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Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities

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The purpose of this paper is to introduce a new method for fitting item response theory models with the latent population distribution estimated from the data using splines. A spline-based density estimation system provides a flexible alternative to existing procedures that use a normal distribution, or a different functional form, for the population distribution. A simulation study shows that the new procedure is feasible in practice, and that when the latent distribution is not well approximated as normal, two-parameter logistic (2PL) item parameter estimates and expected a posteriori scores (EAPs) can be improved over what they would be with the normal model. An example with real data compares the new method and the extant empirical histogram approach.

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Correspondence to Carol M. Woods.

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Woods, C.M., Thissen, D. Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities. Psychometrika 71, 281 (2006). https://doi.org/10.1007/s11336-004-1175-8

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  • item response theory
  • marginal maximum likelihood
  • latent variable
  • population distribution
  • density estimation
  • splines