Part of this research is made possible by a pre-doctoral advanced quantitative methodology training grant (R305B080016) from the Institute of Education Sciences, a statistical methodology grant from the Institute of Education Sciences (R305D100039), and a grant from the National Institute on Drug Abuse (R01DA026943). The author is enormously grateful to Drs. Darren DeWalt, Susan Ennett, Robert Gibbons, Anthony Lehman, and David Thissen for their permission to use the data sets for numerical illustrations. Data collection for the Context project was supported by a grant from the National Institute on Drug Abuse (R01DA13459). The development of the Pediatric Asthma Impact Scale was funded by National Institute of Arthritis And Musculoskeletal and Skin Diseases (1U01AR052181-01). The development of IRTPRO was supported by the National Cancer Institute in the form of an SBIR contract (#HHSN-2612007-00013C) awarded to Scientific Software International. The views expressed in this paper are the author’s alone and do not reflect the views and policies of the funding agencies or grantees.