Tracking Opinion over Time: A method for Reducing Sampling Error

Abstract

Across a wide range of applications, the Kalman filter- ing and smoothing algorithm provides survey researchers with a sin- gle, systematic technique by which to generate four kinds of useful information. First, it enables survey analysts to differentiate between random sampling error and true opinion change. Second, Kalman smoothing provides a means by which to accumulate information across surveys, greatly increasing the precision with which public opinion is gauged at any given point in time. Third, this technique provides a rigorous means by which to interpolate missing observa- tions and calculate the uncertainty associated with these interpola- tions. Finally, the Kalman algorithm improves the accuracy with which public opinion may be forecasted. Our empirical examples, which focus on party identification, show that the Kalman algorithm can dramatically reduce sampling error in survey data. Since soft- ware implementing this technique is readily available, survey ana- lysts are encouraged to use it to make more efficient use of the data at their disposal. Public opinion analysts frequently encounter problems when they attempt to track the opinions of subpopulations over time. A random national sam- ple of 1,000 adults will contain approximately 121 African-Americans, 126 Californians, and 127 respondents over 65 years of age (U.S. Census Bureau 1995). Charting trends in opinion among such small subgroups immediately raises the question of whether movements from poll to poll are due to real opinion change or merely random sampling variability. donald p. green is professor of political science and director of the Institution for Social and Policy Studies at Yale University. alan s. gerber is assistant professor of political science at Yale University. suzanna l. de boef is assistant professor of po- litical science at Pennsylvania State University. The authors wish to thank Jay Emer- son for his programming assistance and the Institution for Social and Policy Studies for its financial support. The data and programs used in this article may be obtained at the Web address http://pantheon.yale.edu/,gogreen.