A Bayesian Modeling Approach for Generalized Semiparametric Structural Equation Models

Song, Xinyuan; Lu, Zhaohua; Cai, Jingheng; Ip, Edward H.

doi:10.1007/s11336-013-9323-7

Cited by 35 publications

(36 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…First, each unknown function in model , including

g_{j u} false(z false)

and h j s ( ω ), for j = 1,…, r , u = 1,…, d , s = 1,…, q , is unidentifiable up to a constant. Following the works of Panagiotelis and Smith and Song et al, we impose the following constraint on these functions:

\int_{Z} g_{j u} false(z false) d z = 0, j = 1, …, r, u = 1, …, d,

\int_{- \infty}^{\infty} h_{j s} false(ω false) p false(ω false) d ω = 0, j = 1, …, r, s = 1, …, q,

where

scriptZ

is the support of z , and p ( ω ) is the density function of ω .…”

Section: Model Descriptionmentioning

confidence: 99%

“…In the analysis of the proposed model, modeling the unknown smooth functions

sans-serifg false(\cdot false) normals

and h (·)s in is an important issue. We propose to use a Bayesian P‐spline approach to approximate these unknown functions. The basic idea of the P‐splines is to estimate the unknown smooth functions through a sum of B‐spline basis functions given a large number of knots in the domains of predictors …”

Section: Bayesian Inferencementioning

confidence: 99%

See 1 more Smart Citation

Bayesian semiparametric failure time models for multivariate censored data with latent variables

Ouyang

Wang

et al. 2018

Statistics in Medicine

View full text Add to dashboard Cite

In this paper, we propose a semiparametric failure time model to analyze multivariate censored data with latent variables. The proposed model generalizes the conventional accelerated failure time model to accommodate latent risk factors that could be measured by multiple observed variables through a factor analysis and to incorporate additive nonparametric functions of observed and latent risk factors to examine their functional effects on multivariate failure times of interest. A Bayesian approach, along with Bayesian P-splines and Markov chain Monte Carlo techniques, is developed to estimate the unknown parameters and functions. The empirical performance of the proposed methodology is evaluated by a simulation study. An application to a study on the risk factors of two diabetes complications is presented.

show abstract

“…First, each unknown function in model , including

g_{j u} false(z false)

\int_{Z} g_{j u} false(z false) d z = 0, j = 1, …, r, u = 1, …, d,

\int_{- \infty}^{\infty} h_{j s} false(ω false) p false(ω false) d ω = 0, j = 1, …, r, s = 1, …, q,

where

scriptZ

is the support of z , and p ( ω ) is the density function of ω .…”

Section: Model Descriptionmentioning

confidence: 99%

“…In the analysis of the proposed model, modeling the unknown smooth functions

sans-serifg false(\cdot false) normals

Section: Bayesian Inferencementioning

confidence: 99%

Bayesian semiparametric failure time models for multivariate censored data with latent variables

Ouyang

Wang

et al. 2018

Statistics in Medicine

View full text Add to dashboard Cite

show abstract

“…As a consequence, most of the approaches for nonlinear structural equation modeling are not applicable. Approaches that are robust against a violation of distributional assumptions Cham, West, Ma, & Aiken, 2012;Marsh et al, 2004;Marsh, Wen, & Hau, 2006), for example, product indicator approaches or the 2SMM estimator by Amemiya (2000, 2003), cannot be specified for the HGM-R. For Bayesian approaches, the necessary prior knowledge about the parameters of the model is not always available (e.g., Kelava & Nagengast, 2012;Song, Li, Cai, & Ip, 2013). Particularly for the HGM-R, there is little information available about the effect size of a heteroscedastic variance component: the semi-parametric information about the heterogeneity that may be retrieved from GMMs do not provide insight in the actual effect size.…”

Section: Model Estimationmentioning

confidence: 99%

A Heterogeneous Growth Curve Model for Nonnormal Data

Brandt

Klein

2015

Multivariate Behavioral Research

View full text Add to dashboard Cite

The heterogeneous growth curve model (HGM; Klein & Muthén, 2006 ) is a method for modeling heterogeneity of growth rates with a heteroscedastic residual structure for the slope factor. It has been developed as an extension of a conventional growth curve model and a complementary tool to growth curve mixture models. In this article, a robust version of the heterogeneous growth curve model (HGM-R) is presented that extends the original HGM with a mixture model to allow for an unbiased parameter estimation under the condition of nonnormal data. In two simulation studies, the performance of the method is examined under the condition of nonnormality and a misspecified heteroscedastic residual structure. The results of the simulation studies suggest an unbiased estimation of the heterogeneity by the HGM-R when sample size was large enough and a good approximation of the heteroscedastic residual structure even when the functional form of the heteroscedasticity was misspecified. The practical application of the approach is demonstrated for a data set from HIV-infected patients.

show abstract

“…Further information about the selection of priors for count or ordinal data can be found in Song et al (2013). …”

Section: Model Estimationmentioning

confidence: 99%

A general non-linear multilevel structural equation mixture model

Kelava

Brandt

2014

Front. Psychol.

View full text Add to dashboard Cite

In the past 2 decades latent variable modeling has become a standard tool in the social sciences. In the same time period, traditional linear structural equation models have been extended to include non-linear interaction and quadratic effects (e.g., Klein and Moosbrugger, 2000), and multilevel modeling (Rabe-Hesketh et al., 2004). We present a general non-linear multilevel structural equation mixture model (GNM-SEMM) that combines recent semiparametric non-linear structural equation models (Kelava and Nagengast, 2012; Kelava et al., 2014) with multilevel structural equation mixture models (Muthén and Asparouhov, 2009) for clustered and non-normally distributed data. The proposed approach allows for semiparametric relationships at the within and at the between levels. We present examples from the educational science to illustrate different submodels from the general framework.

show abstract

A Bayesian Modeling Approach for Generalized Semiparametric Structural Equation Models

Cited by 35 publications

References 54 publications

Bayesian semiparametric failure time models for multivariate censored data with latent variables

Bayesian semiparametric failure time models for multivariate censored data with latent variables

A Heterogeneous Growth Curve Model for Nonnormal Data

A general non-linear multilevel structural equation mixture model

Contact Info

Product

Resources

About