Donald Hedeker, Robin Mermelstein, and Brian FlayHedeker, Mermelstein and Flay provide a cogent synopsis of Item Response Theory (IRT) models, also called latent trait models, have been extensively used in educational testing and psychological measurement. While an IRT model is essentially a mixed-effects regression model for longitudinal categorical data, use of IRT has been somewhat limited outside of education and psychology. In this chapter, the authors describe IRT models and some key developments in the IRT literature, and illustrate their application for intensive longitudinal data. In particular, they relate IRT models to mixed models and indicate how software for the latter can be used to estimate the IRT model parameters. Using Ecological Momentary Assessment (EMA) data from a study of adolescent smoking, they describe how IRT models can be used to address key questions in smoking research.