I would appreciate any help to understand the statistical difference between using random effects and Rubin's rule to obtain pooled parameter estimates from multiply imputed datasets.
For example, if
.imput is a variable representing each imputation stage,
chl the outcome variable,
age the predictor, and
data the multiply imputed dataset, what would be the rationale to choose
results_Rubinin the example below?
data <- mice(nhanes, seed = 23109) results_Random <- lm(chl~ age + (age |.imput), data=data) results_Rubin <- pool(with(data, lm(chl ~ age))))
While I understand the complexity of the law of total variance needed to pool the variance, it seems to me that that would not be an issue using
Bayesian statistics because the uncertainty around the parameter estimate is not estimated using standard error anymore, it is instead based on quantiles of the posterior distribution of pooled estimates of the parameter.