title: Diagnostics for the multivariate linear model analysis of 2 x 2 crossover designs.
abstract: 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.
authors.affiliation: Department of Biometry and Genetics, Louisiana State University Medical Center, New Orleans 70112.
authors.forename: X
authors.initials: X
authors.lastname: Xie
authors.forename: W D
authors.initials: WD
authors.lastname: Johnson
mesh_terms: D001702:Biopharmaceutics; D018592:Cross-Over Studies; D016014:Linear Models; D008433:Mathematics; D015999:Multivariate Analysis; D009716:Numerical Analysis, Computer-Assisted; D012107:Research Design / Q000706:statistics & numerical data