Diagnostics for the multivariate linear model analysis of 2 x 2 crossover designs

The multivariate linear model Y = X beta + epsilon is used to analyze data in 2 x 2 crossover designs with either univariate or multivariate response. Diagnostics are performed on estimating the effect of interest formulated as C beta U and on testing the general linear hypothesis C beta U = k. The multivariate Cook's distance is extended to be the influence measure by incorporating the contrast matrix C and the transformation matrix U, and magnitude of F(1)-F, the difference between the F approximation of a multivariate test statistic, is proposed as a measure to detect influential observations for testing the hypothesis C beta U = k. Both measures prove to be very useful because the diagnostics are now associated with estimating and testing effects of interest in the context of the experimental design.