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Bowling Green State University

1. Yousef, Mohammed A. Two-Stage SCAD Lasso for Linear Mixed Model Selection.

Degree: PhD, Statistics, 2019, Bowling Green State University

Linear regression model is the classical approach to explain the relationship between the response variable (dependent) and predictors (independent). However, when the number of predictors in the data increases, the likelihood of the correlation between predictors also increases, which is problematic. To avoid that, the linear mixed effects model was proposed which consists of a fixed effects term and a random effects term. The fixed effects term represents the traditional linear regression coefficients, and the random effects term represents the values that are drawn randomly from the population. Thus, the linear mixed model allows us to represent the mean as well as the covariance structure of the data in a single model.When the fixed and random effects terms increase in their dimensions, selection as appropriate model, which is the optimum fit, becomes increasingly difficult. Due to this natural complexity inherent in the linear mixed model, in this dissertation we propose a two-stage method for selecting fixed and random effects terms. In the first stage, we select the most significant fixed effects in the model based on the conditional distribution of the response variable given the random effects. This is achieved by minimizing the penalized least square estimator with a SCAD Lasso penalty term. We used the Newton-Raphson optimization algorithm to implement the parameter estimations. In this process, the coefficients of the unimportant predictors shrink towards exactly zero, thus eliminating the noise from the model. Subsequently, in the second stage we choose the most important random effects by maximizing the penalized profile log-likelihood function. This maximization is achieved using the Newton-Raphson optimization algorithm. As in the first stage, the penalty term appended is SCAD Lasso. Unlike the fixed effects, the random effects are drawn randomly from the population; hence, they need to be predicted. This prediction is done by estimating the diagonal elements (variances) of the covariance structure of the random effects. Note that during this step, for all random effects that are unimportant, the corresponding variance components will shrink to exactly zero (similar to the shrinking of fixed effects parameters in the first stage). This is how noise is eliminated from the model while retaining only significant effects. Hence, the selection of the random effects is completed.In both stages of the proposed approach, it is shown that the selection of the effects through elimination is done with the probability tending to one. It is indicative that the proposed method surely identifies all true effects, fixed as well as random. Also, it is shown that the proposed method satisfies the oracle properties, namely asymptotic normality and sparsity. At the end of these two stages, we have the optimal linear mixed model which can be readily applied to correlated data. To test the overall effectiveness of the proposed approach, four simulation studies are conducted. Each scenario has a different number of… Advisors/Committee Members: Shang, Junfeng (Advisor).

Subjects/Keywords: Statistics; Mixed model selection; SCAD Lasso; Linear mixed model; Penalized model selection; two-stage model selection

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APA (6th Edition):

Yousef, M. A. (2019). Two-Stage SCAD Lasso for Linear Mixed Model Selection. (Doctoral Dissertation). Bowling Green State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1558431514460879

Chicago Manual of Style (16th Edition):

Yousef, Mohammed A. “Two-Stage SCAD Lasso for Linear Mixed Model Selection.” 2019. Doctoral Dissertation, Bowling Green State University. Accessed August 24, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1558431514460879.

MLA Handbook (7th Edition):

Yousef, Mohammed A. “Two-Stage SCAD Lasso for Linear Mixed Model Selection.” 2019. Web. 24 Aug 2019.

Vancouver:

Yousef MA. Two-Stage SCAD Lasso for Linear Mixed Model Selection. [Internet] [Doctoral dissertation]. Bowling Green State University; 2019. [cited 2019 Aug 24]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1558431514460879.

Council of Science Editors:

Yousef MA. Two-Stage SCAD Lasso for Linear Mixed Model Selection. [Doctoral Dissertation]. Bowling Green State University; 2019. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1558431514460879

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