New approaches for examining associations with latent categorical variables: applications to substance abuse and aggression.

Assessments of substance use behaviors often include categorical variables that are frequently related to other measures using logistic regression or chi-square analysis. When the categorical variable is latent (e.g., extracted from a latent class analysis [LCA]), classification of observations is often used to create an observed nominal variable from the latent one for use in a subsequent analysis. However, recent simulation studies have found that this classical 3-step analysis championed by the pioneers of LCA produces underestimates of the associations of latent classes with other variables. Two preferable but underused alternatives for examining such linkages-each of which is most appropriate under certain conditions-are (a) 3-step analysis, which corrects the underestimation bias of the classical approach, and (b) 1-step analysis. The purpose of this article is to dissuade researchers from conducting classical 3-step analysis and to promote the use of the 2 newer approaches that are described and compared. In addition, the applications of these newer models-for use when the independent, the dependent, or both categorical variables are latent-are illustrated through substantive analyses relating classes of substance abusers to classes of intimate partner aggressors.