Multilevel Regression and Poststratification

Direct disaggregation computes each state's mean from only its own respondents, so states with small samples get noisy, unstable estimates and states with no respondents get none at all. MRP instead models how opinion depends on demographics and state characteristics, pooling information across states, and then reconstructs each state from its true demographic composition. Lax and Phillips (2009) showed this yields substantially more accurate state estimates than disaggregation, especially for less-populous states, because partial pooling tames sampling noise while poststratification fixes compositional bias.

You need counts of the population in each cell of the cross-classification of your model's demographic and geographic predictors — for example, the number of people in each age-by-race-by-education-by-state combination. In the United States these come from the Census or the Public Use Microdata Sample (PUMS); other countries use their own census microdata or registers. The frame's categories must match how the predictors are coded in the survey, or the weighting will be inconsistent and the corrected estimates invalid.

Partly. Poststratification corrects for differences in demographic composition between the sample and the population, so MRP can substantially improve non-representative or opt-in samples — famously, state and national estimates from non-representative Xbox polling. But it only adjusts for variables included in the model and the stratification frame: if the selection mechanism is correlated with opinion beyond those variables, residual bias remains. MRP is a powerful correction, not a guarantee of representativeness, and its credibility rests on the assumption that adjustment covariates capture the relevant selection.