Bayesian Comparison of Latent Variable Models: Conditional Versus Marginal Likelihoods

Merkle, Edgar C.; Furr, Daniel C.; Rabe‐Hesketh, Sophia

doi:10.1007/s11336-019-09679-0

Cited by 75 publications

(74 citation statements)

References 56 publications

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“…In a Bayesian latent variable modeling analysis, the conditional likelihood is relatively easier to obtain than the marginal likelihood because it does not require integration and is readily available in many Bayesian software programs, such as JAGS, OpenBUGS, and Stan. However, in recent studies (e.g., Merkle et al, 2019;Zhang et al, 2019), it is reported that employing the conditional likelihood in model selection can be misleading. Merkle et al (2019) recommended use of marginal likelihood based information criteria in Bayesian latent variable analysis.…”

Section: Resultsmentioning

confidence: 99%

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Exploring Class Enumeration in Bayesian Growth Mixture Modeling Based on Conditional Medians

Kim

Tong

2021

Front. Educ.

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Growth mixture modeling is a popular analytic tool for longitudinal data analysis. It detects latent groups based on the shapes of growth trajectories. Traditional growth mixture modeling assumes that outcome variables are normally distributed within each class. When data violate this normality assumption, however, it is well documented that the traditional growth mixture modeling mislead researchers in determining the number of latent classes as well as in estimating parameters. To address nonnormal data in growth mixture modeling, robust methods based on various nonnormal distributions have been developed. As a new robust approach, growth mixture modeling based on conditional medians has been proposed. In this article, we present the results of two simulation studies that evaluate the performance of the median-based growth mixture modeling in identifying the correct number of latent classes when data follow the normality assumption or have outliers. We also compared the performance of the median-based growth mixture modeling to the performance of traditional growth mixture modeling as well as robust growth mixture modeling based on t distributions. For identifying the number of latent classes in growth mixture modeling, the following three Bayesian model comparison criteria were considered: deviance information criterion, Watanabe-Akaike information criterion, and leave-one-out cross validation. For the median-based growth mixture modeling and t-based growth mixture modeling, our results showed that they maintained quite high model selection accuracy across all conditions in this study (ranged from 87 to 100%). In the traditional growth mixture modeling, however, the model selection accuracy was greatly influenced by the proportion of outliers. When sample size was 500 and the proportion of outliers was 0.05, the correct model was preferred in about 90% of the replications, but the percentage dropped to about 40% as the proportion of outliers increased to 0.15.

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Section: Resultsmentioning

confidence: 99%

“…We computed the three model comparison criteria based on marginal likelihoods as recommended in Merkle et al (2019). The traditional GMM has a closed form of the marginal likelihood:…”

Section: Model Selectionmentioning

confidence: 99%

Exploring Class Enumeration in Bayesian Growth Mixture Modeling Based on Conditional Medians

Kim

Tong

2021

Front. Educ.

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“…To calculate the likelihood of the model parameters, we follow Merkle et al (2018) and use the marginal likelihood to derive the model selection criteria because we want to infer to a population beyond the specific sample considered. The correlation σ θ 1 θ 2 is the only component of Σ θ 1 ,θ 2 that needs to be estimated, so we define δ = ( ω , σ θ 1 θ 2 false) T as the vector consisting of all model parameters to be estimated.…”

Section: Modeling Item Positions In An Irt Frameworkmentioning

confidence: 99%

“…which is a weighted version of the marginal likelihood described in Merkle et al (2018) with corresponding log pseudo-likelihood…”

Section: Modeling Item Positions In An Irt Frameworkmentioning

confidence: 99%

A Bayesian Item Response Model for Examining Item Position Effects in Complex Survey Data

Trendtel

Robitzsch

2020

Journal of Educational and Behavioral Statistics

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A multidimensional Bayesian item response model is proposed for modeling item position effects. The first dimension corresponds to the ability that is to be measured; the second dimension represents a factor that allows for individual differences in item position effects called persistence. This model allows for nonlinear item position effects on the item side as well as on the person side. Moreover, a flexible loading structure on the two dimensions is allowed. A fully Bayesian estimation procedure is proposed, and its performance is investigated by a simulation study. Further, the model is applied to empirical data collected in the Programme for International Student Assessment 2000 in the reading domain. The additional value of the model’s extended flexibility compared to more restrictive models is shown. The findings show that the linear hypothesis of change in performance during a test does not hold in general.

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“…In recent years, latent variable models have emerged as an important method in various applications. 1−4 The importance of modeling extra constructs representing other latent variables instead of manifest variables has been recognized by many experts and researchers. 5−7 In this case, we consider building a hierarchical latent variable model to establish high-level constructs that reflect other latent variables.…”

Section: Introductionmentioning

confidence: 99%

Comparison of partial least square algorithms in hierarchical latent variable model with missing data

Cheng

2020

SIMULATION

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Missing data is almost inevitable for various reasons in many applications. For hierarchical latent variable models, there usually exist two kinds of missing data problems. One is manifest variables with incomplete observations, the other is latent variables which cannot be observed directly. Missing data in manifest variables can be handled by different methods. For latent variables, there exist several kinds of partial least square (PLS) algorithms which have been widely used to estimate the value of latent variables. In this paper, we not only combine traditional linear regression type PLS algorithms with missing data handling methods, but also introduce quantile regression to improve the performances of PLS algorithms when the relationships among manifest and latent variables are not fixed according to the explored quantile of interest. Thus, we can get the overall view of variables’ relationships at different levels. The main challenges lie in how to introduce quantile regression in PLS algorithms correctly and how well the PLS algorithms perform when missing manifest variables occur. By simulation studies, we compare all the PLS algorithms with missing data handling methods in different settings, and finally build a business sophistication hierarchical latent variable model based on real data.

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Bayesian Comparison of Latent Variable Models: Conditional Versus Marginal Likelihoods

Cited by 75 publications

References 56 publications

Exploring Class Enumeration in Bayesian Growth Mixture Modeling Based on Conditional Medians

Exploring Class Enumeration in Bayesian Growth Mixture Modeling Based on Conditional Medians

A Bayesian Item Response Model for Examining Item Position Effects in Complex Survey Data

Comparison of partial least square algorithms in hierarchical latent variable model with missing data

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