Abstract
How critical is the concept of the latent trait to modern test theory? The appeal to some unobservable characteristic modulating response probability can lead to some confusion and misunderstanding among users of psychometric technology. This paper looks at a geometric formulation of item response theory that avoids the need to appeal to unobservables. It draws on concepts in differential geometry to represent the trait being measured as a differentiate manifold within the space of possible joint item response probabilities given conditional independence. The result is a manifest and in principle observable representation of the trait that is invariant under one to one transformations of trait scores. These concepts are illustrated by analyses of an actual test.
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