The Treatment of Missing Data in Multivariate Analysis

Abstract

Procedures for treating missing data in the statistical analysis of survey data are reviewed. The main topics covered are: (1) how to assess the nature of missing data especially with regard to randomness, (2) a comparison of listwise and pairwise deletion, and (3) methods for using maximum information to estimate (a) parameters or (b) missing values. any large data set it is unlikely that complete information or any large data set it is unlikely that complete information will be present for all the cases. In surveys which rely on respondents' reports of behavior and attitudes, it is almost certain that some information is either missing or in an unusable form. Although statisticians have long appreciated that the existence of such missing information can change an ordinarily simple statistical analysis into a complex one (e.g., Orchard and Woodbury, 1972) and responded to this challenge by producing enormous amounts of literature (see, for example, Afifi and Elashoff, 1966;Hartley and Hocking, 1971;Orchard and Woodbury, 1972;Press and Scott, 1974), there is little indication that survey researchers have paid much attention to the literature. When faced with such missing-data problems, most survey researchers are likely to choose either a listwise deletion or pairwise deletion, and then proceed to interpret the resulting statistics as usual. 1 The primary objective of this paper is to review and organize the procedures for handling missing data, having in mind the practical needs of survey researchers with a relatively complex analysis problem but with little statistical sophistication. To make the task manageable, we will confine our discussion mostly to the situation in which variables are measured at least on an interval scale. Other situations will be dealt with only when such excursion is simple and does not interrupt the flow of the presentation. For researchers with specific problems not discussed in this paper, a brief bibliographical note is included.

The Relative Performance of Full Information Maximum Likelihood Estimation for Missing Data in Structural Equation Models

“…Pairwise deletion outperformed listwise deletion in terms of CFA model bias, whereas the reverse was true for the full structural model. Finally, the regression literature suggests that pairwise deletion may provide optimal performance when the level of association among variables is low (Haitovsky, 1968;Kim & Curry, 1977;Little, 1992). However, this has not been systematically explored in the SEM literature.…”

How to perform multiblock component analysis in practice

“…Imputation is much more favorable than the simplest alternative-namely, to discard all observations that have at least one missing value. The latter may result in large losses of information (Kim & Curry, 1977;Stumpf, 1978) and requires the missing data to be MCAR. In contrast, imputation requires the missing data to be MAR, implying that it is more widely applicable.…”

Can k-NN imputation improve the performance of C4.5 with small software project data sets? A comparative evaluation

“…Most missing data methods assume MAR. Whether the MAR condition holds can be examined by a simple t-test of mean differences between the group with complete data and that with missing data [37,68]. MAR is less restrictive than MCAR because MCAR is a special case of MAR.…”