| Hypothesis testing problems for random-effects in some multivariate mixed-effects models are considered. In particular, models for comparison of two independent groups under the assumption of a common error covariance matrix are considered. Two inference problems are addressed; (i) testing the equality of the random-effects covariance matrices, and (ii) testing whether the random-effects covariance matrices are both equal to zero. An approximate test for the former hypothesis is developed using a multivariate extension of the Satterthwaite approximation. In the univariate case, a test is also developed based on the idea of a generalized p-value. Performance of the tests is numerically investigated and it is noted that the Satterthwaite approximation can be unsatisfactory, whereas the generalized p-value test exhibits satisfactory performance. For testing the hypothesis in (ii), two tests are developed: a test motivated by the Wilks' Λ criterion, and a second test motivated by the idea of a locally best invariant test. The percentiles required to carry out the test have to be numerically obtained. For the problems addressed, likelihood ratio tests are difficult to compute and implement. The proposed tests are computationally straightforward. The test procedures are illustrated with two relevant examples.;Next, sample size determination methodologies for three-level linear mixed-effects model and two-level mixed-effects logistic regression models for the analysis of longitudinal data are considered. Closed form solutions for determining sample size for a three-level linear mixed-effects model when randomization is performed at the subject level and center level are presented. The sample size formulas allow for unequal allocation proportion between treatments and different attrition rates between groups and at different time-points. For two-level mixed-effects logistic regression models, iterative method for sample size determination and power analysis is provided. The properties of the methods were studied via simulation. The methods are illustrated with relevant examples. |
