Accumulating evidence suggests that the Diagnostic and Statistical Manual of Mental Disorders (DSM) diagnostic criteria for cannabis abuse and dependence are best represented by a single underlying factor. However, it remains possible that models with additional factors, or latent class models or hybrid models, may better explain the data. Using structured interviews, 626 adult male and female twins provided complete data on symptoms of cannabis abuse and dependence, plus a craving criterion. We compared latent factor analysis, latent class analysis, and factor mixture modeling using normal theory marginal maximum likelihood for ordinal data. Our aim was to derive a parsimonious, best-fitting cannabis use disorder (CUD) phenotype based on DSM-IV criteria and determine whether DSM-5 craving loads onto a general factor. When compared with latent class and mixture models, factor models provided a better fit to the data. When conditioned on initiation and cannabis use, the association between criteria for abuse, dependence, withdrawal, and craving were best explained by two correlated latent factors for males and females: a general risk factor to CUD and a factor capturing the symptoms of social and occupational impairment as a consequence of frequent use. Secondary analyses revealed a modest increase in the prevalence of DSM-5 CUD compared with DSM-IV cannabis abuse or dependence. It is concluded that, in addition to a general factor with loadings on cannabis use and symptoms of abuse, dependence, withdrawal, and craving, a second clinically relevant factor defined by features of social and occupational impairment was also found for frequent cannabis use.