Abstract
This paper proposes a new type of latent class analysis, joint latent class analysis (JLCA), which provides a set of principles for the systematic identification of the subsets of joint patterns for multiple discrete latent variables. Inferences about the parameters are obtained by a hybrid method of EM and Newton-Raphson algorithms. We apply JLCA in an investigation of adolescent violent behavior and drug-using behaviors. The data are from 4,957 male high-school students who participated in the Youth Risk Behavior Surveillance System 2015. The JLCA approach identifies the different joint patterns of four latent variables: violent behavior, alcohol consumption, tobacco cigarette smoking, and other drug use. The JLCA uncovers four common violent behaviors and three representative behavioral patterns for each of three other latent variables. In addition, the JLCA supports three common joint classes, representing the most probable simultaneous patterns for being violent and being a drug user among adolescent males.