Psychometrika

, Volume 53, Issue 4, pp 553–562

Consistent estimation in the rasch model based on nonparametric margins

  • Dean Follmann
Article

DOI: 10.1007/BF02294407

Cite this article as:
Follmann, D. Psychometrika (1988) 53: 553. doi:10.1007/BF02294407

Abstract

Consider the class of two parameter marginal logistic (Rasch) models, for a test ofm 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 (whenm 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.

Key words

nonparametricEM algorithmconsistencyidentifiabilitymarginal logistic modellatent abilityitem analysisRasch model

Copyright information

© The Psychometric Society 1988

Authors and Affiliations

  • Dean Follmann
    • 1
  1. 1.National Heart, Lung, and Blood Institute Biostatistics Research BranchUSA