Maximum Likelihood Estimators in Growth Curve Model with Monotone Missing Data

Abstract

Abstract This article focuses on the maximum likelihood estimators (MLEs) of the mean parameter vector and the covariance matrix in a one-sample version of the growth curve model when the dataset has a monotone missing pattern. First, a closed form is obtained for the MLE of the mean parameter vector when the covariance matrix is known. Similarly, it is obtained for the MLE of the covariance matrix when the mean parameter vector is known. The distributions of these estimators and their basic properties are also given. Then, considering that these expressions give the likelihood or determining equations, we propose an algorithm that includes an iterative procedure to obtain the MLEs when all the parameters are unknown. Further, a conventional estimator for the mean parameter vector is also proposed. Finally, a numerical example is given to illustrate our estimation procedure.