Maximum Likelihood Estimators in Growth Curve Model with Monotone Missing Data

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.

KEY WORDS AND PHRASES:

• Growth curve model
• maximum likelihood estimator
• monotone missing data

Acknowledgments

The authors would like to thank the referee and the Editor for helpful comments.

Additional information

Funding

The first and second authors’ research is partly supported by a Grant-in-Aid for Young Scientists (Japan Society for the Promotion of Science [JSPS] KAKENHI Grant Number JP19K20225) and a Grant-in-Aid for Scientific Research (C) (JSPS KAKENHI Grant Number JP17K00058), respectively. The third author’s research is partially supported by the Ministry of Education, Science, Sports, and Culture, a Grant-in-Aid for Scientific Research (C) (JSPS KAKENHI Grant Number JP16K00047), 2016–2018.