In the study on subjective well-being (SWB) using 5 Likert-scale (1 = very unhappy to 5 = very happy). It should be natural to use ordered logistic in the multilevel regression step. Is there related literature?
You mean a multilevel model with a binomial outcome? Or if the 5 likert scale is your outcome, probit regression, this is all in the manual. and then MRP happens after, re-weight estimates by population proportion (please double check).
The 5 likert scale is my outcome
What are you looking for in the literature?
Poststratification can be applied to regression models where you know the population distribution of the covariates. It doesn’t even have to be multilevel. The basic idea’s just to fit the regression, then calculate population expectations by weighting estimates for subgroups based on subgroup population.