A Latent Ability Model for Count Data and Application to Processing Speed

A new family of item response theory models for count data, based on item characteristic curves (ICCs) of binary models, is presented. These models assume a Poisson distribution for the observed scores where the mean is given by the product of a speed parameter and an ICC, for example, the curve of the one- or two-parameter logistic model. Joint and marginal maximum likelihood parameter estimations are discussed and the proposed procedures are evaluated by computer simulation. As an application, item level data from a test measuring processing speed are analyzed and item fit and test information are explored.