Addressing Coarsening Induced Measurement Error From Grouped Regressors
Published in Working paper, 2026
How can researchers study the political consequences of economic resources when surveys record only broad income brackets? This question reflects a common challenge in social science: the quantities that theories describe are often observed through grouped responses, leaving researchers to decide how those categories should enter a statistical analysis.
This paper develops a theoretical framework connecting the reconstruction of bracketed predictors to measurement-error theory and regression inference. It examines the assumptions involved in translating categories into numerical values and develops methods for using the information contained in known interval boundaries. Formal analysis and Monte Carlo experiments provide a basis for evaluating these methods and the uncertainty attached to the resulting estimates.
Motivated by research on inequality and political behavior, the paper offers guidance for analyzing grouped data when the substantive question concerns an underlying continuous quantity. It forms the foundation of a broader project on measurement and comparability in social science, with accompanying software for applied research.
Earlier project poster
Earlier versions of the broader project were presented at the 2025 meetings of the European Political Science Association and the American Political Science Association. The poster below was presented at the 2026 Society for Political Methodology meeting (PolMeth XLIII), Michigan State University, July 2026, and reflects an earlier version combining the reconstruction and interaction questions.
Draft available upon request.