Robust Inference for Multivariate Growth Curve Models and High-Dimensional Extensions

点击翻译按钮获取中文摘要

Background: ***Multivariate Growth Curve Model (GCM), also known as the Generalized Analysis of Variance (GMANOVA) model, is useful in the analysis of longitudinal data, growth curves as well as other response curves (eg. dose-response curves). The model arises when the mean is structured due to, for instance, time or dose dependency of the outcome of interest, which is often the case in applications involving longitudinal or dose-response data. Traditional methods for the GCM are developed under the assumption of normality. In practice, however, it is common to encounter outcomes with skewed distributions. A recent simulation study reveals that estimators derived under the normality assumption are sensitive to departure from normality, where the results show that the estimators are associated with increased bias and mean squared error (MSE), when used in the analysis of skewed data. ******Inference for the GCM is also based on the assumption of larger sample size (n) than the number of time points (p), where the covariance matrix is assumed to be positive definite. In high-dimensional data, however, p is often larger than n, leading to singularity of the sample covariance matrix, and hence traditional approaches do not work. Methods for handling high-dimensional data have been developed in recent years. Although these methods account for correlations among measurements taken across the different time points, the methods fail to account for time dependency, which often motivates longitudinal studies, where researchers are interested to determine the change over time. In previous work, we considered two approaches. The first approach involves a transformation to the MANOVA model followed by an empirical Bayes approach. The second method involves use of the Moore-Penrose generalized inverse. Although the approach using a transformation provided a framework for incorporating time dependency in the model, the method lacks statistical power and lead to estimators with increased bias and MSE. On the other hand, the method based on Moore-Penrose inverse provided increased power and precision; and the estimators are in general associated with a bias randomly distributed around zero. Nevertheless, the simulation results show that the optimallity of the estimators and the performance of the test declines near singularity (when n≈p). This proposal attempts to address the limitations of the previous method and provides improved inference for high-dimensional longitudinal data.******The overall objective of this proposal is to provide robust estimators for the parameters of the GCM and provide high-dimensional extensions******Specific Objectives are to *** 1) drive estimators for the model parameters of the GCM under multivariate skewed normal distribution *** 2) derive estimators for the extended GCM under multivariate skewed normal distribution *** 3) provide an optimal inference for the GCM under high-dimensional scenarios