AIC for Growth Curve Model with Monotone Missing Data

Abstract

In this article, we consider an AIC for a one-sample version of the growth curve model when the dataset has a monotone pattern of missing observations. It is well known that the AIC can be regarded as an approximately unbiased estimator of the AIC-type risk defined by the expected $(-2)\hspace{0.17em}\text{log}\hspace{0.17em}$-predictive likelihood. Here, the likelihood is based on the observed data. First, when the covariance matrix is known, we derive an AIC, which is an exact unbiased estimator of the AIC-type risk function. Next, when the covariance matrix is unknown, we derive a conventional AIC using the estimators based on the complete data set only. Finally, a numerical example is presented to illustrate our model selection procedure.

KEYWORDS AND PHRASES:

• AIC-type risk
• maximum likelihood estimator
• model selection; quasi MLE

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 (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.