Estimating quasi-loglinear models for a Rasch table if the numbers of items is large

Henk Kelderman

Research output: Book/ReportReportOther research output

9 Downloads (Pure)

Abstract

The Rasch Model and various extensions of this model can be formulated as a quasi loglinear model for the incomplete subgroup x score x item response 1 x ... x item response k contingency table. By comparing various loglinear models, specific deviations of the Rasch model can be tested. Parameter estimates can be computed using programs such as GLIM, ECTA, and MULTIQUAL, but this becomes impractical if the number of items is large. In that case, the tables of observed and expected counts become too large for computer storage. In this paper, a method of parameter estimation is described that does not require the internal representation of all observed and expected counts, but rather uses only the observed and expected sufficient statistics of the parameter estimates, which are the marginal tables corresponding to the model terms only. The computational problem boils down to computation of the expected sufficient statistics which, in its raw form, amounts to summation of a very large number of expected counts. However, it is shown that, depending on the structure of the model, the number of computations can be reduced considerably by making use of the distributive law. As a result, simpler models may be computed much more efficiently in terms of both storage and processing times.
Original languageUndefined
Place of PublicationEnschede, the Netherlands
PublisherUniversity of Twente, Faculty Educational Science and Technology
Number of pages49
Publication statusPublished - 1987

Publication series

NameOMD research report
PublisherUniversity of Twente, Faculty of Educational Science and Technology
No.87-5

Keywords

  • Latent Trait Theory
  • Linear Programing
  • Computer Assisted Testing
  • Computer Simulation
  • Mathematical Models
  • Estimation (Mathematics)
  • Sample Size
  • Equations (Mathematics)
  • IR-104193
  • Computer Software

Cite this

Kelderman, H. (1987). Estimating quasi-loglinear models for a Rasch table if the numbers of items is large. (OMD research report; No. 87-5). Enschede, the Netherlands: University of Twente, Faculty Educational Science and Technology.
Kelderman, Henk. / Estimating quasi-loglinear models for a Rasch table if the numbers of items is large. Enschede, the Netherlands : University of Twente, Faculty Educational Science and Technology, 1987. 49 p. (OMD research report; 87-5).
@book{da9bd9109c6a4e5395dc7864a7dda03d,
title = "Estimating quasi-loglinear models for a Rasch table if the numbers of items is large",
abstract = "The Rasch Model and various extensions of this model can be formulated as a quasi loglinear model for the incomplete subgroup x score x item response 1 x ... x item response k contingency table. By comparing various loglinear models, specific deviations of the Rasch model can be tested. Parameter estimates can be computed using programs such as GLIM, ECTA, and MULTIQUAL, but this becomes impractical if the number of items is large. In that case, the tables of observed and expected counts become too large for computer storage. In this paper, a method of parameter estimation is described that does not require the internal representation of all observed and expected counts, but rather uses only the observed and expected sufficient statistics of the parameter estimates, which are the marginal tables corresponding to the model terms only. The computational problem boils down to computation of the expected sufficient statistics which, in its raw form, amounts to summation of a very large number of expected counts. However, it is shown that, depending on the structure of the model, the number of computations can be reduced considerably by making use of the distributive law. As a result, simpler models may be computed much more efficiently in terms of both storage and processing times.",
keywords = "Latent Trait Theory, Linear Programing, Computer Assisted Testing, Computer Simulation, Mathematical Models, Estimation (Mathematics), Sample Size, Equations (Mathematics), IR-104193, Computer Software",
author = "Henk Kelderman",
year = "1987",
language = "Undefined",
series = "OMD research report",
publisher = "University of Twente, Faculty Educational Science and Technology",
number = "87-5",

}

Kelderman, H 1987, Estimating quasi-loglinear models for a Rasch table if the numbers of items is large. OMD research report, no. 87-5, University of Twente, Faculty Educational Science and Technology, Enschede, the Netherlands.

Estimating quasi-loglinear models for a Rasch table if the numbers of items is large. / Kelderman, Henk.

Enschede, the Netherlands : University of Twente, Faculty Educational Science and Technology, 1987. 49 p. (OMD research report; No. 87-5).

Research output: Book/ReportReportOther research output

TY - BOOK

T1 - Estimating quasi-loglinear models for a Rasch table if the numbers of items is large

AU - Kelderman, Henk

PY - 1987

Y1 - 1987

N2 - The Rasch Model and various extensions of this model can be formulated as a quasi loglinear model for the incomplete subgroup x score x item response 1 x ... x item response k contingency table. By comparing various loglinear models, specific deviations of the Rasch model can be tested. Parameter estimates can be computed using programs such as GLIM, ECTA, and MULTIQUAL, but this becomes impractical if the number of items is large. In that case, the tables of observed and expected counts become too large for computer storage. In this paper, a method of parameter estimation is described that does not require the internal representation of all observed and expected counts, but rather uses only the observed and expected sufficient statistics of the parameter estimates, which are the marginal tables corresponding to the model terms only. The computational problem boils down to computation of the expected sufficient statistics which, in its raw form, amounts to summation of a very large number of expected counts. However, it is shown that, depending on the structure of the model, the number of computations can be reduced considerably by making use of the distributive law. As a result, simpler models may be computed much more efficiently in terms of both storage and processing times.

AB - The Rasch Model and various extensions of this model can be formulated as a quasi loglinear model for the incomplete subgroup x score x item response 1 x ... x item response k contingency table. By comparing various loglinear models, specific deviations of the Rasch model can be tested. Parameter estimates can be computed using programs such as GLIM, ECTA, and MULTIQUAL, but this becomes impractical if the number of items is large. In that case, the tables of observed and expected counts become too large for computer storage. In this paper, a method of parameter estimation is described that does not require the internal representation of all observed and expected counts, but rather uses only the observed and expected sufficient statistics of the parameter estimates, which are the marginal tables corresponding to the model terms only. The computational problem boils down to computation of the expected sufficient statistics which, in its raw form, amounts to summation of a very large number of expected counts. However, it is shown that, depending on the structure of the model, the number of computations can be reduced considerably by making use of the distributive law. As a result, simpler models may be computed much more efficiently in terms of both storage and processing times.

KW - Latent Trait Theory

KW - Linear Programing

KW - Computer Assisted Testing

KW - Computer Simulation

KW - Mathematical Models

KW - Estimation (Mathematics)

KW - Sample Size

KW - Equations (Mathematics)

KW - IR-104193

KW - Computer Software

M3 - Report

T3 - OMD research report

BT - Estimating quasi-loglinear models for a Rasch table if the numbers of items is large

PB - University of Twente, Faculty Educational Science and Technology

CY - Enschede, the Netherlands

ER -

Kelderman H. Estimating quasi-loglinear models for a Rasch table if the numbers of items is large. Enschede, the Netherlands: University of Twente, Faculty Educational Science and Technology, 1987. 49 p. (OMD research report; 87-5).