Cross-level/ecological Inference

The cross-level or ecological inference problem has fascinated scholars for nearly a century (Ogburn and Goltra 1919, Allport 1924, Gehlke and Biehl 1934). The problem occurs when one is interested in the behavior of individuals, but has data only at an aggregated level (e.g., precincts, hospital wards, counties). This data limitation creates a situation where the behavior of individuals must be surmised from data on aggregated sets of individuals rather than on individuals themselves. Since the goal is to make inferences from aggregate units that are often derived from an “environmental level” (i.e. geographical/ecological units such as a county or precinct), the term “ecological inference” is used to describe this type of analysis. Relatedly, while it is often the case that one is interested in individual-level behavior, this problem occurs more generally whenever the level of interest is less aggregated than the level of the data. For instance, one might be interested in behavior at the county level when only state-level data is available. Accordingly, the term “cross-level inference” is often used as a synonym for ecological inference. The ecological inference problem is an especially intriguing puzzle because it is a very long-standing problem with an exceptionally wide-ranging impact. Occurrences are common across many disciplines, and scholars with diverse backgrounds and interests have a stake in approaches to this problem. Political scientists, for instance, confront these issues when they try to detect whether members of different racial groups cast their ballots differently, using only data at the precinct level that identify vote totals and racial demographics but not vote totals broken down by racial categories. In a completely different substantive area, epidemiologists confront identical methodological issues when they seek to explain which environmental factors influence disease susceptibility using only data from counties or hospital wards, rather than individual patients. Economists studying consumer demand and marketing strategies might need to infer individual spending habits from an analysis of sales data from a specific region and the aggregate characteristics of individuals in that region, rather than from data on individuals’ characteristics and purchases. These examples are but a few of the myriad applications and fields where the ecological inference problem has emerged.