This paper is a nice introduction to the topic: https://www.sciencedirect.com/science/article/abs/pii/S0022249612000065
At its core, it really is just "Bayesian" + "Structural Equation Modeling". Please indicate which one of these remains unclear after reading through the source above.
Bayesian structural equation modeling (SEM) is a powerful and flexible technique for analyzing complex relationships among observed and latent variables.
Bayesian structural equation modeling (BSEM):
- BSEM is a statistical method that combines structural equation modeling (SEM) with Bayesian inference.
- BSEM offers a number of advantages over traditional SEM methods, including the ability to incorporate prior information about the parameters of the model and the ability to provide a more complete picture of the uncertainty about the parameters of the model.
- BSEM allows for handling complex models and incorporating prior knowledge, providing researchers with a powerful tool to analyze relationships among variables in a dataset.
I suggest you go through the basics of Latent Growth Curve Models and Structural Equation Models as well to capture this efficiently.
Some Resources for application in R and Stan:
- https://www.r-bloggers.com/2023/06/bayesian-structural-equation-model-tutorial/
- https://mc-stan.org/users/documentation/case-studies/sem.html
Statistical method that uses Bayesian techniques to analyze complex relationships between variables, incorporating prior knowledge and uncertainty for more accurate estimates and model inferences.
SEM is a multivariate statistical method used to analyze the relationships between observed and latent (unobserved) variables, representing complex causal or correlational structures. On the other hand, Bayesian inference is a probabilistic approach that combines prior knowledge (prior distribution) with observed data to estimate the posterior distribution of the model parameters.
BSEM extends traditional SEM by incorporating Bayesian principles and methods. It offers several advantages over classical SEM methods:
1. Flexibility in Model Specification: BSEM allows for the inclusion of prior distributions on model parameters, providing a way to incorporate prior knowledge or beliefs about the relationships between variables. This flexibility is particularly useful when dealing with small sample sizes or complex models.
2. Uncertainty Quantification: BSEM provides a posterior distribution for model parameters, which allows for the estimation of uncertainty associated with the parameter estimates. This is in contrast to classical SEM, which typically provides point estimates and standard errors.
3. Model Comparison and Selection: BSEM enables researchers to compare different competing models by evaluating their posterior probabilities. This facilitates model selection based on the data and prior knowledge, considering both model fit and complexity.
4. Missing Data Handling: BSEM handles missing data through a process called data imputation. It allows for the estimation of missing values based on the posterior distribution, taking into account the uncertainty associated with the imputed values.
The Bayesian approach in BSEM requires the specification of prior distributions for model parameters. These priors can be informed by previous studies, expert opinions, or non-informative priors when little prior knowledge is available. The posterior distribution is then obtained through Markov Chain Monte Carlo (MCMC) techniques, such as Gibbs sampling or the Metropolis-Hastings algorithm.
Hope it helps
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