Using ASGSCA

The ASGSCA (Association Study using GSCA) package provides tools to model and test the associations between multiple genotypes and multiple traits, taking into account prior biological knowledge. Functional genomic regions, e.g., genes and clinical pathways, are incorporated in the model as latent variables that are not directly observed. See Romdhani et al. (2014) for details. The method is based on Generalized Structured Component Analysis (GSCA) (Hwang and Takane , 2004). GSCA is an approach to structural equation models (SEM) and thus constitutes two sub-models: measurement and structural models. The former specifies the relationships between observed variables (here genotypes and traits) and latent variables (here genes or more generally genomic regions and clinical pathways), whereas the structural model expresses the relationships between latent variables. Assume we have data on J candidate SNPs (X1, · · · , XJ) and K traits (XJ+1, · · · , XJ+K). Let I = J + K denote the total number of observed variables. Suppose that the J SNPs are mapped to G different genes or regions (γ1, · · · , γG) and the K traits are involved in T different clinical pathways (γG+1, · · · , γG+T ). The measurement model is given by