When analysing causal questions, we use DAGs that give us covariates needed for modelling. But another time we assess model fit to get the best prediction. These two approaches have different purposes and are mostly used separately (?). But is there also a place for their simultaneous use?
For instance, we have a nested data, and we would like to analyse temporal trends on an outcome.
Minimal sufficient adjustment sets for estimating the direct effect of year on outcome:
covariate, state
Though the DAG gives us model structure, we still have multiple options for specifying our model. For example, we can use hierarchical modelling if we know that there were regionally different baselines and/or varying temporal trends.
outcome ~ covariate + state
outcome ~ covariate + (1 | state)
outcome ~ covariate + (covariate | state)
Thus, would it be a case in causal analysis where we should also assess the model fit? Meaning that the published model was chosen according to the DAG and model fit comparison?
And is there also another dimension - interpretation. When reporting predicted country-wide trends (not regional trends), isn't it so that the first additive model only gives us the temporal trend for one state (state and covariate variables needs to be fixed on one value)? In contrast, hierarchical models' temporal trends predictions are somewhat done for all states at once? If my understanding is true, the first additive model is poor for reporting country-wide trends?
