To further investigate the nature of the relations between the ages of tobacco, alcohol, and cannabis initiation, two types of multivariate models were fit to the data: an independent pathway model (IPM; Figure 1) and a common pathway model (CPM; Figure 2). The IPM specifies common genetic, common shared environmental, and common unique environmental factors that load onto the ages of tobacco, alcohol, and cannabis initiation, as well as genetic and environmental factors specific to each substance. The CPM, by contrast, specifies that all common genetic and environmental factors are mediated through a latent phenotype (indicated here as “initiation”). In the IPM, the common genetic and environmental factors influencing an outcome are allowed to have different variances and different loadings. In the CPM, these factors have different variances, but their loadings are the same. The CPM has fewer parameters than the IPM and is considered more parsimonious than the IPM, if it fits as well to the data. Because the CPM is nested within the IPM, the fits of the two models can be formally compared. Two indices were used
