Linear Mixed Models with Heterogeneous within-Cluster Variances

Lin, Xihong; Raz, Jonathan; Harlow, Sioḃán D.

doi:10.2307/2533552

Cited by 41 publications

(44 citation statements)

References 23 publications

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“…The technical report by Cleveland, Denby, and Liu (2002) provides a detailed description of this general class of models and summarizes much of the relevant work. These models have been developed using both Bayesian (Lindley, 1971;Leonard, 1975;Myles et al, 2003) and frequentist approaches (James et al, 1994;Chinchilli, Esinhart, and Miller, 1995;Lin et al, 1997). Most of these authors take the random scale distribution to be square root inverse gamma, though some consider the log-normal distribution.…”

Section: Introductionmentioning

confidence: 99%

An Application of a Mixed‐Effects Location Scale Model for Analysis of Ecological Momentary Assessment (EMA) Data

2008

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SummaryFor longitudinal data, mixed models include random subject effects to indicate how subjects influence their responses over repeated assessments. The error variance and the variance of the random effects are usually considered to be homogeneous. These variance terms characterize the within-subjects (i.e., error variance) and between-subjects (i.e., random-effects variance) variation in the data. In studies using ecological momentary assessment (EMA), up to 30 or 40 observations are often obtained for each subject, and interest frequently centers around changes in the variances, both within and between subjects. In this article, we focus on an adolescent smoking study using EMA where interest is on characterizing changes in mood variation. We describe how covariates can influence the mood variances, and also extend the standard mixed model by adding a subject-level random effect to the within-subject variance specification. This permits subjects to have influence on the mean, or location, and variability, or (square of the) scale, of their mood responses. Additionally, we allow the location and scale random effects to be correlated. These mixed-effects location scale models have useful applications in many research areas where interest centers on the joint modeling of the mean and variance structure.

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Section: Introductionmentioning

confidence: 99%

An Application of a Mixed‐Effects Location Scale Model for Analysis of Ecological Momentary Assessment (EMA) Data

2008

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“…Modelling the heterogeneity and identifying covariates that are related to variance can fully characterize the intraindividual variation [5] and provide a better understanding of the research problems [16] . Studying the heteroscedasticity of the model is not only of practical interest, but is also of important theoretical significance.…”

Section: Introductionmentioning

confidence: 99%

“…Vonesh [26] also extended several estimation procedures for nonlinear mixed models in which the variance was related to the mean response. Lin, et al [16] estimated the regression coefficients, variance components, and heterogeneity parameters in linear mixed models based on quasi-likelihood and method of moments. Other researchers employed Bayesian approaches [7,15] and quantile regression methods [29] to assess the heterogeneity of residual variances in mixed models and multilevel models.…”

Section: Introductionmentioning

confidence: 99%

Semiparametric hierarchical model with heteroscedasticity

Tian

Pan

2017

Statistics and Its Interface

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Recent work on hierarchical data analysis mainly focuses on the multilevel structure of the mean response. Little research for hierarchical heteroscedasticity was done in the literature. In this paper, we propose a class of hierarchical models with heteroscedasticity and then investigate the semi-parametric statistical inferences. Laplace's approximation is employed to obtain an approximated marginal likelihood function and splines method is used to estimate the unknown functions. We also provide the consistency of the estimators. Simulation studies and real data analysis show that the proposed estimation procedures work well.

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“…Pourahmadi and Daniels [4] develop a class of models they call dynamic conditionally linear mixed models in which the marginal covariance matrix is allowed to vary across individuals, but they consider the random effects covariance matrix to be constant across subjects. In the context of linear mixed models, Lin et al, [5] examined heterogeneity in the within-individual variances in linear mixed models and Zhang and Weiss [6] discussed heterogeneity in the random effects covariance matrix but mainly consider models that allow the entire matrix to differ by a multiplicative factor. Little work has been done on modelling the entire random effects covariance matrix.…”

Section: Introductionmentioning

confidence: 99%

“…Table of models fit with W i, kj (design vector for GARP) and H ik (design vector for IV) defined as in (4) and (5). Posterior means and 95 per cent credible intervals for depression score at week 16 and the change from baseline for the best model.…”

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confidence: 99%

Modelling the random effects covariance matrix in longitudinal data

Daniels

Zhao

2003

Statistics in Medicine

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SUMMARYA common class of models for longitudinal data are random effects (mixed) models. In these models, the random effects covariance matrix is typically assumed constant across subject. However, in many situations this matrix may differ by measured covariates. In this paper, we propose an approach to model the random effects covariance matrix by using a special Cholesky decomposition of the matrix. In particular, we will allow the parameters that result from this decomposition to depend on subjectspecific covariates and also explore ways to parsimoniously model these parameters. An advantage of this parameterization is that there is no concern about the positive definiteness of the resulting estimator of the covariance matrix. In addition, the parameters resulting from this decomposition have a sensible interpretation. We propose fully Bayesian modelling for which a simple Gibbs sampler can be implemented to sample from the posterior distribution of the parameters. We illustrate these models on data from depression studies and examine the impact of heterogeneity in the covariance matrix on estimation of both fixed and random effects.

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Linear Mixed Models with Heterogeneous within-Cluster Variances

Cited by 41 publications

References 23 publications

An Application of a Mixed‐Effects Location Scale Model for Analysis of Ecological Momentary Assessment (EMA) Data

An Application of a Mixed‐Effects Location Scale Model for Analysis of Ecological Momentary Assessment (EMA) Data

Semiparametric hierarchical model with heteroscedasticity

Modelling the random effects covariance matrix in longitudinal data

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