Semiparametric Methods: Introduction and Overview

Introduction and Overview

Authored by: M. Fitzmaurice Garrett

Missing Data Methodology

Print publication date:  November  2014
Online publication date:  November  2014

Print ISBN: 9781439854617
eBook ISBN: 9781439854624
Adobe ISBN:

10.1201/9781439854624-11

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Abstract

Parametric methods for handling missing data have been well developed since the early 1970s. Much of the statistical literature on parametric models for the data-generating and missing data mechanisms was summarized in the landmark book on missing data by Little and Rubin (1987); see Little and Rubin (2002) for an updated survey that incorporates more recent developments. A potential limitation of these methods is that inferences about parameters of scientific interest depend heavily on parametric assumptions about other nuisance parameters that are of much less interest. For example, parametric selection models directly model the marginal distribution of the complete data, f( Y i |Xi, γ), and a common target of inference is E( Y i |Xi, β), where γ = (β′, α′)′, β is the parameter vector of interest relating the mean of Y i to Xi , and α is the vector of nuisance parameters for the within-subject association (e.g., covariances and/or variance components parameters). Consistency of the estimator of β requires correct specification of the entire parametric model for the complete data, f( Y i |Xi, γ); identification comes from assumptions about f( Y i |Xi, γ) and from postulating unverifiable models for the dependence of the non-response process on the unobserved outcomes. Similarly, valid inferences from pattern-mixture and shared-parameter models also require correct specification of joint parametric models for the response vector and the missing data mechanism.

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