AbstractIn genome-wide mixed model association analysis, we stratified the genomic mixed model into two hierarchies to estimate genomic breeding values (GBVs) using the genomic best linear unbiased prediction and statistically infer the association of GBVs with each SNP using the generalized least square. The hierarchical mixed model (Hi-LMM) can correct confounders effectively with polygenic effects as residuals for association tests, preventing potential false-negative errors produced with genome-wide rapid association using mixed model and regression or an efficient mixed-model association expedited (EMMAX). Meanwhile, the Hi-LMM performs the same statistical power as the exact mixed model association and the same computing efficiency as EMMAX. When the GBVs have been estimated precisely, the Hi-LMM can detect more quantitative trait nucleotides (QTNs) than existing methods. Especially under the Hi-LMM framework, joint association analysis can be made straightforward to improve the statistical power of detecting QTNs.