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    Multilevel Model Selection: A Regularization Approach Incorporating Heredity Constraints

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    Genre
    Thesis/Dissertation
    Date
    2013
    Author
    Stone, Elizabeth Anne
    Advisor
    Izenman, Alan Julian
    Committee member
    Heiberger, Richard M., 1945-
    Zhao, Zhigen
    Mennis, Jeremy
    Department
    Statistics
    Subject
    Statistics
    Hierarchical Linear Model
    Mixed-effects Model
    Variable Selection
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/2466
    
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    DOI
    http://dx.doi.org/10.34944/dspace/2448
    Abstract
    This dissertation focuses on estimation and selection methods for a simple linear model with two levels of variation. This model provides a foundation for extensions to more levels. We propose new regularization criteria for model selection, subset selection, and variable selection in this context. Regularization is a penalized-estimation approach that shrinks the estimate and selects variables for structured data. This dissertation introduces a procedure (HM-ALASSO) that extends regularized multilevel-model estimation and selection to enforce principles of fixed heredity (e.g., including main effects when their interactions are included) and random heredity (e.g., including fixed effects when their random terms are included). The goals in developing this method were to create a procedure that provided reasonable estimates of all parameters, adhered to fixed and random heredity principles, resulted in a parsimonious model, was theoretically justifiable, and was able to be implemented and used in available software. The HM-ALASSO incorporates heredity-constrained selection directly into the estimation process. HM-ALASSO is shown to enjoy the properties of consistency, sparsity, and asymptotic normality. The ability of HM-ALASSO to produce quality estimates of the underlying parameters while adhering to heredity principles is demonstrated using simulated data. The performance of HM-ALASSO is illustrated using a subset of the High School and Beyond (HS&B) data set that includes math-achievement outcomes modeled via student- and school-level predictors. The HM-ALASSO framework is flexible enough that it can be adapted for various rule sets and parameterizations.
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