Multiple Overimputation: A Unified Approach to Measurement Error and Missing Data

Although social scientists devote considerable effort to mitigating measurement error during data collection, they usually ignore the issue during data analysis. And although many statistical methods have been proposed for reducing measurement error-induced biases, few have been widely used because of implausible assumptions, high levels of model dependence, difficult computation, or inapplicability with multiple mismeasured variables. We develop an easy-to-use alternative without these problems; it generalizes the popular multiple imputation (mi) framework by treating missing data problems as a special case of extreme measurement error and corrects for both. Like mi, the proposed “multiple overimputation” (mo) framework is a simple two-step procedure. First, multiple (≈ 5) completed copies of the data set are created where cells measured without error are held constant, those missing are imputed from the distribution of predicted values, and cells (or entire variables) with measurement error are “overimputed,” that is imputed from the predictive distribution with observation-level priors defined by the mismeasured values and available external information, if any. In the second step, analysts can then run whatever statistical method they would have run on each of the overimputed data sets as if there had been no missingness or measurement error; the results are then combined via a simple averaging procedure. We also offer easy-to-use open source software that implements all the methods described herein. Word count: 8488 (Excludes supplementary appendices to appear on the web) ∗For helpful comments, discussions, and data we thank Walter Mebane, Gretchen Casper, Simone Dietrich, Justin Grimmer, Sunshine Hillygus, Burt Monroe, Adam Nye, Michael Peress, Eric Plutzer, Mo Tavano, Shawn Treier, Joseph Wright and Chris Zorn. †Assistant Professor, Department of Political Science, University of Rochester, 322 Harkness Hall, Rochester, NY 14627 (m.blackwell@rochester.edu, http://www.mattblackwell.org) ‡Senior Research Scientist, Institute for Quantitative Social Science, 1737 Cambridge Street, Cambridge, MA 02138 (jhonaker@iq.harvard.edu, http://scholar.harvard.edu/honaker) §Albert J. Weatherhead III University Professor, Harvard University, Institute for Quantitative Social Science, 1737 Cambridge Street, Cambridge, MA 02138 (king@harvard.edu, http://gking.harvard.edu)