Properties of Item Response Models
Roderick P. McDonald · Psychology Press eBooks · 2013
A natural choice of φ would be, for example, the log-odds function of the mean of the item scores, as used in Table 4.1. This transforms a score confined between 0 and 1 to a measurement that, like a common factor/latent trait, may be unbounded. Because a formula score includes the simple sum score, we add the word formula to emphasize the generality of the concept. Where necessary to avoid confusion, henceforward we refer to the ordinary test score as the sum score. Any estimator of the factor attribute/latent trait from an examinee&s;s response pattern is a formula score, and in the last section of this chapter we see how to understand the nonlinear relation given by the test characteristic curve between the sum score measure of the trait in its bounded metric, and an estimator of the trait in the unbounded metric imposed by the choice of a (nonlinear) item response model.