Statistical Analysis with Missing Data., 3rd Edition

11Multivariate Normal Examples, Ignoring the Missingness Mechanism

11.1 Introduction

In this chapter, we apply the tools of Part II to a variety of common problems involving incomplete data on multivariate normally distributed variables: estimation of the mean vector and covariance matrix; estimation of these quantities when there are restrictions on the mean and covariance matrix; multiple linear regression, including analysis of variance (ANOVA), and multivariate regression; repeated measures models, including random coefficient regression models where the coefficients themselves are regarded for maximum likelihood (ML) computations as missing data; and selected time series models. Robust estimation with missing data is discussed in Chapter 12, the analysis of partially-observed categorical data is considered in Chapter 13, and the analysis of mixed continuous and categorical data is considered in Chapter 14. Chapter 15 concerns models with data missing not at random.

11.2 Inference for a Mean Vector and Covariance Matrix with Missing Data Under Normality

Many multivariate statistical analyses, including multiple linear regression, principal components analysis, discriminant analysis, and canonical correlation analysis, are based on the initial summary of the data matrix into the sample mean and covariance matrix of the variables. Thus inference for the population mean and covariance matrix for an arbitrary pattern of missing values is a particularly important problem. ...