Inference in the Growth Curve Model under Multivariate Skew Normal Distribution

Abstract

Existing methods for estimating the parameters of the Growth Curve Model (GCM) rely on the assumption that the underlying distribution for the error terms is multivariate normal. However, we often come across skewed data in practical applications; and estimators developed under the normality assumption may not be valid in such situations. Simulation studies conducted in this paper, in fact, show that existing methods are sensitive to skewness, where normal based estimators are associated with increased bias and mean squared error (MSE), when the normality assumption is violated. Methods appropriate for skewed distributions are, therefore, required. In this paper, estimators for the mean and covariance matrices of the GCM under multivariate skew normal (MSN) distribution are proposed. An estimator for the additional skewness parameter of the MSN distribution is also provided. The estimators are derived using the expectation maximization (EM) algorithm and extensive simulations are performed to examine the performance of the estimators. Comparisons with existing estimators show that our estimators perform better than the existing estimators, when the underlying distribution is multivariate skew normal. Illustration using real data set is also provided.