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In genome-wide association studies (GWAS), penalization is an importantapproach for identifying genetic markers associated with trait while mixedmodel is successful in accounting for a complicated dependence structure amongsamples. Therefore, penalized linear mixed model is a tool that combines theadvantages of penalization approach and linear mixed model. In this study, aGWAS with multiple highly correlated traits is analyzed. For GWAS with multiplequantitative traits that are highly correlated, the analysis using traitsmarginally inevitably lose some essential information among multiple traits. Wepropose a penalized-MTMM, a penalized multivariate linear mixed model thatallows both the within-trait and between-trait variance componentssimultaneously for multiple traits. The proposed penalized-MTMM estimatesvariance components using an AI-REML method and conducts variable selection andpoint estimation simultaneously using group MCP and sparse group MCP. Bestlinear unbiased predictor (BLUP) is used to find predictive values and thePearson's correlations between predictive values and their correspondingobservations are used to evaluate prediction performance. Both prediction andselection performance of the proposed approach and its comparison with theuni-trait penalized-LMM are evaluated through simulation studies. We apply theproposed approach to a GWAS data from Genetic Analysis Workshop (GAW) 18.

A Penalized Multi-trait Mixed Model for Association Mapping in Pedigree-based GWAS