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Bayesian measures of model complexity and fit
 Journal of the Royal Statistical Society, Series B
, 2002
"... [Read before The Royal Statistical Society at a meeting organized by the Research ..."
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Cited by 138 (2 self)
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[Read before The Royal Statistical Society at a meeting organized by the Research
The Covariance Between Level and Shape in the Latent Growth Curve Model With Estimated Basis Vector Coefficients
, 1998
"... A LISREL representation of the Latent Growth Curve Model is used to generate the set of equations for the expectation of the vector of means and the covariance matrix in terms of the unknown population parameters. A dependency between the covariance of the level and shape parameters and the scal ..."
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Cited by 4 (1 self)
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A LISREL representation of the Latent Growth Curve Model is used to generate the set of equations for the expectation of the vector of means and the covariance matrix in terms of the unknown population parameters. A dependency between the covariance of the level and shape parameters and the scalings of the shape basis vector is shown. A simulation is presented based on data presented by McArdle and Hamagami (1991) to show how the covariance changes as the basis vector coecients are rescaled. The relationship is explained in terms of the algebraic solution to a system of equations. Keywords: Latent growth curves, structural equation modeling, LISREL. 1 Introduction The latent growth curve model has become a popular method used to analyze repeatedly measured data (McArdle and Epstein, 1987; McArdle and Aber, 1990) when the interest is modeling "individual change as a function of time" (McArdle and Epstein, 1987, p. 110). As originally described the method combines ideas from bo...
1 The Natural History of Smoking: A PatternMixture Randome®ects Regression Model
"... This article describes and illustrates use of randome®ects regression models (RRM) to examine the natural history of smoking from adolescence to adulthood. For longitudinal data analysis, RRM are useful because they allow for the presence of missing data, timevarying or invariant covariates, and s ..."
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This article describes and illustrates use of randome®ects regression models (RRM) to examine the natural history of smoking from adolescence to adulthood. For longitudinal data analysis, RRM are useful because they allow for the presence of missing data, timevarying or invariant covariates, and subjects measured at di®erent timepoints. Thus, a key advantage of RRM is that it can accomodate \unbalanced " longitudinal data, where a sample of subjects are not all measured at each and every timepoint. Also, variants of RRM have been developed to model dichotomous and ordinal outcomes, which are common in substance use research. A patternmixture approach (Little, 1995) can also be accommodated within RRM to further handle and describe the in°uence of missing data in longitudinal studies. For this approach, subjects are ¯rst divided into groups depending on their missingdata pattern, and then variables based on these groups are used as model covariates. Researchers are then able to examine the e®ect of missingdata patterns on the outcome(s) of interest. In this article we will illustrate these methods using an example from a study examining smoking status from early adolescence to young adulthood. 3
A Bayesian Approach for Assessing Heterogeneity in Generalized Linear Models
"... Generalized linear mixed models (GLMMs) are used... In this article, we propose a new class of prior distributions based on a Gaussian structure for variance component parameters underlying the random effects covariance. The proposed prior assigns positive probability not only to the full model but ..."
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Generalized linear mixed models (GLMMs) are used... In this article, we propose a new class of prior distributions based on a Gaussian structure for variance component parameters underlying the random effects covariance. The proposed prior assigns positive probability not only to the full model but also to reduced models that exclude one or more of the random effects. This structure facilitates Bayesian inferences about the covariance structure, while also accounting for uncertainty in the random effects model in estimating the population parameters. A Markov chain Monte Carlo algorithm is proposed for posterior computation, and the approach is illustrated using data on prenatal exposure to PCBs and psychomotor development
StageWise Outlier Detection in Hierarchical Bayesian Repeated Measures Models
"... We propose numerical and graphical methods for outlier detection in hierarchical Bayes analyses of repeated measures regression data. We consider a model that allows observations on the same subject (typically a curve of measurements taken at equidistant time points or locations) to have autoregress ..."
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We propose numerical and graphical methods for outlier detection in hierarchical Bayes analyses of repeated measures regression data. We consider a model that allows observations on the same subject (typically a curve of measurements taken at equidistant time points or locations) to have autoregressive errors of a prespecified order. Firststage regression vectors for different subjects are "tied together" in a secondstage modeling step, possibly involving additional regression variables. Outlier detection is accomplished by embedding the null model into a larger parametric model that can accommodate unusual observations. As a first diagnostic, we propose the examination, for each subject's curve, of the posterior probability of a firststage, secondstage, or neither stage outlier relative to the modeling assumptions. These three posterior probabilities are computed for each subject and displayed in a barycentric coordinate plot, a useful device for assessing withinsubject and betwe...
Bayesian Modeling and Optimization of Functional Responses A↵ected by Noise Factors
"... Experiments in systems where each run generates a curve, that is, where the response of interest is a set of observed values of a function, are common in engineering. In this paper, we present a Bayesian predictive modeling approach for functional response systems. The goal is to optimize the shape, ..."
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Experiments in systems where each run generates a curve, that is, where the response of interest is a set of observed values of a function, are common in engineering. In this paper, we present a Bayesian predictive modeling approach for functional response systems. The goal is to optimize the shape, or profile, of the functional response. A robust parameter design scenario is assumed where there are controllable factors and noise factors that vary randomly according to some distribution. The approach incorporates the uncertainty in the model parameters in the optimization phase, extending earlier approaches by J. Peterson (in the multivariate regression case) to the functional response case based on a hierarchical twostage mixede↵ects model. The method is illustrated with real examples taken from the literature and from simulated data, and practical aspects related to model building and diagnostics of the assumed mixede↵ects model are discussed.