A Random-Coefficients Analysis with a Multivariate Random-Coefficients Linear Model

Random-coefficients linear models can be considered as a particular case of linear mixed models. Different sources of variation are treated by random effects, which depend on some specific model design matrices. A redundancy analysis of estimates of the multivariate random effects may be able to capture the leading contribution to the covariance between the observed responses and the model covariates. We introduce the random effects of reduced space by a weighted least-squares closed-form solution, starting from the standardized multivariate best linear predictors. The application shows the effect of the linear dependence of the random effects in the space of the model covariates.