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Browsing by Subject "Multilevel model"
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Item Longitudinal regression of covariance matrix outcomes(Oxford, 2022-12-01) Zhao, Yi; Caffo, Brian S.; Luo, Xi; Alzheimer’s Disease Neuroimaging Initiative; Biostatistics and Health Data Science, School of MedicineIn this study, a longitudinal regression model for covariance matrix outcomes is introduced. The proposal considers a multilevel generalized linear model for regressing covariance matrices on (time-varying) predictors. This model simultaneously identifies covariate-associated components from covariance matrices, estimates regression coefficients, and captures the within-subject variation in the covariance matrices. Optimal estimators are proposed for both low-dimensional and high-dimensional cases by maximizing the (approximated) hierarchical-likelihood function. These estimators are proved to be asymptotically consistent, where the proposed covariance matrix estimator is the most efficient under the low-dimensional case and achieves the uniformly minimum quadratic loss among all linear combinations of the identity matrix and the sample covariance matrix under the high-dimensional case. Through extensive simulation studies, the proposed approach achieves good performance in identifying the covariate-related components and estimating the model parameters. Applying to a longitudinal resting-state functional magnetic resonance imaging data set from the Alzheimer’s Disease (AD) Neuroimaging Initiative, the proposed approach identifies brain networks that demonstrate the difference between males and females at different disease stages. The findings are in line with existing knowledge of AD and the method improves the statistical power over the analysis of cross-sectional data.Item The effect of missing levels of nesting in multilevel analysis(Korea Genome Organization, 2022) Park, Seho; Chung, Yujin; Biostatistics, School of Public HealthMultilevel analysis is an appropriate and powerful tool for analyzing hierarchical structure data widely applied from public health to genomic data. In practice, however, we may lose the information on multiple nesting levels in the multilevel analysis since data may fail to capture all levels of hierarchy, or the top or intermediate levels of hierarchy are ignored in the analysis. In this study, we consider a multilevel linear mixed effect model (LMM) with single imputation that can involve all data hierarchy levels in the presence of missing top or intermediate-level clusters. We evaluate and compare the performance of a multilevel LMM with single imputation with other models ignoring the data hierarchy or missing intermediate-level clusters. To this end, we applied a multilevel LMM with single imputation and other models to hierarchically structured cohort data with some intermediate levels missing and to simulated data with various cluster sizes and missing rates of intermediate-level clusters. A thorough simulation study demonstrated that an LMM with single imputation estimates fixed coefficients and variance components of a multilevel model more accurately than other models ignoring data hierarchy or missing clusters in terms of mean squared error and coverage probability. In particular, when models ignoring data hierarchy or missing clusters were applied, the variance components of random effects were overestimated. We observed similar results from the analysis of hierarchically structured cohort data.