Maximum Likelihood Estimation for Sample Surveys

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.

IntroductionNature and role of sample surveysSample designsSurvey data, estimation and analysisWhy analysts of survey data should be interested in maximum likelihood estimationWhy statisticians should be interested in the analysis of survey dataA sample survey exampleMaximum likelihood estimation for infinite populationsBibliographic notesMaximum likelihood theory for sample surveysIntroductionMaximum likelihood using survey dataIllustrative examples with complete responseDealing with nonresponseIllustrative examples with nonresponseBibliographic notesAlternative likelihood-based methods for sample survey dataIntroductionPseudo-likelihoodSample likelihoodAnalytic comparisons of maximum likelihood, pseudolikelihood and sample likelihood estimationThe role of sample inclusion probabilities in analytic analysisBayesian analysisBibliographic notesPopulations with independent unitsIntroductionThe score and information functions for independent unitsBivariate Gaussian populationsMultivariate Gaussian populationsNon-Gaussian auxiliary variablesStratified populationsMultinomial populationsHeterogeneous multinomial logistic populationsBibliographic notesRegression modelsIntroductionA Gaussian exampleParameterization in the Gaussian modelOther methods of estimationNon-Gaussian modelsDifferent auxiliary variable distributionsGeneralized linear modelsSemiparametric and nonparametric methodsBibliographic notesClustered populationsIntroductionA Gaussian group dependent modelA Gaussian group dependent regression modelExtending the Gaussian group dependent regression modelBinary group dependent modelsGrouping modelsBibliographic notesInformative nonresponseIntroductionNonresponse in innovation surveysRegression with item nonresponseRegression with arbitrary nonresponseImputation versus estimationBibliographic notesMaximum likelihood in other complicated situationsIntroductionLikelihood analysis under informative selectionSecondary analysis of sample survey dataCombining summary population information with likelihood analysisLikelihood analysis with probabilistically linked dataBibliographic notes