A Robust Bayesian Approach for Structural Equation Models with Missing Data

Lee, Sik‐Yum; Xia, Ye-Mao

doi:10.1007/s11336-008-9060-5

Cited by 27 publications

(14 citation statements)

References 54 publications

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“…When individuals are randomly assigned to respective pairs of stimuli, however, missing data is trivial issue since likelihood constructed from only observed data provides sound estimates. On the other hand, for sports data such as the results of sumo tournaments, where missing processes likely depend on the ability of teams (or players) themselves, some Bayes strategies such as data augmentation (e.g., Lee & Xia, 2008;Song & Lee, 2001) are useful.…”

Section: Discussionmentioning

confidence: 99%

Individual Differences Multidimensional Bradley-Terry Model Using Reversible Jump Markov Chain Monte Carlo Algorithm

Usami

2010

Behaviormetrika

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The Bradley-Terry model has been widely and effectively used to rank stimuli from paired comparison data. Existing approaches for paired comparison data analysis, however, have a number of limitations. First, among applied Bradley-Terry models in which multidimensionality is assumed, the effects of individual differences are not considered. Second, in these multidimensional Bradley-Terry models, the number of dimensions is generally evaluated only after analyzing several models with different dimensions separately, thus causing computational inconvenience.In this study, a multidimensional Bradley-Terry model that considers the effects of individual differences is proposed. The proposed model allows estimation of parameters for both scale values of stimuli and individual differences in multidimensional space. A procedure of parameter estimation is presented that uses a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm to estimate the optimal number of dimensions as well as associated parameters simultaneously. Simulation studies for examining the utility of the RJMCMC algorithm are performed, and real sports data from sumo are used in a representative example, where the time periods of tournaments are used as parameters for individual differences, in order to verify the validity of the proposed model.

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Section: Discussionmentioning

confidence: 99%

Individual Differences Multidimensional Bradley-Terry Model Using Reversible Jump Markov Chain Monte Carlo Algorithm

Usami

2010

Behaviormetrika

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“…Several studies have been completed which rely on fewer replications and an ANOVA approach to analysis (e.g., 100 replications as reported in Kankaraš, Vermunt, & Moors, 2011;Lee, Song, & Lee, 2003;Lee & Xia, 2008;Lee & Zhu, 2002; Song, Lee, & Hser, 2008;and 200 replications as reported in Fan, Thompson, & Wang, 1999;Hu & Bentler, 1999;Jackson, 2003Jackson, , 2007. The plsSEM package (Monecke & Leisch, 2012) developed for R (R Development Core Team, 2012) was used to obtain model parameter and standard error estimates.…”

Section: Simulation Designmentioning

confidence: 99%

Evaluation of partial least squares parameter recovery

Chumney

2015

Proceedings of the 2nd International Symposium on Partial Least Squares Path Modeling: The Conference for PLS Users

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The purpose of this study was to evaluate the performance of Partial Least Squares under lessthan-ideal conditions selected to imitate real-world data. A simulation study with a 3×3×2×2 design was conducted. The design and data features of interest were sample size (50, 300, 1000), number of items per latent variable (3, 5, 7), degree of model misspecification (correctly specified, misspecified), and nature of the relationships between items and latent variables in the measurement models (reflective, formative). Bias of model parameter estimates, and bias and accuracy of standard error estimates were examined to evaluate the performance of PLS for each experimental condition.

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“…For example, Student's t distributions have been applied under the structural equation modeling framework and were found to produce reliable parameter estimates and inferences [15,16]; in robust mixture models, Wang et al [30] used the multivariate t distribution to fit heavy-tailed data and data with missing information, Shoham [24] implemented a robust clustering algorithm in mixture models by modeling data that are contaminated by outliers using multivariate t distributions, Seltzer et al [21] and Seltzer and Choi [22] conducted sensitivity analysis employing Student's t distributions in robust multilevel models and downweighted outliers in level two (the between-subject level), and Tong and Zhang [28] and Zhang et al [36] advanced the Student's t distributions to robust growth curve models and provided online software to carry out the analysis. Although robust methods based on Student's t distributions have been used in different modeling frameworks, few have been adopted in the causal modeling, where heavy-tailed data or data containing outliers are not uncommon [18].…”

Section: Introductionmentioning

confidence: 99%

Bayesian Two-Stage Robust Causal Modeling with Instrumental Variables using Student's t Distributions

Shi¹,

Tong²

2017

Bayesian Inference

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In causal inference research, the issue of the treatment endogeneity is commonly addressed using the two-stage least squares (2SLS) modeling with instrumental variables (IVs), where the local average treatment effect (LATE) is the causal effect of interest. Because practical data are usually heavy tailed or contain outliers, using traditional 2SLS modeling based on normality assumptions may result in inefficient or even biased LATE estimate. This study proposes four types of Bayesian two-stage robust causal models with IVs to model normal and nonnormal data, and evaluates the performance of the four types of models with IVs. The Monte Carlo simulation results show that the Bayesian two-stage robust causal modeling produces reliable parameter estimates and model fits. Particularly, in different types of the two-stage robust models with IVs, the models that take outliers into consideration and use Student's t distributions in the second stage to model heavy-tailed data or data containing outliers provide more accurate and efficient LATE estimates and better model fits than other distribution models when data are contaminated. The preferred models are recommended to be adopted in general in the two-stage causal modeling with IVs.

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A Robust Bayesian Approach for Structural Equation Models with Missing Data

Abstract: robust Bayesian methods, normal/independent distributions, nonlinear structural equation models with covariates, model comparison,

Cited by 27 publications

References 54 publications

Individual Differences Multidimensional Bradley-Terry Model Using Reversible Jump Markov Chain Monte Carlo Algorithm

Individual Differences Multidimensional Bradley-Terry Model Using Reversible Jump Markov Chain Monte Carlo Algorithm

Evaluation of partial least squares parameter recovery

Bayesian Two-Stage Robust Causal Modeling with Instrumental Variables using Student's t Distributions

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