Based on substantial prior research indicating that 1) substance dependence symptoms are unidimensional within each substance, and 2) multiple substances are indicators of a single latent trait of multi-substance dependence, we fit a hierarchical confirmatory factor model (depicted in Figure 1). Within this model, substance-specific dependence symptoms (along with ever use of the substance) were indicators of a factor specific to their respective substance (i.e., alcohol, marijuana, or cocaine). The estimation of a continuous factor model of symptoms, rather than restriction to dichotomous diagnoses, makes full use of the available information. Those substance-specific factors were in turn indicators of a higher-order multi-substance dependence factor. In modeling dichotomous substance criteria as indicators of a continuous latent trait, we estimate threshold parameters, in addition to the loading parameters estimated for both categorical and continuous indicators. Thresholds represent the standardized latent trait level (Z-score) at which the probability of an individual endorsing that criterion is 50%; therefore, higher thresholds represent less frequently endorsed criteria.
