Teacher’s Corner: Negative Information and The Three-Parameter Logistic Model

Abstract

The 3-parameter logistic model is commonly used to describe the relationship among an unobserved latent trait (ability), unobserved item properties, and an observed binary outcome. We show that for certain values of the item properties and latent ability, the observed information about ability contained in the binary response is negative. This result has implications for maximization procedures, such as Newton-Raphson; approximate sampling methods, such as the Metropolis-Hastings algorithm; and Bayesian adaptive testing. All of these typically utilize the observed information. This result is contrasted with the fact that observed negative information does not occur in the limiting case with no guessing (2-parameter logistic model). The probability of negative information is expressed by a simple formula. This research extends the work of Samejima (1973) and Yen, Burket, and Sykes (1991).