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The problem of testing the intercept and slope parameters of doubly multivariate linear models with site-dependent covariates using Rao's score test (RST) is studied. The RST statistic is developed for a block exchangeable covariance structure on the error vector under the assumption of multivariate normality. We compare our developed RST statistic with the likelihood ratio test (LRT) statistic. Monte Carlo simulations indicate that the RST statistic is much more accurate than its counterpart LRT statistic and it takes significantly less computation time than the LRT statistic. The proposed method is illustrated with an example of multiple response variables measured on multiple trees in a single plot in an agricultural study.

Doubly multivariate linear models with block exchangeable distributed errors and site-dependent covariates