On modelling mean-covariance structures in longitudinal studies

Pan, Jianxin; MacKenzie, Gilbert

doi:10.1093/biomet/90.1.239

Cited by 144 publications

(125 citation statements)

References 6 publications

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“…Pan & MacKenzie (2003) give an inter-dependent iteratively re-weighted least squares algorithm for computing the maximum likelihood estimates. Their algorithm is more general than Pourahmadi's procedure which is restricted to balanced longitudinal data.…”

Section: Augmented Regression Modelmentioning

confidence: 99%

“…(4) implies a direct search of the 3-dimensional joint model space which may be thought computationally expensive. However, a general procedure is required, because the simple regressogram-based model selection procedures proposed by Pourahmadi (1999) ignore the covariance structure between the parameters evident in the observed and expected information matrices (Pan & MacKenzie, 2003) and are therefore not optimal for model selection. Accordingly, to minimize computational labour we propose an efficient search strategy to identify the global optimum model.…”

Section: Augmented Regression Modelmentioning

confidence: 99%

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The Use of Score Tests for Inference on Variance Components

Verbeke¹,

Molenberghs²

2003

Biometrics

203

144

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Summary Whenever inference for variance components is required, the choice between one‐sided and two‐sided tests is crucial. This choice is usually driven by whether or not negative variance components are permitted. For two‐sided tests, classical inferential procedures can be followed, based on likelihood ratios, score statistics, or Wald statistics. For one‐sided tests, however, one‐sided test statistics need to be developed, and their null distribution derived. While this has received considerable attention in the context of the likelihood ratio test, there appears to be much confusion about the related problem for the score test. The aim of this paper is to illustrate that classical (two‐sided) score test statistics, frequently advocated in practice, cannot be used in this context, but that well‐chosen one‐sided counterparts could be used instead. The relation with likelihood ratio tests will be established, and all results are illustrated in an analysis of continuous longitudinal data using linear mixed models.

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Section: Augmented Regression Modelmentioning

confidence: 99%

Section: Augmented Regression Modelmentioning

confidence: 99%

The Use of Score Tests for Inference on Variance Components

Verbeke¹,

Molenberghs²

2003

Biometrics

203

144

View full text Add to dashboard Cite

show abstract

“…where t ∼ N(0, 1), the φ ts are the sub-diagonal elements of T, and the d t are the diagonal elements of D. Pan and MacKenzie (2003) use the modified Cholesky decomposition to jointly model the mean and covariance in longitudinal studies. Pourahmadi, Daniels, and Park (2007) develop a method of simultaneously modelling several covariance matrices based on this decomposition, thereby giving an alternative to common principal components analysis (Flury 1988) for longitudinal data.…”

Section: Clustering Longitudinal Datamentioning

confidence: 99%

Model-Based Clustering

McNicholas

2016

J Classif

185

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Abstract:The notion of defining a cluster as a component in a mixture model was put forth by Tiedeman in 1955; since then, the use of mixture models for clustering has grown into an important subfield of classification. Considering the volume of work within this field over the past decade, which seems equal to all of that which went before, a review of work to date is timely. First, the definition of a cluster is discussed and some historical context for model-based clustering is provided. Then, starting with Gaussian mixtures, the evolution of model-based clustering is traced, from the famous paper by Wolfe in 1965 to work that is currently available only in preprint form. This review ends with a look ahead to the next decade or so.

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“…Pourahmadi [1] proposed a likelihood based approach of estimating the mean function and the covariance matrix based on Cholesky decomposition. Pan and Mackenzie [2] extended Pourahmadi's approach to irregular sparse longitudinal data. Mao et al [3] proposed a joint mean-covariance estimation with basis function approximation.…”

Section: Introductionmentioning

confidence: 99%

A Semiparametric Bayesian Approach for Analyzing Longitudinal Data from Multiple Related Groups

Das

Afriyie

Spirko

2015

The International Journal of Biostatistics

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Often the biological and/or clinical experiments result in longitudinal data from multiple related groups. The analysis of such data is quite challenging due to the fact that groups might have shared information on the mean and/or covariance functions. In this article, we consider a Bayesian semiparametric approach of modeling the mean trajectories for longitudinal response coming from multiple related groups. We consider matrix stick-breaking process priors on the group mean parameters which allows information sharing on the mean trajectories across the groups. Simulation studies are performed to demonstrate the effectiveness of the proposed approach compared to the more traditional approaches. We analyze data from a one-year follow-up of nutrition education for hypercholesterolemic children with three different treatments where the children are from different age-groups. Our analysis provides more clinically useful information than the previous analysis of the same dataset. The proposed approach will be a very powerful tool for analyzing data from clinical trials and other medical experiments.

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On modelling mean-covariance structures in longitudinal studies

Cited by 144 publications

References 6 publications

The Use of Score Tests for Inference on Variance Components

The Use of Score Tests for Inference on Variance Components

Model-Based Clustering

A Semiparametric Bayesian Approach for Analyzing Longitudinal Data from Multiple Related Groups

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