Eliptik Konturlu Dağılımlara Dayalı Çok Değişkenli Tekrarlı Ölçümlü Varyans Analizi

Abstract

Repeated measures data describe multiple measurements taken from the same experimental unit under different treatment conditions. In particular, researches with repeated measures data in various fields such as health and behavioral sciences, education, and psychology has an important role in applied statistics. The structure of dependency between different measurements taken from the same experimental unit appears as an issue that requires more attention in the analysis of repeated measures data and makes it more difficult than other statistical analyzes. There are many methods used to analyze the results of research designs planned with these measurements. The most important difference between these methods is the assumptions on which the models are based. By satisfying the assumptions that the models are based on among these methods, it is important to determine an appropriate method that can model the repeated measures data with the dependency structure. One of the most important assumptions needed by classical methods is the normality assumption. Many methods are valid under the assumption of normality. However, it is not always possible to hold this assumption in applications. For this reason, in the analysis of repeated measures data, different distributions are necessary that can provide flexibility beyond the normal distribution, especially in cases where the assumption of normality does not hold. In this study, it is proposed to use the Multivariate Laplace distribution by examining the multivariate variance analysis model (MANOVA), which is a frequently used method for analysis of multivariate repeated measures data under Elliptically Contoured distributions, which is an alternative distribution family, in cases where normality assumption does not hold. Under this distribution assumption, the parameter estimates for the MANOVA model are carried out with the Maximum Likelihood method and, test statistics based on these estimators are proposed. The EM algorithm is used for parameter estimates based on the Maximum Likelihood method. In addition, the use of Matrix Variate Laplace distribution is proposed for the analysis of repeated measures data from nested designs under different treatment conditions, and model parameter estimates based on this distribution are made with the Maximum Likelihood estimation method. The Euclidean distances are calculated between the true parameter values and the estimates. Additionally, the power values are calculated for the test statistics.