Hypothesis testing via residuals in two GMANOVA models

Statistics for testing di®erent hypotheses in the Growth and Extended Growth Curve models are proposed. The tests are constructed using the restricted maximum likelihood approach followed by an estimated likelihood ratio. They are all functions of the residuals in the respec- tive models. This property makes them more reasonable and natural and gives the advantage of being easy to apply. Moreover, the tests have resemblance with the Lawley-Hotelling's trace test for the classical MANOVA model. We interpret the tests in accordance with the interpretation of the residuals of the models. We also show that the distribution of the tests under the corresponding null hypotheses does not depend on the unknown covariance matrix. Conditional and unconditional expectations for the tests are given