Bayesian Mediation Analysis
Atanu Bhattacharjee · 2024
Methods proposed on mediation analysis are mostly based on the frequentist perspective [22 , 23 , 24 , 25 , 10 , 26] . Recently, some extension has been carried out with Bayesian inference by computing the posterior distribution of the products of coefficient and preparing inference on the causal effects of interest [27 , 28 , 29 , 30 , 31] . The non-parametric bounds of principal strata on the dichotomous mediator and dichotomous outcomes are prepared by the prior distribution of possible range [28] . The mediator distribution is attempted by the Dirichlet process of the mixture model. Mostly, the causal effects are attempted by principal causal effects, natural direct and indirect effects. However, the Bayesian non-parametric method has not been explored for the natural direct and indirect impact. The reason to use Bayesian mediation analysis is the availability of several features to work within this direction. It works nicely in the multilevel mediation analysis, which is not difficult to work with the conventional frequentist approach. Now the Bayesian approach is not an attractive choice in multilevel modeling. It is also attractive conceptually and becomes powerful with the Markov Chain Monte Carlo (MCMC) approach. Software with OpenBUGS and R strengthen it with computational advancement. It becomes an attractive choice because it is a free large sample approximation. The inference is strong enough for small sample data. The features available with Bayesian make it appealing for a small sample size. Sometimes simulation studies prove that Bayesian mediation is more potent than the frequentist approach. It shows that the Bayesian noninformative prior provides similar outcomes as the frequentist method. Bayesian works nicely for testing sensitivity toward assumed the prior value by changing prior distribution values. The Bayesian often helps to accommodate the prior information through mediated effects from different studies. It may provide different results by changing the power of the study. The objective of the consideration of different prior densities helps us to cover different noninformative and conjugate priors by model parameters in the single-level and multilevel mediation model. Other types of prior distribution stand with Cauchy distribution [32] as an alternative to the normal distribution to generate posterior estimates of the regression coefficients. However, it is anticipated that the likelihood will make an impact on the Bayesian inference [33] than prior. So assumptions with priors become irrelevant while probability takes the leading role in the inference. If the prior is incorrect, the Bayesian mediation estimate becomes biased. So prior selection technique requires scrutinizing and making it appropriate. The standard approach while quantifying prior information is based on understanding the associated uncertainty of the preceding information. The strong prior that influences the likelihood should be avoided. Inference requires to be taken from observed data. Sometimes the dispersed priors can be considered as an alternative of the Bayesian inference from bias. Sometimes, the sensitivity can also be considered to explore the influence of different prior assumptions. It is suggested to have noninformative prior and combine the information from the meta analysis [34] . The consideration of previous evidence from conducted studies also useful to form correct hypothesis and suitable prior assumption.