I use multilevel regression with synthetic poststratification (MrsP) to estimate subjective well-being across 31 provinces in China, which falls under the scope of small area estimation. I am wondering how to conduct robustness checks for small area estimation using MrsP. I have read two related papers on this topic (Zhang, 2015, American Journal of Epidemiology, 182(2); Zheng, 2014, Annals of Epidemiology, 78). Both studies implemented internal validation and external validation. With a decade having passed since these papers were published, are there other methods for model checking—for example, using alternative priors like Gelman and Carpenter ( Journal of royal statistical society C Applied Statistics，2020,69(5))?
You may want to take a look through:
“Using leave-one-out cross validation (LOO) in a multilevel regression and poststratification (MRP) workflow: A cautionary tale” by Kuh et al. (2023)
and
“Model validation for aggregate inferences in out-of-sample prediction” by Kennedy, Vehtari, and Gelman (2024)