A Functional Approach to Modeling Test Data
The central problem in psychometric data analysis using item response theory is to model the response curve linking a level θ of ability and the probability of choosing a specific option on a particular item. Most approaches to this problem have assumed that the curve to be estimated is within a restricted class of functions defined by a specific mathematical model. The Rasch model or the three-parameter logistic model for binary data are best known examples. In this chapter, however, the aim is to estimate the response curve directly, thereby escaping the restrictions imposed by what can be achieved with a particular parametric family of curves. It will also be assumed that the responses to an item are polytomous, and can involve any number of options.
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