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1 results

  • Consistent Estimation in the Rasch Model based on Nonparametric Margins

  • Dean Follmann
  • Journal:
    Psychometrika / Volume 53 / Issue 4 / December 1988
    Published online by Cambridge University Press:
    01 January 2025, pp. 553-562

  • Consider the class of two parameter marginal logistic (Rasch) models, for a test of m True-False items, where the latent ability is assumed to be bounded. Using results of Karlin and Studen, we show that this class of nonparametric marginal logistic (NML) models is equivalent to the class of marginal logistic models where the latent ability assumes at most (m + 2)/2 values. This equivalence has two implications. First, estimation for the NML model is accomplished by estimating the parameters of a discrete marginal logistic model. Second, consistency for the maximum likelihood estimates of the NML model can be shown (when m is odd) using the results of Kiefer and Wolfowitz. An example is presented which demonstrates the estimation strategy and contrasts the NML model with a normal marginal logistic model.