Browsing by Subject "Model Selection"

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    Adaptive model selection in linear mixed models.
    (2009-08) Zhang, Bo
    Linear mixed models are commonly used models in the analysis of correlated data, in which the observed data are grouped according to one or more clustering factors. The selection of covariates, the variance structure and the correlation structure is crucial to the accuracy of both estimation and prediction in linear mixed models. Information criteria such as Akaike's information criterion, Bayesian information criterion, and the risk inflation criterion are mostly applied to select linear mixed models. Most information criteria penalize an increase in the size of a model through a fixed penalization parameter. In this dissertation, we firstly derive the generalized degrees of freedom for linear mixed models. A resampling technique, data perturbation, is employed to estimate the generalized degrees of freedom of linear mixed models. Further, based upon the generalized degrees of freedom of linear mixed models, we develop an adaptive model selection procedure with a data-adaptive model complexity penalty for selecting linear mixed models. The asymptotic optimality of the adaptive model selection procedure in linear mixed models is shown over a class of information criteria. The performance of the adaptive model selection procedure in linear mixed models is studied by numerical simulations. Simulation results show that the adaptive model selection procedure outperforms information criteria such as Akaike's information criterion and Bayesian information criterion in selecting covariates, the variance structure and the correlation structure in linear mixed models. Finally, an application to diabetic retinopathy is examined.
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    Model selection with the linear mixed effects model for longitudinal data.
    (2010-05) Ryoo, Ji Hoon
    Model building or model selection with linear mixed models (LMM) is complicated by the presence of both fixed effects and random effects. The fixed effects structure and random effects structure are co-dependent, so selection of one influences the other. Most presentations of LMM in psychology and education are based on a multi-level or hierarchical approach in which the variance-covariance matrix of the random effects is assumed to be positive definite with non-zero values for the variances. When the number of fixed effects and random effects is not known, the predominant approach to model building is a step-up procedure in which one starts with a limited model (e.g., few fixed and random intercepts) and then additional fixed effects and random effects are added based on statistical tests. A procedure that has received less attention in psychology and education is top-down model building. In the top-down procedure, the initial model has a single random intercept but is loaded with fixed effects (also known as an ”over-elaborate” model). Based on the over-elaborate fixed effects model, the need for additional random effects is determined. Once the number of random effects is selected, the fixed effects are tested to see if any can be omitted from the model. There has been little if any examination of the ability of these procedures to identify a true population model (i.e., identifying a model that generated the data). The purpose of this dissertation is to examine the performance of the various model building procedures for exploratory longitudinal data analysis. Exploratory refers to the situation in which the correct number of fixed effects and random effects is unknown before the analysis.