Statistical Analysis with Missing Data., 3rd Edition

5Accounting for Uncertainty from Missing Data

5.1 Introduction

Chapter 4 is concerned with the point estimation of population quantities in the presence of missingness. In this chapter, we discuss estimates of uncertainty for these point estimates that incorporate the additional variability due to missingness. The sampling variance estimates presented here all effectively assume that the method of adjustment for missingness has succeeded in essentially eliminating bias due to missingness. In many applications, the issue of bias is more crucial than that of increased sampling variance. In fact, it can be argued that providing a valid estimate of sampling variance is worse than providing no estimate if the point estimator has a large bias that dominates the mean squared error.

We distinguish four general approaches to accounting for uncertainty from missing data:

1. Apply explicit sampling variance formulas that allow for missingness. For example, in Example 4.1, we showed that the weighting class estimator (5.15) is obtained by substituting means within adjustment cells. Thus, if selection is by simple random sampling, and missing data are missing completely at random (MCAR) within adjustment cells, then the explicit formula (5.16) for mean squared error can be applied to estimate the precision, with the corresponding large-sample confidence interval . Equation (5.14) gives the ...