, Volume 53, Issue 4, pp 553-562

First online:

Consistent estimation in the rasch model based on nonparametric margins

  • Dean FollmannAffiliated withNational Heart, Lung, and Blood Institute Biostatistics Research Branch

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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

nonparametric EM algorithm consistency identifiability marginal logistic model latent ability item analysis Rasch model