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An Approach to Estimation and Selection in Linear Mixed Models with Missing Data

Lee, Yi-Ching
http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1562754262770979

Abstract Details

2019, Doctor of Philosophy (Ph.D.), Bowling Green State University, Statistics.
In the case of analyzing multilevel, correlated, or longitudinal data, linear mixed models are often incorporated. Such models can be thought of an extension of linear models in the sense that the additional random components are introduced to capture the dependency in observations. In practice, missing data occur in many disciplines, especially in the area of longitudinal studies where observations are taken repeatedly over time on samples in an experiment. Our primary goal in the dissertation is to propose an approach to estimation and model selection in linear mixed models when missing data present. The dissertation pays particular attention to the multivariate normal models. With such models, we propose an approach that incorporates the missingness in an indicator matrix and develop likelihood-based estimators under two specific covariance structures: compound symmetric and first-order autoregressive (AR(1)). Distinguishing from the existing maximum likelihood estimation (MLE) that relies on Newton-Raphson (NR), Expectation-Maximization (EM), or Fisher algorithms for obtaining the final estimates, we implement matrix theories to circumvent the difficulties in the estimation process imposed by the inversion and the determinant of the variance-covariance matrix. Numerous simulations are conducted in evaluations of the proposed approach. For instance, in the study of the comparison between the proposed method and MLE, the former yields better estimates in the variance component with the compound symmetric covariance and presents remarkable improvements in estimating both the variance and the autocorrelation components in AR(1). In the study of investigating the model selection performance using the proposal estimation approach with the Schwarz Information Criterion (SIC) serving as the selection criterion, the simulation results demonstrate that the proposed approach to estimation performs effectively with a moderate amount of missing proportion regardless of the missing behaviors, missing completely at random (MCAR) or missing not at random (MNAR). Two real data applications are provided for revealing the performance of the proposed approach in practice. In evidence of the developed method, the conducted simulations, and the applications, we provide the concluding remarks and the future research directions as the closing of the dissertation.
Junfeng Shang, Ph.D. (Advisor)
Hanfeng Chen, Ph.D. (Committee Member)
John Chen, Ph.D. (Committee Member)
Jonathan Bostic, Ph.D. (Other)
143 p.
Statistics
linear mixed models; missing data; model slection in linear mixed models; estimation in linear mixed models

Recommended Citations

Citations

  • Lee, Y.-C. (2019). An Approach to Estimation and Selection in Linear Mixed Models with Missing Data [Doctoral dissertation, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1562754262770979

    APA Style (7th edition)

  • Lee, Yi-Ching. An Approach to Estimation and Selection in Linear Mixed Models with Missing Data. 2019. Bowling Green State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1562754262770979.

    MLA Style (8th edition)

  • Lee, Yi-Ching. "An Approach to Estimation and Selection in Linear Mixed Models with Missing Data." Doctoral dissertation, Bowling Green State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1562754262770979

    Chicago Manual of Style (17th edition)

bgsu1562754262770979
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© 2019, all rights reserved.
This open access ETD is published by Bowling Green State University and OhioLINK.