Stochastic order in dichotomous item response models for fixed tests, research adaptive tests, or multiple abilities

Research output: Book/ReportReportOther research output

10 Downloads (Pure)

Abstract

Dichotomous item response theory (IRT) models can be viewed as families of stochastically ordered distributions of responses to test items. This paper explores several properties of such distributiom. The focus is on the conditions under which stochastic order in families of conditional distributions is transferred to their inverse distributions, from two families 'of related distributions to a third family, or from multivariate conditional distributions to a marginal distribution. The main results are formulated as two theorems that apply immediately to dichotomous IRT models. One theorem holds for unidimensional models with fixed item parameters. The other theorem holds for models with multiple abilities or with random item parameters as used, for example, in adaptive testing.
Original languageUndefined
Place of PublicationEnschede, the Netherlands
PublisherUniversity of Twente, Faculty Educational Science and Technology
Publication statusPublished - 1995

Publication series

NameOMD research report
PublisherUniversity of Twente, Faculty of Educational Science and Technology
No.95-02

Keywords

  • Test Items
  • IR-103602
  • Computer Assisted Testing
  • Adaptive Testing
  • Ability
  • Item Response Theory
  • Multivariate Analysis
  • Mathematical Models
  • Foreign Countries

Cite this

van der Linden, W. J. (1995). Stochastic order in dichotomous item response models for fixed tests, research adaptive tests, or multiple abilities. (OMD research report; No. 95-02). Enschede, the Netherlands: University of Twente, Faculty Educational Science and Technology.
van der Linden, Willem J. / Stochastic order in dichotomous item response models for fixed tests, research adaptive tests, or multiple abilities. Enschede, the Netherlands : University of Twente, Faculty Educational Science and Technology, 1995. (OMD research report; 95-02).
@book{c4561d0b2e5b42a2aedf985130746c89,
title = "Stochastic order in dichotomous item response models for fixed tests, research adaptive tests, or multiple abilities",
abstract = "Dichotomous item response theory (IRT) models can be viewed as families of stochastically ordered distributions of responses to test items. This paper explores several properties of such distributiom. The focus is on the conditions under which stochastic order in families of conditional distributions is transferred to their inverse distributions, from two families 'of related distributions to a third family, or from multivariate conditional distributions to a marginal distribution. The main results are formulated as two theorems that apply immediately to dichotomous IRT models. One theorem holds for unidimensional models with fixed item parameters. The other theorem holds for models with multiple abilities or with random item parameters as used, for example, in adaptive testing.",
keywords = "Test Items, IR-103602, Computer Assisted Testing, Adaptive Testing, Ability, Item Response Theory, Multivariate Analysis, Mathematical Models, Foreign Countries",
author = "{van der Linden}, {Willem J.}",
year = "1995",
language = "Undefined",
series = "OMD research report",
publisher = "University of Twente, Faculty Educational Science and Technology",
number = "95-02",

}

van der Linden, WJ 1995, Stochastic order in dichotomous item response models for fixed tests, research adaptive tests, or multiple abilities. OMD research report, no. 95-02, University of Twente, Faculty Educational Science and Technology, Enschede, the Netherlands.

Stochastic order in dichotomous item response models for fixed tests, research adaptive tests, or multiple abilities. / van der Linden, Willem J.

Enschede, the Netherlands : University of Twente, Faculty Educational Science and Technology, 1995. (OMD research report; No. 95-02).

Research output: Book/ReportReportOther research output

TY - BOOK

T1 - Stochastic order in dichotomous item response models for fixed tests, research adaptive tests, or multiple abilities

AU - van der Linden, Willem J.

PY - 1995

Y1 - 1995

N2 - Dichotomous item response theory (IRT) models can be viewed as families of stochastically ordered distributions of responses to test items. This paper explores several properties of such distributiom. The focus is on the conditions under which stochastic order in families of conditional distributions is transferred to their inverse distributions, from two families 'of related distributions to a third family, or from multivariate conditional distributions to a marginal distribution. The main results are formulated as two theorems that apply immediately to dichotomous IRT models. One theorem holds for unidimensional models with fixed item parameters. The other theorem holds for models with multiple abilities or with random item parameters as used, for example, in adaptive testing.

AB - Dichotomous item response theory (IRT) models can be viewed as families of stochastically ordered distributions of responses to test items. This paper explores several properties of such distributiom. The focus is on the conditions under which stochastic order in families of conditional distributions is transferred to their inverse distributions, from two families 'of related distributions to a third family, or from multivariate conditional distributions to a marginal distribution. The main results are formulated as two theorems that apply immediately to dichotomous IRT models. One theorem holds for unidimensional models with fixed item parameters. The other theorem holds for models with multiple abilities or with random item parameters as used, for example, in adaptive testing.

KW - Test Items

KW - IR-103602

KW - Computer Assisted Testing

KW - Adaptive Testing

KW - Ability

KW - Item Response Theory

KW - Multivariate Analysis

KW - Mathematical Models

KW - Foreign Countries

M3 - Report

T3 - OMD research report

BT - Stochastic order in dichotomous item response models for fixed tests, research adaptive tests, or multiple abilities

PB - University of Twente, Faculty Educational Science and Technology

CY - Enschede, the Netherlands

ER -

van der Linden WJ. Stochastic order in dichotomous item response models for fixed tests, research adaptive tests, or multiple abilities. Enschede, the Netherlands: University of Twente, Faculty Educational Science and Technology, 1995. (OMD research report; 95-02).