Causal graphs of the mediation models. A, Traditional mediation analysis where the exposure influences the biomarkers. B, Latent-variable mediation analysis where the exposure influences a set of q latent, or unmeasured, factors and those factors influence both the biomarkers and the outcome. To simplify the figure, we highlight the arrows and notation for only a single factor. In the sparse scenario, we expect most effects to be 0 (i.e., λ, βEY, and βFY, are usually 0). We define the p × q matrix, Λ, so that the m, jth entry is λmj