An Explicit Mean-Covariance Parameterization for Multivariate Response Linear Regression

We develop a new method to fit the multivariate response linear regression model that exploits parametric link between coefficient matrix and error covariance matrix. Specifically, we assume correlations entries in random vector are proportional cosines of angles their corresponding columns, so as angle two columns decreases, correlation errors increases. highlight models under which this parameterization arises: latent variable reduced-rank errors-in-variables model. propose novel non-convex weighted residual sum squares criterion admits class penalized estimators. The optimization is solved with an accelerated proximal gradient descent algorithm. Our used study association microRNA expression cancer drug activity measured on NCI-60 cell lines. An R package implementing our method, MCMVR, available at github.com/ajmolstad/MCMVR.