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A Penalized Approach to Mixed Model Selection Via Cross Validation

Xiong, Jingwei
http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1510965832174342

Abstract Details

2017, Doctor of Philosophy (Ph.D.), Bowling Green State University, Mathematics/Mathematical Statistics.
A linear mixed model is a useful technique to explain observations by regarding them as realizations of random variables, especially when repeated measurements are made to statistical units, such as longitudinal data. However, in practice, there are often too many potential factors considered affecting the observations, while actually, they are not. Therefore, statisticians have been trying to select significant factors out of all the potential factors, where we call the process model selection. Among those approaches for linear mixed model selection, penalized methods have been developed profoundly over the last several decades. In this dissertation, to solve the overfitting problem in most penalized methods and improve the selection accuracy, we mainly focus on a penalized approach via cross-validation. Unlike the existing methods using the whole data to fit and select models, we split the fitting process and selection into two stages. More specifically, an adaptive lasso penalized function is customized in the first stage and marginal BIC criterion is used in the second stage. We consider that the main advantage of our approach is to reduce the dependency between models construction and evaluation. Because of the complex structure of mixed models, we adopt a modified Cholesky decomposition to reparameterize the model, which in turn significantly reduces the dimension of the penalized function. Additionally, since random effects are missing, there is no closed form for the maximizer of the penalized function, thus we implement EM algorithm to obtain a full inference of parameters. Furthermore, due to the computation limit and moderately small samples in practice, some noisy factors may still remain in the model, which is particularly obvious for fixed effects. To eliminate the noisy factors, a likelihood ratio test is employed to screen the fixed effects. Regarding the overall process, we call it adaptive lasso via cross-validation. Additionally, we demonstrate that the proposed approach possesses selection and estimation consistency simultaneously. Moreover, simulation studies and real data examples are both provided to justify the method validity. At the very end, a brief conclusion is drawn and some possible further improvements are discussed.
Junfeng Shang (Advisor)
Angela Thomas (Other)
Hanfeng Chen (Committee Member)
John Chen (Committee Member)
95 p.
Statistics
linear mixed models; penalized approaches; variable selection; cross validation

Recommended Citations

Citations

  • Xiong, J. (2017). A Penalized Approach to Mixed Model Selection Via Cross Validation [Doctoral dissertation, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1510965832174342

    APA Style (7th edition)

  • Xiong, Jingwei. A Penalized Approach to Mixed Model Selection Via Cross Validation. 2017. Bowling Green State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1510965832174342.

    MLA Style (8th edition)

  • Xiong, Jingwei. "A Penalized Approach to Mixed Model Selection Via Cross Validation." Doctoral dissertation, Bowling Green State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1510965832174342

    Chicago Manual of Style (17th edition)

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This open access ETD is published by Bowling Green State University and OhioLINK.