Semiparametric Mean–Covariance Regression Analysis for Longitudinal Data

Abstract

Efficient estimation of the regression coefficients in longitudinal data analysis requires a correct specification of the covariance structure. Existing approaches usually focus on modeling the mean with specification of certain covariance structures, which may lead to inefficient or biased estimators of parameters in the mean if misspecification occurs. In this paper, we propose a data-driven approach based on semiparametric regression models for the mean and the covariance simultaneously, motivated by the modified Cholesky decomposition. A regression spline based approach using generalized estimating

A Semiparametric Regression Model for Longitudinal Data with Non‐stationary Errors

“…This is also important due to the fact that misspecification of the error structure will resultant in inefficient estimation and uncorrect statistical inference. It should also be noted that the non-stationary error structure in (2) is essentially different from that of Leng et al (2010). Specifically, the number of autoregressive coefficient in Leng et al (2010), generated from Cholesky decomposition of covariance matrix, is T (T − 1)/2 with T = max(m i ) and too large to be estimated for large T , while that in our error structure is finite and usually small, no matter how large T is.…”

“…There was also a large literature for developing new models for characterizing the covariance structure, see for example, Pourahmadi (1999), Fan et al (2007), Wu & Pourahmadi (2003), Fan & Li (2004), Fan & Wu (2008), Leng et al (2010), Li (2011), Zhang & Leng (2012, Zhou & Qu (2012). A recent line of research for variable selection has also undergone rapid development, see e.g., Fan & Li (2001), Wang et al (2009, Ma et al (2013).…”

“…Specifically, the number of autoregressive coefficient in Leng et al (2010), generated from Cholesky decomposition of covariance matrix, is T (T − 1)/2 with T = max(m i ) and too large to be estimated for large T , while that in our error structure is finite and usually small, no matter how large T is. So, our method could be used to model the functional data sets as well, however, the method of Leng et al (2010) does not work for the the functional data sets.…”

“…, m i , and the total sample size is N = ∑ n i=1 m i . Model (2) allows more nonparametric covariates to be included than the partially linear structure of Leng et al (2010), and employs a non-stationary and time-adaptive autoregressive process for identifying the within-subject correlation of repeated measurements. We use Y i,j for denoting the jth measurement of the ith subject, X i,j = (1, X i,j,1 , .…”

Discrete Longitudinal Data Modeling with a Mean-Correlation Regression Approach

“…Zhang et al (2015) recently proposed models to investigate marginal variances and correlations from a geometric perspective. Other important works on joint modeling for continuous longitudinal data include Pan and Mackenzie (2003); Ye and Pan (2006); Pourahmadi (2007); Daniels and Pourahmadi (2009); Leng et al (2010); Xu and Mackenzie (2012).…”