Abstract
In this paper we reparameterize covariance structures in longitudinal data analysis through the modified Cholesky decomposition of itself. Based on this modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit lower triangular matrix involving moving average coefficients and a diagonal matrix involving innovation variances, which are modeled as linear functions of covariates. Then, we propose a penalized maximum likelihood method for variable selection in joint mean and covariance models based on this decomposition. Under certain regularity conditions, we establish the consistency and asymptotic normality of the penalized maximum likelihood estimators of parameters in the models. Simulation studies are undertaken to assess the finite sample performance of the proposed variable selection procedure.
Highlights
In recent years, the method of joint modeling of mean and covariance on the general linear model with multivariate normal errors, was heuristically introduced by Pourahmadi [1,2]
In this paper we reparameterize covariance structures in longitudinal data analysis through the modified Cholesky decomposition of itself. Based on this modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit lower triangular matrix involving moving average coefficients and a diagonal matrix involving innovation variances, which are modeled as linear functions of covariates
We propose a penalized maximum likelihood method for variable selection in joint mean and covariance models based on this decomposition
Summary
The method of joint modeling of mean and covariance on the general linear model with multivariate normal errors, was heuristically introduced by Pourahmadi [1,2]. Rothman et al [6] proposed a new regression interpretation of the Cholesky factor of the covariance matrix by parameterizing itself and guaranteed the positivedefiniteness of the estimated covariance at no additional computational cost Based on this decomposition [6], Zhang and Leng [7] proposed efficient maximum likelihood estimates for joint mean-covariance analysis. Efficient penalized likelihood based method to select important explanatory variables that make a significant contribution to the joint modelling of mean and covariance structures for longitudinal data. Our method can select significant variables and obtain the parameter estimators simultaneously in the joint modelling of mean and covariance structures for longitudinal data, that implies that our method can avoid the heavy computational burden.
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