Abstract

Commonly applied item response theory (IRT) measurement models stipulate a single continuous latent variable (typically labeled “θ”) to represent individual differences on a psychological construct. For example, Equation 2.1 is the item response curve for the commonly applied two-parameter logistic model (2PL) for dichotomous item responses, where α_i is an item slope, β_i is an item location, θ is a continuous latent variable, and 1.7 is a scaling factor that makes the value of the item slope parameter in logistic models comparable to a normal-ogive model. This scaling is important for researchers who wish to link IRT parameters with factor analytic results.