1st Edition

Maximum Likelihood Estimation for Sample Surveys

    391 Pages 10 B/W Illustrations
    by Chapman & Hall

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    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.

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

    Maximum likelihood in other complicated situations
    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


    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