1st Edition

# Maximum Likelihood Estimation for Sample Surveys

391 Pages 10 B/W Illustrations
by Chapman & Hall

391 Pages
by Chapman & Hall

Also available as eBook on:

Sample surveys provide data used by researchers in a large range of disciplines to analyze important relationships using well-established and widely used likelihood methods. The methods used to select samples often result in the sample differing in important ways from the target population and standard application of likelihood methods can lead to biased and inefficient estimates.

Maximum Likelihood Estimation for Sample Surveys presents an overview of likelihood methods for the analysis of sample survey data that account for the selection methods used, and includes all necessary background material on likelihood inference. It covers a range of data types, including multilevel data, and is illustrated by many worked examples using tractable and widely used models. It also discusses more advanced topics, such as combining data, non-response, and informative sampling.

The book presents and develops a likelihood approach for fitting models to sample survey data. It explores and explains how the approach works in tractable though widely used models for which we can make considerable analytic progress. For less tractable models numerical methods are ultimately needed to compute the score and information functions and to compute the maximum likelihood estimates of the model parameters. For these models, the book shows what has to be done conceptually to develop analyses to the point that numerical methods can be applied.

Designed for statisticians who are interested in the general theory of statistics, Maximum Likelihood Estimation for Sample Surveys is also aimed at statisticians focused on fitting models to sample survey data, as well as researchers who study relationships among variables and whose sources of data include surveys.

Introduction
Nature and role of sample surveys
Sample designs
Survey data, estimation and analysis
Why analysts of survey data should be interested in maximum likelihood estimation
Why statisticians should be interested in the analysis of survey data
A sample survey example
Maximum likelihood estimation for infinite populations
Bibliographic notes

Maximum likelihood theory for sample surveys
Introduction
Maximum likelihood using survey data
Illustrative examples with complete response
Dealing with nonresponse
Illustrative examples with nonresponse
Bibliographic notes

Alternative likelihood-based methods for sample survey data
Introduction
Pseudo-likelihood
Sample likelihood
Analytic comparisons of maximum likelihood, pseudolikelihood and sample likelihood estimation
The role of sample inclusion probabilities in analytic analysis
Bayesian analysis
Bibliographic notes

Populations with independent units
Introduction
The score and information functions for independent units
Bivariate Gaussian populations
Multivariate Gaussian populations
Non-Gaussian auxiliary variables
Stratified populations
Multinomial populations
Heterogeneous multinomial logistic populations
Bibliographic notes

Regression models
Introduction
A Gaussian example
Parameterization in the Gaussian model
Other methods of estimation
Non-Gaussian models
Different auxiliary variable distributions
Generalized linear models
Semiparametric and nonparametric methods
Bibliographic notes

Clustered populations
Introduction
A Gaussian group dependent model
A Gaussian group dependent regression model
Extending the Gaussian group dependent regression model
Binary group dependent models
Grouping models
Bibliographic notes

Informative nonresponse
Introduction
Nonresponse in innovation surveys
Regression with item nonresponse
Regression with arbitrary nonresponse
Imputation versus estimation
Bibliographic notes

Maximum likelihood in other complicated situations
Introduction
Likelihood analysis under informative selection
Secondary analysis of sample survey data
Combining summary population information with likelihood analysis
Likelihood analysis with probabilistically linked data
Bibliographic notes

### Biography

Raymond L. Chambers, David G. Steel, Suojin Wang, Alan Welsh

"This book makes a strong contribution to the model-based approach. … This book is the first thorough, self-contained development of the likelihood theory on sample survey data. … The authors demonstrate application of their maximum likelihood method in many important estimation problems. … the maximum likelihood approach presented in this book allows for further scientific discoveries and further new results when dealing with complex statistical data."
—Imbi Traat, International Statistical Review (2013), 81, 2

"The authors masterfully accomplish their goal and present us with an excellent and well-written book on model-based analysis for sample surveys. For the models with a mathematically tractable likelihood function, the authors develop the theory to the point ready for numerical implementation; for the mathematical intractable case, they also establish a conceptual procedure that allows future numerical research and implementation. … the book has something for just about every applied statistician and practitioner whose work is related to sampling survey design and analysis. … elegant presentation of the theory and clarity of writing make it easy to read. … a valuable theoretical contribution to the area of survey sampling and provides a thoughtful basis for further applied research. … I also recommend this book as a key reference for graduate students in applied statistics and related areas."
—Cheng Peng, Mathematical Reviews, May 2013

"This sinewy and satisfying book presents a thorough development of the use of likelihood techniques for the analysis of sample survey data, that is, for model-based analysis. … the authors have taken care to lace the presentation with generous explanations, drawing connections between the content and familiar examples in thoughtful ways, and occasionally providing guidance from their own experience. I particularly enjoyed the use of a stratified population to explain the difference between aggregated and disaggregated estimation. Here, and in similar places, the book shines. … well organized … [and] extremely well edited …"
—Andrew Robinson, Australian & New Zealand Journal of Statistics, 2013