Semiparametric Bayesian analysis of structural equation models with fixed covariates

Lee, Sik‐Yum; Lu, Bin; Song, Xinyuan

doi:10.1002/sim.3098

Cited by 44 publications

(43 citation statements)

References 40 publications

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“…Like all statistical methods, SEM has its limitations, such as the assumption of normality of latent factors and error terms in the model. Our group has recently developed a semiparametric Bayesian method [51] that does not require the normality assumption. Moreover, our current SEM cannot be used to assess changes in longitudinal effects over time; this would require the extension of dynamic SEMs [4,52] to include non-ranking categorical variables.…”

Section: Effects Of Genotypes and Phenotypes On Renal Functionmentioning

confidence: 99%

Phenotype–genotype interactions on renal function in type 2 diabetes: an analysis using structural equation modelling

Song

Lee

et al. 2009

Diabetologia

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Aims/hypothesis Cardiovascular and renal diseases share common risk factors. We used structural equation modelling (SEM) to evaluate the independent and combined effects of phenotypes and genotypes implicated in cardiovascular diseases on renal function in type 2 diabetes.Methods 1,188 type 2 diabetic patients were stratified into high-risk and low-risk groups according to bimodal distributions of the logarithmically transformed (log e ) urinary albumin:creatinine ratio and plasma creatinine levels. Models for these groups, comprising continuous and non-ranking categorical data, were developed separately to evaluate the inter-relationships among measured variables and latent factors using non-linear SEMs, Bayesian estimation and model selection as assessed by a goodness-of-fit statistic. Results Inter-correlated measured variables (obesity, glycaemia, lipid, blood pressure) and variants of the genes encoding endothelial nitric oxide synthase (NOS), β-adrenergic receptor (ADRB), components of the reninangiotensin system (RAS) and lipid metabolism were loaded onto their respective latent factors of phenotypes and genotypes. In addition to direct and indirect effects, latent factors of obesity, lipid and BP interacted with latent factors of ADRB and RAS genotypes to influence renal function. Together with variants of the genes encoding peroxisome proliferator-activated receptor γ, atrial natriuretic peptide, adducin, G protein β 3 subunit, epithelial sodium channel α subunit and matrix metallopeptidase 3, these parameters explained 39-80% of the variance in renal function in the high-risk and low-risk models. Conclusions/interpretation SEM is a useful tool for confirming and quantifying multiple interactions of biological pathways with genetic determinants. The combined and interactive effects of blood pressure, lipid and obesity on renal function may have therapeutic implications, especially in type 2 diabetic individuals with genetic risk factors.

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Section: Effects Of Genotypes and Phenotypes On Renal Functionmentioning

confidence: 99%

Phenotype–genotype interactions on renal function in type 2 diabetes: an analysis using structural equation modelling

Song

Lee

et al. 2009

Diabetologia

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“…Following Lee et al (2008), we use the DP mixture model to specify the distribution of u i j . That is, u i j…”

Section: Generalized Linear Measurement Error Modelsmentioning

confidence: 99%

“…The nonparametric method has been successfully used to make statistical inference on various random effects models. For example, see Kleinman and Ibrahim (1998), Dunson (2006), Guha (2008), Lee et al (2008), Chow et al (2011), Tang and Duan (2012) and Tang et al (2014). However, to the best of our knowledge, little work is done on Bayesian analysis of GLMEMs with the covariate MEs following a nonparametric distribution.…”

Section: Introductionmentioning

confidence: 99%

Semiparametric Bayesian inference on generalized linear measurement error models

Tang

2016

Stat Papers

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The classical assumption in generalized linear measurement error models (GLMEMs) is that measurement errors (MEs) for covariates are distributed as a fully parametric distribution such as the multivariate normal distribution. This paper uses a centered Dirichlet process mixture model to relax the fully parametric distributional assumption of MEs, and develops a semiparametric Bayesian approach to simultaneously obtain Bayesian estimations of parameters and covariates subject to MEs by combining the stick-breaking prior and the Gibbs sampler together with the Metropolis-Hastings algorithm. Two Bayesian case-deletion diagnostics are proposed to identify influential observations in GLMEMs via the Kullback-Leibler divergence and Cook's distance. Computationally feasible formulae for evaluating Bayesian casedeletion diagnostics are presented. Several simulation studies and a real example are used to illustrate our proposed methodologies.

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“…The usual single multivariate normal model for the latent variables is replaced by a mixture of normal priors with infinite number of components. And, for the latent variable model with fixed covariates and continuous responses, Lee et al [17] established the semiparametric Bayesian hierarchal model for the structural equation models (SEMs) by relaxing the common normal distribution of exogenous factors to follow a finitedimensional Dirichlet process [18]. Song et al [19] developed a semiparametric Bayesian procedure for analyzing the latent variable model with unordered categorical data.…”

Section: Introductionmentioning

confidence: 99%

Assessing Heterogeneity for Factor Analysis Model with Continuous and Ordinal Outcomes

Xia

Gou

2016

Journal of Applied Mathematics

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Factor analysis models with continuous and ordinal responses are a useful tool for assessing relations between the latent variables and mixed observed responses. These models have been successfully applied to many different fields, including behavioral, educational, and social-psychological sciences. However, within the Bayesian analysis framework, most developments are constrained within parametric families, of which the particular distributions are specified for the parameters of interest. This leads to difficulty in dealing with outliers and/or distribution deviations. In this paper, we propose a Bayesian semiparametric modeling for factor analysis model with continuous and ordinal variables. A truncated stick-breaking prior is used to model the distributions of the intercept and/or covariance structural parameters. Bayesian posterior analysis is carried out through the simulation-based method. Blocked Gibbs sampler is implemented to draw observations from the complicated posterior. For model selection, the logarithm of pseudomarginal likelihood is developed to compare the competing models. Empirical results are presented to illustrate the application of the methodology.

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Semiparametric Bayesian analysis of structural equation models with fixed covariates

Cited by 44 publications

References 40 publications

Phenotype–genotype interactions on renal function in type 2 diabetes: an analysis using structural equation modelling

Phenotype–genotype interactions on renal function in type 2 diabetes: an analysis using structural equation modelling

Semiparametric Bayesian inference on generalized linear measurement error models

Assessing Heterogeneity for Factor Analysis Model with Continuous and Ordinal Outcomes

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