Compare methods

	Ecological Inference	Multilevel Regression and Poststratification
Field	Political Science	Political Science
Family	Regression model	Regression model
Year of origin	1997	2004
Originator	Leo Goodman (ecological regression); Gary King (statistical EI solution)	Gelman and Little (method); Park, Gelman & Bafumi (state-level application)
Type	Aggregate-data model inferring individual-level rates from grouped totals	Survey small-area estimation model combining multilevel regression with census poststratification
Seminal source	King, G. (1997). A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data. Princeton: Princeton University Press. ISBN: 9780691012414	Park, D. K., Gelman, A., & Bafumi, J. (2004). Bayesian Multilevel Estimation with Poststratification: State-Level Estimates from National Polls. Political Analysis, 12(4), 375–385.
Aliases	EI, Ecological regression, King's ecological inference, Aggregate-to-individual inference	MRP, Mister P, Multilevel regression with poststratification, Small-area opinion estimation
Related	5	5
Summary	Ecological inference is the problem of learning about individual behavior — such as how Black and white voters cast their ballots — when only aggregate data are available, like precinct-level turnout and racial composition. Because individual-level data are missing, the within-group rates are not directly observed; ecological inference recovers them by combining the deterministic accounting constraints that each precinct must satisfy with a statistical model of how the unobserved rates vary across precincts. Gary King's 1997 solution unified the deterministic method of bounds with Leo Goodman's classic ecological regression, sharply reducing the long-standing risk of the ecological fallacy.	Multilevel regression and poststratification (MRP) estimates opinion or behavior in small subpopulations — states, districts, demographic groups — from a single national survey that is far too small to support direct estimates in each unit. It first fits a multilevel model that predicts the outcome from individual demographic and geographic characteristics, borrowing strength across units through partial pooling, and then poststratifies the predicted values to known population counts of demographic-by-geographic cells. Introduced for state-level opinion by Park, Gelman, and Bafumi (2004) and shown by Lax and Phillips (2009) to outperform disaggregation, MRP has become the standard tool for subnational opinion estimation.