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

Henk Kelderman

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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 languageEnglish
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

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Keywords

  • Latent trait theory
  • Linear programming
  • Computer Assisted Testing
  • Computer simulation
  • Mathematical Models
  • Estimation (Mathematics)
  • Sample size
  • Equations (Mathematics)
  • 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.