Hierarchical Generalized Linear Mixed Model for Genome-wide Association Analysis

In genome-wide association analysis (GWAS) for binary traits, we stratified the genomic generalized linear mixed model (GLMM) into two hierarchies—the GLMM regarding genomic breeding values (GBVs) and a generalized linear regression of the normally distributed GBVs to the tested marker effects. In the first hierarchy, the GBVs were predicted by solving for the genomic best linear unbiased prediction for GLMM with the estimated variance components or genomic heritability in advance, and in the second hierarchy, association tests were performed using the generalized least square (GLS) method for the GBVs. Like the Hi-LMM for regular quantitative traits, the so-called Hi-GLMM method exhibited higher statistical power to detect quantitative trait nucleotides (QTNs) with better genomic control for complex population structure than existing methods, especially when the GBVs were estimated precisely and using joint association analysis for QTN candidates obtained from a test at once. Application of the Hi-GLMM to re-analyze maize kernel colors and six human diseases illustrated its advantage over existing GLMM-based association methods in terms of computing efficiency and statistical power. ### Competing Interest Statement The authors have declared no competing interest.