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- Articles and reports: 12-001-X202200200001Description:
Conceptual arguments and examples are presented suggesting that the Bayesian approach to survey inference can address the many and varied challenges of survey analysis. Bayesian models that incorporate features of the complex design can yield inferences that are relevant for the specific data set obtained, but also have good repeated-sampling properties. Examples focus on the role of auxiliary variables and sampling weights, and methods for handling nonresponse. The article offers ten top reasons for favoring the Bayesian approach to survey inference.
Release date: 2022-12-15 - Articles and reports: 12-001-X201600114545Description:
The estimation of quantiles is an important topic not only in the regression framework, but also in sampling theory. A natural alternative or addition to quantiles are expectiles. Expectiles as a generalization of the mean have become popular during the last years as they not only give a more detailed picture of the data than the ordinary mean, but also can serve as a basis to calculate quantiles by using their close relationship. We show, how to estimate expectiles under sampling with unequal probabilities and how expectiles can be used to estimate the distribution function. The resulting fitted distribution function estimator can be inverted leading to quantile estimates. We run a simulation study to investigate and compare the efficiency of the expectile based estimator.
Release date: 2016-06-22 - 3. A weighted composite likelihood approach to inference for two-level models from survey data ArchivedArticles and reports: 12-001-X201300211887Description:
Multi-level models are extensively used for analyzing survey data with the design hierarchy matching the model hierarchy. We propose a unified approach, based on a design-weighted log composite likelihood, for two-level models that leads to design-model consistent estimators of the model parameters even when the within cluster sample sizes are small provided the number of sample clusters is large. This method can handle both linear and generalized linear two-level models and it requires level 2 and level 1 inclusion probabilities and level 1 joint inclusion probabilities, where level 2 represents a cluster and level 1 an element within a cluster. Results of a simulation study demonstrating superior performance of the proposed method relative to existing methods under informative sampling are also reported.
Release date: 2014-01-15 - Articles and reports: 12-001-X201000111250Description:
We propose a Bayesian Penalized Spline Predictive (BPSP) estimator for a finite population proportion in an unequal probability sampling setting. This new method allows the probabilities of inclusion to be directly incorporated into the estimation of a population proportion, using a probit regression of the binary outcome on the penalized spline of the inclusion probabilities. The posterior predictive distribution of the population proportion is obtained using Gibbs sampling. The advantages of the BPSP estimator over the Hájek (HK), Generalized Regression (GR), and parametric model-based prediction estimators are demonstrated by simulation studies and a real example in tax auditing. Simulation studies show that the BPSP estimator is more efficient, and its 95% credible interval provides better confidence coverage with shorter average width than the HK and GR estimators, especially when the population proportion is close to zero or one or when the sample is small. Compared to linear model-based predictive estimators, the BPSP estimators are robust to model misspecification and influential observations in the sample.
Release date: 2010-06-29 - Articles and reports: 11-536-X200900110806Description:
Recent work using a pseudo empirical likelihood (EL) method for finite population inferences with complex survey data focused primarily on a single survey sample, non-stratified or stratified, with considerable effort devoted to computational procedures. In this talk we present a pseudo empirical likelihood approach to inference from multiple surveys and multiple-frame surveys, two commonly encountered problems in survey practice. We show that inferences about the common parameter of interest and the effective use of various types of auxiliary information can be conveniently carried out through the constrained maximization of joint pseudo EL function. We obtain asymptotic results which are used for constructing the pseudo EL ratio confidence intervals, either using a chi-square approximation or a bootstrap calibration. All related computational problems can be handled using existing algorithms on stratified sampling after suitable re-formulation.
Release date: 2009-08-11 - 6. Comparison of design-based and model-based methods in analyzing complex health survey data: A case study ArchivedArticles and reports: 11-522-X20020016708Description:
In this paper, we discuss the analysis of complex health survey data by using multivariate modelling techniques. Main interests are in various design-based and model-based methods that aim at accounting for the design complexities, including clustering, stratification and weighting. Methods covered include generalized linear modelling based on pseudo-likelihood and generalized estimating equations, linear mixed models estimated by restricted maximum likelihood, and hierarchical Bayes techniques using Markov Chain Monte Carlo (MCMC) methods. The methods will be compared empirically, using data from an extensive health interview and examination survey conducted in Finland in 2000 (Health 2000 Study).
The data of the Health 2000 Study were collected using personal interviews, questionnaires and clinical examinations. A stratified two-stage cluster sampling design was used in the survey. The sampling design involved positive intra-cluster correlation for many study variables. For a closer investigation, we selected a small number of study variables from the health interview and health examination phases. In many cases, the different methods produced similar numerical results and supported similar statistical conclusions. Methods that failed to account for the design complexities sometimes led to conflicting conclusions. We also discuss the application of the methods in this paper by using standard statistical software products.
Release date: 2004-09-13
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- Articles and reports: 12-001-X202200200001Description:
Conceptual arguments and examples are presented suggesting that the Bayesian approach to survey inference can address the many and varied challenges of survey analysis. Bayesian models that incorporate features of the complex design can yield inferences that are relevant for the specific data set obtained, but also have good repeated-sampling properties. Examples focus on the role of auxiliary variables and sampling weights, and methods for handling nonresponse. The article offers ten top reasons for favoring the Bayesian approach to survey inference.
Release date: 2022-12-15 - Articles and reports: 12-001-X201600114545Description:
The estimation of quantiles is an important topic not only in the regression framework, but also in sampling theory. A natural alternative or addition to quantiles are expectiles. Expectiles as a generalization of the mean have become popular during the last years as they not only give a more detailed picture of the data than the ordinary mean, but also can serve as a basis to calculate quantiles by using their close relationship. We show, how to estimate expectiles under sampling with unequal probabilities and how expectiles can be used to estimate the distribution function. The resulting fitted distribution function estimator can be inverted leading to quantile estimates. We run a simulation study to investigate and compare the efficiency of the expectile based estimator.
Release date: 2016-06-22 - 3. A weighted composite likelihood approach to inference for two-level models from survey data ArchivedArticles and reports: 12-001-X201300211887Description:
Multi-level models are extensively used for analyzing survey data with the design hierarchy matching the model hierarchy. We propose a unified approach, based on a design-weighted log composite likelihood, for two-level models that leads to design-model consistent estimators of the model parameters even when the within cluster sample sizes are small provided the number of sample clusters is large. This method can handle both linear and generalized linear two-level models and it requires level 2 and level 1 inclusion probabilities and level 1 joint inclusion probabilities, where level 2 represents a cluster and level 1 an element within a cluster. Results of a simulation study demonstrating superior performance of the proposed method relative to existing methods under informative sampling are also reported.
Release date: 2014-01-15 - Articles and reports: 12-001-X201000111250Description:
We propose a Bayesian Penalized Spline Predictive (BPSP) estimator for a finite population proportion in an unequal probability sampling setting. This new method allows the probabilities of inclusion to be directly incorporated into the estimation of a population proportion, using a probit regression of the binary outcome on the penalized spline of the inclusion probabilities. The posterior predictive distribution of the population proportion is obtained using Gibbs sampling. The advantages of the BPSP estimator over the Hájek (HK), Generalized Regression (GR), and parametric model-based prediction estimators are demonstrated by simulation studies and a real example in tax auditing. Simulation studies show that the BPSP estimator is more efficient, and its 95% credible interval provides better confidence coverage with shorter average width than the HK and GR estimators, especially when the population proportion is close to zero or one or when the sample is small. Compared to linear model-based predictive estimators, the BPSP estimators are robust to model misspecification and influential observations in the sample.
Release date: 2010-06-29 - Articles and reports: 11-536-X200900110806Description:
Recent work using a pseudo empirical likelihood (EL) method for finite population inferences with complex survey data focused primarily on a single survey sample, non-stratified or stratified, with considerable effort devoted to computational procedures. In this talk we present a pseudo empirical likelihood approach to inference from multiple surveys and multiple-frame surveys, two commonly encountered problems in survey practice. We show that inferences about the common parameter of interest and the effective use of various types of auxiliary information can be conveniently carried out through the constrained maximization of joint pseudo EL function. We obtain asymptotic results which are used for constructing the pseudo EL ratio confidence intervals, either using a chi-square approximation or a bootstrap calibration. All related computational problems can be handled using existing algorithms on stratified sampling after suitable re-formulation.
Release date: 2009-08-11 - 6. Comparison of design-based and model-based methods in analyzing complex health survey data: A case study ArchivedArticles and reports: 11-522-X20020016708Description:
In this paper, we discuss the analysis of complex health survey data by using multivariate modelling techniques. Main interests are in various design-based and model-based methods that aim at accounting for the design complexities, including clustering, stratification and weighting. Methods covered include generalized linear modelling based on pseudo-likelihood and generalized estimating equations, linear mixed models estimated by restricted maximum likelihood, and hierarchical Bayes techniques using Markov Chain Monte Carlo (MCMC) methods. The methods will be compared empirically, using data from an extensive health interview and examination survey conducted in Finland in 2000 (Health 2000 Study).
The data of the Health 2000 Study were collected using personal interviews, questionnaires and clinical examinations. A stratified two-stage cluster sampling design was used in the survey. The sampling design involved positive intra-cluster correlation for many study variables. For a closer investigation, we selected a small number of study variables from the health interview and health examination phases. In many cases, the different methods produced similar numerical results and supported similar statistical conclusions. Methods that failed to account for the design complexities sometimes led to conflicting conclusions. We also discuss the application of the methods in this paper by using standard statistical software products.
Release date: 2004-09-13
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