Linear Mixed Models with Flexible Distributions of Random Effects for Longitudinal Data

Zhang, Daowen; Davidian, Marie

doi:10.1111/j.0006-341x.2001.00795.x

Cited by 263 publications

(317 citation statements)

References 16 publications

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“…Even then, however, mixture distributions are not the only answer. Other approaches for semiparametrically modeling the continuous (but not necessarily normal) distribution of the individual trajectories exist that do not resolve the population into artificial groups (e.g., Chen, Zhang, & Davidian, 2002;Zhang & Davidian, 2001).…”

Section: Groups That Do Not Existmentioning

confidence: 99%

Observations on the Use of Growth Mixture Models in Psychological Research

Bauer

2007

Multivariate Behavioral Research

261

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Psychologists are applying growth mixture models at an increasing rate. This article argues that most of these applications are unlikely to reproduce the underlying taxonic structure of the population. At a more fundamental level, in many cases there is probably no taxonic structure to be found. Latent growth classes then categorically approximate the true continuum of individual differences in change. This approximation, although in some cases potentially useful, can also be problematic. The utility of growth mixture models for psychological science thus remains in doubt. Some ways in which these models might be more profitably used are suggested.Growth mixture models (GMMs) are designed to separate a general population of individuals into subgroups characterized by qualitatively distinct patterns of change over time. In this article, I offer a few observations on the application of these models in psychological science. Like many, I was initially excited about the potential of GMMs. After several years of evaluating these models and reviewing applications, however, I am now skeptical that they will meaningfully advance our understanding of psychosocial development. In what follows, I outline key methodological and theoretical concerns that I have with current applications of GMMs.

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Section: Groups That Do Not Existmentioning

confidence: 99%

Observations on the Use of Growth Mixture Models in Psychological Research

Bauer

2007

Multivariate Behavioral Research

261

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“…where φ(·) is the standard normal density function, (ξ, η, a 0 , a 1 , a 2 ) are unknown parameters, and (a 0 , a 1 , a 2 ) are constrained so that (4) integrates to one (Zhang & Davidian, 2001). …”

Section: ·1 Full Latent-model Robustnessmentioning

confidence: 99%

Latent-model robustness in structural measurement error models

2006

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SummaryWe present methods for diagnosing the effects of model misspecification of the truepredictor distribution in structural measurement error models. We first formulate latent-model robustness theoretically. Then we provide practical technique for examining the adequacy of an assumed latent predictor model. The methods are illustrated via analytical examples, application to simulated data and with data from a study of coronary heart disease.

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“…There are, however, many other situations when the underlying distribution no longer satisfies the symmetric property (e.g., Zhang and Davidian [24]). Robust joint modeling can be found in Li et al [25] and Huang et al [26] where a student's t distribution in different structures of joint modeling of longitudinal and survival data is applied.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Analysis of Joint Modeling of Longitudinal and Time to Event Data Using Some Skew-Elliptical Distributions

Khoundabi¹,

Kazemnejad²,

Mansourian³

et al. 2017

BBIJ

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Joint modeling of longitudinal and time to event data have been widely used for analyzing medical data, where longitudinal measurements is gathered with a time to event or survival data. In most of these studies, distributional assumption for modeling longitudinal response is normal, which leads to vulnerable inference in the presence of outliers in longitudinal measurements and violation of this assumption. Violation of the normality assumption can also make the statistical inference vague. Powerful distributions for robust analyzing and relaxing normality assumption, are skew-elliptical distributions, which include univariate and multivariate versions of the student's t, the Laplace and normal distributions. In this paper, a linear mixed effects model with skew-elliptical distribution for both random effects and residuals and a Cox's model for time to event data are used for joint modeling. This strategy allows for the skewness and the heavy tails of random effect distributions and thus makes inferences robust to the violation. For estimation, a Bayesian parametric approach using Markov chain Monte Carlo is adopted. The method is illustrated in a real Intensive Care Unit (ICU) data set and the best model is selected using some Bayesian criteria for model selection.

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Linear Mixed Models with Flexible Distributions of Random Effects for Longitudinal Data

Cited by 263 publications

References 16 publications

Observations on the Use of Growth Mixture Models in Psychological Research

Observations on the Use of Growth Mixture Models in Psychological Research

Latent-model robustness in structural measurement error models

Bayesian Analysis of Joint Modeling of Longitudinal and Time to Event Data Using Some Skew-Elliptical Distributions

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