tests measuring multiple traits. The values of the variance functions of the estimators of the traits are minimized, while test specifications are met. The approach is based on Lagrangian relaxation techniques and provides good results for the two dimensional case in a small amount of time. Empirical examples of a test assembly problem from a two dimensional mathematics item pool illustrate the method. In the area of ability measurement, Item Response Theory (IRT) is usually used as a psychometric theory underlying the test assembly process. In this process, three steps can be distinguished. First, an IRT model has to be chosen and the items in the item bank have to be calibrated. From this item bank, many different tests can be assembled. Therefore, the second step consists of specifying the properties of the desired test. One could specify, for example, the test length, the desired amount of information, or the administration time of the test. The third step of the test assembly process is to formulate a model that selects items from the item bank so that test specifications are met. A mathematical programming approach is often used for this step.

AB - In this paper, a mathematical programming approach is presented for the assembly of ability tests measuring multiple traits. The values of the variance functions of the estimators of the traits are minimized, while test specifications are met. The approach is based on Lagrangian relaxation techniques and provides good results for the two dimensional case in a small amount of time. Empirical examples of a test assembly problem from a two dimensional mathematics item pool illustrate the method. In the area of ability measurement, Item Response Theory (IRT) is usually used as a psychometric theory underlying the test assembly process. In this process, three steps can be distinguished. First, an IRT model has to be chosen and the items in the item bank have to be calibrated. From this item bank, many different tests can be assembled. Therefore, the second step consists of specifying the properties of the desired test. One could specify, for example, the test length, the desired amount of information, or the administration time of the test. The third step of the test assembly process is to formulate a model that selects items from the item bank so that test specifications are met. A mathematical programming approach is often used for this step.

KW - METIS-136544

KW - IR-104087

M3 - Report

T3 - OMD research report

BT - Multidimensional test assembly based on Lagrangian relaxation techniques

PB - Universiteit Twente TO/OMD

CY - Enschede

ER -

Veldkamp BP. Multidimensional test assembly based on Lagrangian relaxation techniques. Enschede: Universiteit Twente TO/OMD, 1998. 23 p. (OMD research report; 98-08).