Title: Linear models for multivariate repeated measures data from a skew normal distribution
Authors: Anuradha Roy - The University of Texas at San Antonio (United States) [presenting]
Timothy Opheim - The University of Texas at San Antonio (United States)
Abstract: The theory of linear models is generalized for doubly multivariate data from matrix-variate normally distributed errors to matrix-variate skew normally distributed errors. In addition, we assume that the covariance matrix defining the location-scale matrix-variate skew normal distribution has a block compound symmetry structure. We derive the maximum likelihood estimators of the model's parameters, the Fisher information matrix for the direct, working, and centered parametrizations, and Rao's score tests and likelihood ratio tests for model building tests of hypotheses and a hypothesis test for the centered intercept. A profiling argument is used to reduce the dimensionality of the optimization method used to obtain the maximum likelihood estimators. Finally, we provide a real-world example to illustrate these derivations.