Testing equality of mean vectors in a one-way MANOVA with monotone missing data

ABSTRACT

In this study, testing the equality of mean vectors in a one-way multivariate analysis of variance (MANOVA) is considered when each dataset has a monotone pattern of missing observations. The likelihood ratio test (LRT) statistic in a one-way MANOVA with monotone missing data is given. Furthermore, the modified test (MT) statistic based on likelihood ratio (LR) and the modified LRT (MLRT) statistic with monotone missing data are proposed using the decomposition of the LR and an asymptotic expansion for each decomposed LR. The accuracy of the approximation for the Chi-square distribution is investigated using a Monte Carlo simulation. Finally, an example is given to illustrate the methods.

KEYWORDS:

• Asymptotic expansion
• Chi-square distribution
• Decomposition of likelihood ratio
• Maximum likelihood estimator
• Monte Carlo simulation.

Acknowledgments

The authors would like to thank two referees for their helpful comments and suggestions.

Funding

The first and second authors’ research was partly supported by a Grant-in-Aid for JSPS Fellows (15J00414) and a Grant-in-Aid for Scientific Research (C) (17K00058), respectively.