Consistent estimation in the rasch model based on nonparametric margins
Received: 13 August 1986 Revised: 27 August 1987 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 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. Key words nonparametric EM algorithm consistency identifiability marginal logistic model latent ability item analysis Rasch model
This research was supported by NIMH traning grant, 2 T32 MH 15758-06 and by ONR contract N00014-84-K-0588. The author would like to thank Diane Lambert, John Rolph, and Stephen Fienberg for their assistance. Also, the comments of the referees helped to substantially improve the final version of this paper.
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