book

Statistical Analysis with Missing Data., 3rd Edition

Name: Statistical Analysis with Missing Data., 3rd Edition
ISBN: 9780470526798

by Roderick J. A. Little, Donald B. Rubin

April 2019

Intermediate to advanced

464 pages

13h 23m

English

Wiley

Read now

Unlock full access

Cover
Preface to the Third Edition
Part I Overview and Basic Approaches
1 Introduction
1.1 The Problem of Missing Data1.2 Missingness Patterns and Mechanisms1.3 Mechanisms That Lead to Missing Data1.4 A Taxonomy of Missing Data MethodsProblemsNote
2 Missing Data in Experiments
2.1 Introduction2.2 The Exact Least Squares Solution with Complete Data2.3 The Correct Least Squares Analysis with Missing Data2.4 Filling in Least Squares Estimates2.5 Bartlett's ANCOVA Method2.6 Least Squares Estimates of Missing Values by ANCOVA Using Only Complete-Data Methods2.7 Correct Least Squares Estimates of Standard Errors and One Degree of Freedom Sums of Squares2.8 Correct Least-Squares Sums of Squares with More Than One Degree of FreedomProblems
3 Complete-Case and Available-Case Analysis, Including Weighting Methods
3.1 Introduction3.2 Complete-Case Analysis3.3 Weighted Complete-Case Analysis3.4 Available-Case AnalysisProblems
4 Single Imputation Methods
4.1 Introduction4.2 Imputing Means from a Predictive Distribution4.3 Imputing Draws from a Predictive Distribution4.4 ConclusionProblems
5 Accounting for Uncertainty from Missing Data
5.1 Introduction5.2 Imputation Methods that Provide Valid Standard Errors from a Single Filled-in Data Set5.3 Standard Errors for Imputed Data by Resampling5.4 Introduction to Multiple Imputation5.5 Comparison of Resampling Methods and Multiple ImputationProblems
Part II Likelihood-Based Approaches to the Analysis of Data with Missing Values
6 Theory of Inference Based on the Likelihood Function
6.1 Review of Likelihood-Based Estimation for Complete Data6.2 Likelihood-Based Inference with Incomplete Data6.3 A Generally Flawed Alternative to Maximum Likelihood: Maximizing over the Parameters and the Missing Data6.4 Likelihood Theory for Coarsened DataProblemsNotes

7 Factored Likelihood Methods When the Missingness Mechanism Is Ignorable
7.1 Introduction7.2 Bivariate Normal Data with One Variable Subject to Missingness: ML Estimation7.3 Bivariate Normal Monotone Data: Small-Sample Inference7.4 Monotone Missingness with More Than Two Variables7.5 Factored Likelihoods for Special Nonmonotone PatternsProblems
8 Maximum Likelihood for General Patterns of Missing Data: Introduction and Theory with Ignorable Nonresponse
8.1 Alternative Computational Strategies8.2 Introduction to the EM Algorithm8.3 The E Step and The M Step of EM8.4 Theory of the EM Algorithm8.5 Extensions of EM8.6 Hybrid Maximization MethodsProblems
9 Large-Sample Inference Based on Maximum Likelihood Estimates
9.1 Standard Errors Based on The Information Matrix9.2 Standard Errors via Other MethodsProblems
10 Bayes and Multiple Imputation
10.1 Bayesian Iterative Simulation Methods10.2 Multiple ImputationProblemsNotes
Part III Likelihood-Based Approaches to the Analysis of Incomplete Data: Some Examples
11 Multivariate Normal Examples, Ignoring the Missingness Mechanism
11.1 Introduction11.2 Inference for a Mean Vector and Covariance Matrix with Missing Data Under Normality11.3 The Normal Model with a Restricted Covariance Matrix11.4 Multiple Linear Regression11.5 A General Repeated-Measures Model with Missing Data11.6 Time Series Models11.7 Measurement Error Formulated as Missing DataProblems
12 Models for Robust Estimation
12.1 Introduction12.2 Reducing the Influence of Outliers by Replacing the Normal Distribution by a Longer-Tailed Distribution12.3 Penalized Spline of Propensity PredictionProblemsNotes
13 Models for Partially Classified Contingency Tables, Ignoring the Missingness Mechanism
13.1 Introduction13.2 Factored Likelihoods for Monotone Multinomial Data13.3 ML and Bayes Estimation for Multinomial Samples with General Patterns of Missingness13.4 Loglinear Models for Partially Classified Contingency TablesProblems
14 Mixed Normal and Nonnormal Data with Missing Values, Ignoring the Missingness Mechanism
14.1 Introduction14.2 The General Location Model14.3 The General Location Model with Parameter Constraints14.4 Regression Problems Involving Mixtures of Continuous and Categorical Variables14.5 Further Extensions of the General Location ModelProblems
15 Missing Not at Random Models
15.1 Introduction15.2 Models with Known MNAR Missingness Mechanisms: Grouped and Rounded Data15.3 Normal Models for MNAR Missing Data15.4 Other Models and Methods for MNAR Missing DataProblems
References
Author Index
Subject Index
End User License Agreement

Content preview from Statistical Analysis with Missing Data., 3rd Edition

9Large-Sample Inference Based on Maximum Likelihood Estimates

9.1 Standard Errors Based on The Information Matrix

We noted in Chapter 6 that large-sample maximum likelihood (ML) inferences can be based on Approximation 6.1, namely that

(9.1)

where C is an estimate of the d × d covariance matrix of , for example,

(9.2)

the inverse of the observed information evaluated at , or

(9.3)

the inverse of the expected information evaluated at , or

(9.4)

the sandwich estimator. The estimate (9.2) is computed as part of the Newton–Raphson algorithm for ML estimation, and (9.3) is computed as part of the scoring algorithm. When the expectation–maximization (EM) algorithm or one of the variants described in Chapter 8 is used for ML estimation, additional steps are needed to compute standard errors ...

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.

Read now

Unlock full access

More than 5,000 organizations count on O’Reilly

O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.

Julian F.

Head of Cybersecurity

I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.

Addison B.

Field Engineer

I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.

Amir M.

Data Platform Tech Lead

I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.

Mark W.

Embedded Software Engineer

Bayesian Data Analysis, Third Edition, 3rd Edition

Publisher Resources

ISBN: 9780470526798Purchase book

Cloud Computing

Data Engineering

Data Science

AI & ML

Programming Languages

Software Architecture

IT/Ops

Security

Design

Business

Soft Skills

Statistical Analysis with Missing Data., 3rd Edition

by Roderick J. A. Little, Donald B. Rubin

9Large-Sample Inference Based on Maximum Likelihood Estimates

9.1 Standard Errors Based on The Information Matrix

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.