Seminars

General Departmental Seminar Series

On the Identifiability of Nonparametric Item Response Models

Jeff Douglas, Department of Biostatistics & Medical Informatics
University of Wisconsin

Friday, Sep 29, 2000, 12:00-1:00 pm

G5/136-142 Clinical Science Center
600 Highland Avenue

ABSTRACT

The identifiability of item response models with nonparametrically specified item characteristic curves is considered. Strict identifiability is achieved, with a fixed latent trait distribution, when only a single set of item characteristic curves can possibly generate the manifest distribution of the item responses. When item characteristic curves are allowed to live in a very general class, this property cannot be achieved. However, for assessments with many items, it is shown that all models for the manifest distribution have item characteristic curves that are very near one another and pointwise differences between them converge to zero at all values of the latent trait as the number of items increases. An upper bound for the rate at which this convergence takes place is given. The main result provides theoretical support to the practice of nonparametric item response modeling, by showing that models for long assessments have the property of asymptotic identifiability.

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