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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

URL: http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1558431514460879

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 (6^{th} 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 (16^{th} 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 (7^{th} 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