Missing data

Abstract

In most of statistical enterprise, inferences are made about specified (or implied) populations. Multilevel analysis, as many other generic methods of analysis, assume that the analysed dataset is representative of the studied population. Good representation is often eroded by selective missingness, and so methods for dealing with incomplete data should be in the toolkit of every statistical analyst. This imperative is even stronger in studying human populations because human subjects are often poorly motivated, easily distracted while responding, and do not cooperate with study protocols perfectly. Although several kinds of data incompleteness can be handled by multilevel analysis without having to make special arrangements, invisible bias may be incurred when the analysed dataset is treated as complete. This chapter discussed two general approaches to dealing with missing values-the EM algorithm and multiple imputation. Both approaches consider an efficient complete-data analysis (typically, by maximizing a likelihood). In the EM algorithm, this analysis is adjusted, and applied iteratively. In multiple imputation, the complete-data analysis is used without any alteration, but multiple sets of replacements for the missing values have to be generated. Multiple imputation is more versatile, applicable with complex complete-data analyses in which EM would be very difficult to implement. Methods for missing data are applicable in a much wider range of problems. Many complex problems could be simplified if some additional information (data) were available. If such data is regarded as missing a general approach to dealing with missing information can be invoked. The chapter discussed measurement error and complex random coefficient models as examples in which secondary applications of missing-data methods can be applied, leading to a reduction in the computational (programming) effort and enabling us to exploit available algorithms constructed for simpler problems. © 2008 Springer Science+Business Media, LLC.