Multiple Imputation For Missing Data

In many, if not most, studies, some data that were meant to be collected are missing. For example, in a survey, some people may not respond to all the questions. Or, in a randomized experiment, some units' outcomes may not be measured because of equipment failure. Multiple imputation is one principled method for handling such missing data. The general idea is to fill in the missing data with plausible values, analyze the completed data set, and repeat the process multiple times. The analyses from each completed data set are combined to result in inferences that properly account for the missing data. Multiple imputation has been used in large governmental surveys such as the National Health and Nutrition Examination Survey and the Survey of Consumer Finances, and in numerous studies by individual researchers.

Before we review multiple imputation, it is worth-while to consider the most common and convenient approach to handling missing data: Analyze only the cases that have complete data for the variables of interest. This available cases approach can lead to inaccurate estimates. For a simple illustration of this point, consider the hypothetical data in Table 1 for a random sample of five people. Suppose that weights of all people over 6 feet tall are missing—so that the observed data are 130, 140, and 150—because the height/weight instrument is unable to record information for people over 6 feet tall. Researchers interested in estimating the population average weight are in[Page 664] trouble if they use only the three available cases: their sample average is a severe underestimate.

Many times, researchers are interested in relationships among variables, such as regression coefficients. In the hypothetical example, the fitted regression of weight on height obtained using the three available cases results in reasonable (unbiased) estimates of the slope and intercept, because the regression holds for all heights. However, in data sets with many variables and complicated missing data patterns, using only the available cases might exclude a large fraction of the observations, which could dramatically increase the variability of the estimates. Additionally, different specifications of models may use different units for estimation, making theoretical properties of resulting inferences nearly impossible to understand and practical comparisons of different models difficult.