Most genetic analyses of quantitative traits have focused on a single trait association analysis, analyzing each phenotype independently. Dependence relationship among genetic variants are classically measured using linkage disequilibrium. Directed graphical models and structural equations can be used as a tool to model the complex structures among phenotypes, risk factors, and genotypes, which are referred to as the genotype–phenotype networks. In the genotype–phenotype networks, the phenotype variables such as BMI, blood pressure, high-density lipoprotein and low-density lipoprotein, are endogenous variables, age, sex, race, environments, and genotypes are exogenous variables. The structural equation models (SEMs) are a powerful mathematic tool to describe such data generating mechanisms and infer causal relationships among the variables. The SEMs classify variables into two class variables: endogenous and exogenous variables. An essential issue for node-based joint estimation of multiple graphical models is how to define the penalty function.