Title: A Maximum Entropy Framework for IRT-Modeling

Author: Georg Hosoya

Affiliation: Freie Universität Berlin

Abstract: Maximum entropy methods allow for modeling system states based on
observable data and prior information. In testing situations, the system
typically consists of testees, items and a response format. In this talk, a
framework is presented that allows for the derivation of a large Portion of
IRT- and especially Rasch models as special cases from a discrete maximum
entropy distribution by changing functions that describe the relevant system
properties of interest. The discrete base distribution belongs to the
exponential family and is closely related to the loglinear model and the
general model formulation by Rasch (1961). Some advantages of adopting the
framework are:  the underlying formalism of Rasch models is simplified, which
allows for the derivation of important properties, such as the gradient and
Hessian with relative ease , b) new models  may be generated by focussing on
relevant sufficient statistics and c) due to the generality of the approach,
implementation in computer software is simplified. Implementation
considerations with regard to estimating a latent trait distribution based on
maximum entropy priors in combination with MML will be discussed and
demonstrated in R.