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

Abstract

The multivariate linear model 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 CβU and on testing the general linear hypothesis CβU = 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 , the difference between the F approximation of a multivariate test statistic, is proposed as a measure to detect influential observations for testing the hypothesis CβU = 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.

Keywords:

• Crossover design
• Multivariate linear model
• Multivariate Cook's distance
• Multivariate residual
• Bilinear form
• Influential observation