Statistical Analysis with Missing Data., 3rd Edition

14Mixed Normal and Nonnormal Data with Missing Values, Ignoring the Missingness Mechanism

14.1 Introduction

In Chapters 11 and 12, we considered a variety of complete-data models for continuous variables, based on the multivariate normal distribution and longer-tailed distributions, with missing data that were missing at random (MAR). The role of categorical variables was confined to that of fully observed covariates in regression models. In Chapter 13, we discussed complete-data models for categorical variables when there were missing values. In this chapter, we consider missing data methods for mixtures of normal and nonnormal variables, with MAR missingness.

Little and Schluchter (1985) discuss a model for missing data with mixed normal and categorical variables and provide relatively simple and computationally feasible expectation–maximization (EM) algorithms with incomplete data. Schafer (1997) discusses Bayes' inference for this model, and Liu and Rubin (1998) develop a variety of extensions. The basic version of this model is presented in Section 14.2, and extensions are outlined in Section 14.3. Relationships with previously considered algorithms are examined in Section 14.4.

14.2 The General Location Model

14.2.1 The Complete-Data Model and Parameter Estimates

Suppose that the complete data consist of a random sample of size n on K continuous variables (X ) and V categorical variables (Y ). Categorical variable j has I_j levels so that the categorical variables ...