Mixed Effects Modeling and Correlation Structure Selection for High Dimensional Correlated Data

Conditional score;Generalized estimating equation;Penalized\rquasi-likelihood;Quadratic inference function;Random-effects model;Generalized information criterion;Longitudinal data;Oracle property;Penalized estimating functions;SCAD penalty;Spatial data;Smoothly Clipped Absolute Deviation (SCAD)

Wang, Peng

关键词: Conditional score;    Generalized estimating equation;    Penalized\rquasi-likelihood;    Quadratic inference function;    Random-effects model;    Generalized information criterion;    Longitudinal data;    Oracle property;    Penalized estimating functions;    SCAD penalty;    Spatial data;    Smoothly Clipped Absolute Deviation (SCAD);   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/26016/Wang_Peng.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Longitudinal data arise frequently in many studies wheremeasurements are obtained from a subject repeatedly over time.Consequently, measurements within a subject are correlated. We address two rather important but challenging issues in this thesis: mixed-effect modeling with unspecified random effects and correlation structure selection for high-dimensional data.In longitudinal studies, mixed-effects models are important for addressingsubject-specific effects. However, most existing approachesassumenormal distributions for the random effects, which could affect the bias and efficiency of the fixed-effects estimators.Even in the cases where the estimation of the fixed effects is robust against a misspecified distribution of the random effects, theinference based on the random effects could be invalid.We propose a new approach to estimatefixed and random effects using conditional quadratic inferencefunctions. The new approach does not require any specification of thelikelihood functions. It canalso accommodate serial correlation between observations within the same cluster,in addition to mixed-effectsmodeling. Other advantages include notrequiring the estimation of the unknown variance components associatedwith the random effects, or the nuisance parameters associated with the workingcorrelations. Real data examples and simulations are used tocompare the new approach with the penalized quasi-likelihoodapproach, {and SAS the GLIMMIX and nonlinear mixed effects model (NLMIXED) procedures.}Model selection of correlation structure for non-normal correlated datais very challenging when the cluster size increases with the sample size, because of the high dimensional correlation parameters involved and%due to lack ofthe likelihood function for non-normal correlated data.% andwhen the cluster size diverges as the sample size increases. However, identifying the correct correlation structure can improve estimation efficiency and the power of tests for correlated data. We propose to approximate the inverse of the empirical correlation matrix using a linear combination of candidate basis matrices, and select the correlation structure by identifying non-zero coefficients of the basis matrices. This iscarried out by minimizingpenalized estimating functions, which balances the complexity and informativeness of modeling for the correlation matrix. The new approach does not require estimating each entry of the correlation matrix, northe specification of the likelihood function, andcan effectively handle non-normal correlated data. Asymptotic theory on model selection consistency and oracle properties are established in the framework of diverging cluster size of correlated data, where the derivation of the asymptotic results is challenging. Our numerical studiesindicate that even when the cluster size is very large, the correlation structure can be identified effectively for both normal responses and binary responses.