A robust approach to joint modeling of mean and scale covariance for longitudinal data

Lin, Tsung‐I; Wang, Yun-Jen

doi:10.1016/j.jspi.2009.02.008

Cited by 19 publications

(18 citation statements)

References 25 publications

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“…(4), is the first place where this problem was encountered and not addressed properly. Another source is Lin and Wang (2009) and the references therein. For ease of reference we call such a method the naive method in what follows.…”

Section: The Incoherency Problem In Incomplete Longitudinal Datamentioning

confidence: 99%

“…This unconstrained reparameterization and its statistical interpretability makes it easy to incorporate covariates in covariance modeling and to cast the joint modeling of mean and covariance into the generalized linear model framework. The methodology has proved to be useful in recent literature; see for example, Pourahmadi and Daniels (2002), Pan and MacKenzie (2003), Ye and Pan (2006), Daniels (2006), Huang et al (2006), Levina et al (2008), Yap et al (2009), and Lin and Wang (2009).…”

Section: Introductionmentioning

confidence: 99%

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A cautionary note on generalized linear models for covariance of unbalanced longitudinal data

Huang

Chen

Maadooliat

et al. 2012

Journal of Statistical Planning and Inference

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Missing data in longitudinal studies can create enormous challenges in data analysis when coupled with the positive-definiteness constraint on a covariance matrix. For complete balanced data, the Cholesky decomposition of a covariance matrix makes it possible to remove the positive-definiteness constraint and use a generalized linear model setup to jointly model the mean and covariance using covariates (Pourahmadi, 2000). However, this approach may not be directly applicable when the longitudinal data are unbalanced, as coherent regression models for the dependence across all times and subjects may not exist. Within the existing generalized linear model framework, we show how to overcome this and other challenges by embedding the covariance matrix of the observed data for each subject in a larger covariance matrix and employing the familiar EM algorithm to compute the maximum likelihood estimates of the parameters and their standard errors. We illustrate and assess the methodology using real data sets and simulations.

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Section: The Incoherency Problem In Incomplete Longitudinal Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A cautionary note on generalized linear models for covariance of unbalanced longitudinal data

Huang

Chen

Maadooliat

et al. 2012

Journal of Statistical Planning and Inference

View full text Add to dashboard Cite

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“…In this situation, a number of authors have used the multivariate t-distribution for robust estimation of the parameters of general linear models (Zellner 1976, Lange et al 1989); Lin & Wang (2009) has used it for robust estimation under the M.CD decomposition. Robust estimation for linear mixed models using the multivariate t-distribution has been studied by Welsh & Richardson (1997) and Pinheiro et al (2001).…”

Section: MCD and Acd Of A Covariance Matrixmentioning

confidence: 99%

“…Following the general approach in Pourahmadi (2000), Lin & Wang (2009) we model µ i , L = (θ tj ) and D = diag(σ t ) as:…”

Section: MCD and Acd Of A Covariance Matrixmentioning

confidence: 99%

“…The correlation matrix itself might be of scientific interest (Diggle & Verbyla 1998) in which case it is desirable to develop a bona fide data-based framework for modeling correlation matrices following the familiar three stages of model formulation, estimation and diagnostics in the modeling process for the mean vector (McCullagh & Nelder 1989). Attempts to develop such methods have been made in recent years by Chiu et al (1996), Pourahmadi (1999Pourahmadi ( , 2000, Pan & MacKenzie (2003), Ye & Pan (2006), Lin & Wang (2009), Leng et al (2010) and references therein, using the spectral and Cholesky decompositions of covariance matrices, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Robust estimation of the correlation matrix of longitudinal data

2011

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We propose a double-robust procedure for modeling the correlation matrix of a longitudinal dataset. It is based on an alternative Cholesky decomposition of the form Σ = DLL D where D is a diagonal matrix proportional to the square roots of the diagonal entries of Σ and L is a unit lower-triangular matrix determining solely the correlation matrix. The first robustness is with respect to model misspecification for the innovation variances in D, and the second is robustness to outliers in the data. The latter is handled using heavy-tailed multivariate t-distributions with unknown degrees of freedom. We develop a Fisher scoring algorithm for computing the maximum likelihood estimator of the parameters when the nonredundant and unconstrained entries of (L, D) are modeled parsimoniously using covariates. We compare our results with those based on the modified Cholesky decomposition of the form LD 2 L using simulations and a real dataset.

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Bayesian modeling of location, scale, and shape parameters in skew‐normal regression models

Corrales

Cepeda-Cuervo

2021

Statistical Analysis

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In this paper, we propose Bayesian skew‐normal regression models where the location, scale and shape parameters follow (linear or nonlinear) regression structures, and the variable of interest follows the Azzalini skew‐normal distribution. A Bayesian method is developed to fit the proposed models, using working variables to build the kernel transition functions. To illustrate the performance of the proposed Bayesian method and application of the model to analyze statistical data, we present results of simulated studies and of the application to studies of forced displacement in Colombia.

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A robust approach to joint modeling of mean and scale covariance for longitudinal data

Cited by 19 publications

References 25 publications

A cautionary note on generalized linear models for covariance of unbalanced longitudinal data

A cautionary note on generalized linear models for covariance of unbalanced longitudinal data

Robust estimation of the correlation matrix of longitudinal data

Bayesian modeling of location, scale, and shape parameters in skew‐normal regression models

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