Inference and foundations
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- 21. Bayesian predictive inference of a proportion under a two-fold small area model with heterogeneous correlations ArchivedArticles and reports: 12-001-X201700114822Description:
We use a Bayesian method to infer about a finite population proportion when binary data are collected using a two-fold sample design from small areas. The two-fold sample design has a two-stage cluster sample design within each area. A former hierarchical Bayesian model assumes that for each area the first stage binary responses are independent Bernoulli distributions, and the probabilities have beta distributions which are parameterized by a mean and a correlation coefficient. The means vary with areas but the correlation is the same over areas. However, to gain some flexibility we have now extended this model to accommodate different correlations. The means and the correlations have independent beta distributions. We call the former model a homogeneous model and the new model a heterogeneous model. All hyperparameters have proper noninformative priors. An additional complexity is that some of the parameters are weakly identified making it difficult to use a standard Gibbs sampler for computation. So we have used unimodal constraints for the beta prior distributions and a blocked Gibbs sampler to perform the computation. We have compared the heterogeneous and homogeneous models using an illustrative example and simulation study. As expected, the two-fold model with heterogeneous correlations is preferred.
Release date: 2017-06-22 - Articles and reports: 12-001-X201600214662Description:
Two-phase sampling designs are often used in surveys when the sampling frame contains little or no auxiliary information. In this note, we shed some light on the concept of invariance, which is often mentioned in the context of two-phase sampling designs. We define two types of invariant two-phase designs: strongly invariant and weakly invariant two-phase designs. Some examples are given. Finally, we describe the implications of strong and weak invariance from an inference point of view.
Release date: 2016-12-20 - 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 - 24. Methodological Challenges in Official Statistics ArchivedArticles and reports: 11-522-X201700014704Description:
We identify several research areas and topics for methodological research in official statistics. We argue why these are important, and why these are the most important ones for official statistics. We describe the main topics in these research areas and sketch what seems to be the most promising ways to address them. Here we focus on: (i) Quality of National accounts, in particular the rate of growth of GNI (ii) Big data, in particular how to create representative estimates and how to make the most of big data when this is difficult or impossible. We also touch upon: (i) Increasing timeliness of preliminary and final statistical estimates (ii) Statistical analysis, in particular of complex and coherent phenomena. These topics are elements in the present Strategic Methodological Research Program that has recently been adopted at Statistics Netherlands
Release date: 2016-03-24 - 25. Big Data: A Survey Research Perspective ArchivedArticles and reports: 11-522-X201700014713Description:
Big data is a term that means different things to different people. To some, it means datasets so large that our traditional processing and analytic systems can no longer accommodate them. To others, it simply means taking advantage of existing datasets of all sizes and finding ways to merge them with the goal of generating new insights. The former view poses a number of important challenges to traditional market, opinion, and social research. In either case, there are implications for the future of surveys that are only beginning to be explored.
Release date: 2016-03-24 - Articles and reports: 11-522-X201700014727Description:
"Probability samples of near-universal frames of households and persons, administered standardized measures, yielding long multivariate data records, and analyzed with statistical procedures reflecting the design – these have been the cornerstones of the empirical social sciences for 75 years. That measurement structure have given the developed world almost all of what we know about our societies and their economies. The stored survey data form a unique historical record. We live now in a different data world than that in which the leadership of statistical agencies and the social sciences were raised. High-dimensional data are ubiquitously being produced from Internet search activities, mobile Internet devices, social media, sensors, retail store scanners, and other devices. Some estimate that these data sources are increasing in size at the rate of 40% per year. Together their sizes swamp that of the probability-based sample surveys. Further, the state of sample surveys in the developed world is not healthy. Falling rates of survey participation are linked with ever-inflated costs of data collection. Despite growing needs for information, the creation of new survey vehicles is hampered by strained budgets for official statistical agencies and social science funders. These combined observations are unprecedented challenges for the basic paradigm of inference in the social and economic sciences. This paper discusses alternative ways forward at this moment in history. "
Release date: 2016-03-24 - Articles and reports: 11-522-X201700014738Description:
In the standard design approach to missing observations, the construction of weight classes and calibration are used to adjust the design weights for the respondents in the sample. Here we use these adjusted weights to define a Dirichlet distribution which can be used to make inferences about the population. Examples show that the resulting procedures have better performance properties than the standard methods when the population is skewed.
Release date: 2016-03-24 - Articles and reports: 11-522-X201700014759Description:
Many of the challenges and opportunities of modern data science have to do with dynamic aspects: evolving populations, the growing volume of administrative and commercial data on individuals and establishments, continuous flows of data and the capacity to analyze and summarize them in real time, and the deterioration of data absent the resources to maintain them. With its emphasis on data quality and supportable results, the domain of Official Statistics is ideal for highlighting statistical and data science issues in a variety of contexts. The messages of the talk include the importance of population frames and their maintenance; the potential for use of multi-frame methods and linkages; how the use of large scale non-survey data as auxiliary information shapes the objects of inference; the complexity of models for large data sets; the importance of recursive methods and regularization; and the benefits of sophisticated data visualization tools in capturing change.
Release date: 2016-03-24 - Articles and reports: 11-522-X201300014251Description:
I present a modeller's perspective on the current status quo in official statistics surveys-based inference. In doing so, I try to identify the strengths and weaknesses of the design and model-based inferential positions that survey sampling, at least as far as the official statistics world is concerned, finds itself at present. I close with an example from adaptive survey design that illustrates why taking a model-based perspective (either frequentist or Bayesian) represents the best way for official statistics to avoid the debilitating 'inferential schizophrenia' that seems inevitable if current methodologies are applied to the emerging information requirements of today's world (and possibly even tomorrow's).
Release date: 2014-10-31 - Articles and reports: 11-522-X201300014252Description:
Although estimating finite populations characteristics from probability samples has been very successful for large samples, inferences from non-probability samples may also be possible. Non-probability samples have been criticized due to self-selection bias and the lack of methods for estimating the precision of the estimates. The wide spread access to the Web and the ability to do very inexpensive data collection on the Web has reinvigorated interest in this topic. We review of non-probability sampling strategies and summarize some of the key issues. We then propose conditions under which non-probability sampling may be a reasonable approach. We conclude with ideas for future research.
Release date: 2014-10-31
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- 21. Bayesian predictive inference of a proportion under a two-fold small area model with heterogeneous correlations ArchivedArticles and reports: 12-001-X201700114822Description:
We use a Bayesian method to infer about a finite population proportion when binary data are collected using a two-fold sample design from small areas. The two-fold sample design has a two-stage cluster sample design within each area. A former hierarchical Bayesian model assumes that for each area the first stage binary responses are independent Bernoulli distributions, and the probabilities have beta distributions which are parameterized by a mean and a correlation coefficient. The means vary with areas but the correlation is the same over areas. However, to gain some flexibility we have now extended this model to accommodate different correlations. The means and the correlations have independent beta distributions. We call the former model a homogeneous model and the new model a heterogeneous model. All hyperparameters have proper noninformative priors. An additional complexity is that some of the parameters are weakly identified making it difficult to use a standard Gibbs sampler for computation. So we have used unimodal constraints for the beta prior distributions and a blocked Gibbs sampler to perform the computation. We have compared the heterogeneous and homogeneous models using an illustrative example and simulation study. As expected, the two-fold model with heterogeneous correlations is preferred.
Release date: 2017-06-22 - Articles and reports: 12-001-X201600214662Description:
Two-phase sampling designs are often used in surveys when the sampling frame contains little or no auxiliary information. In this note, we shed some light on the concept of invariance, which is often mentioned in the context of two-phase sampling designs. We define two types of invariant two-phase designs: strongly invariant and weakly invariant two-phase designs. Some examples are given. Finally, we describe the implications of strong and weak invariance from an inference point of view.
Release date: 2016-12-20 - 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 - 24. Methodological Challenges in Official Statistics ArchivedArticles and reports: 11-522-X201700014704Description:
We identify several research areas and topics for methodological research in official statistics. We argue why these are important, and why these are the most important ones for official statistics. We describe the main topics in these research areas and sketch what seems to be the most promising ways to address them. Here we focus on: (i) Quality of National accounts, in particular the rate of growth of GNI (ii) Big data, in particular how to create representative estimates and how to make the most of big data when this is difficult or impossible. We also touch upon: (i) Increasing timeliness of preliminary and final statistical estimates (ii) Statistical analysis, in particular of complex and coherent phenomena. These topics are elements in the present Strategic Methodological Research Program that has recently been adopted at Statistics Netherlands
Release date: 2016-03-24 - 25. Big Data: A Survey Research Perspective ArchivedArticles and reports: 11-522-X201700014713Description:
Big data is a term that means different things to different people. To some, it means datasets so large that our traditional processing and analytic systems can no longer accommodate them. To others, it simply means taking advantage of existing datasets of all sizes and finding ways to merge them with the goal of generating new insights. The former view poses a number of important challenges to traditional market, opinion, and social research. In either case, there are implications for the future of surveys that are only beginning to be explored.
Release date: 2016-03-24 - Articles and reports: 11-522-X201700014727Description:
"Probability samples of near-universal frames of households and persons, administered standardized measures, yielding long multivariate data records, and analyzed with statistical procedures reflecting the design – these have been the cornerstones of the empirical social sciences for 75 years. That measurement structure have given the developed world almost all of what we know about our societies and their economies. The stored survey data form a unique historical record. We live now in a different data world than that in which the leadership of statistical agencies and the social sciences were raised. High-dimensional data are ubiquitously being produced from Internet search activities, mobile Internet devices, social media, sensors, retail store scanners, and other devices. Some estimate that these data sources are increasing in size at the rate of 40% per year. Together their sizes swamp that of the probability-based sample surveys. Further, the state of sample surveys in the developed world is not healthy. Falling rates of survey participation are linked with ever-inflated costs of data collection. Despite growing needs for information, the creation of new survey vehicles is hampered by strained budgets for official statistical agencies and social science funders. These combined observations are unprecedented challenges for the basic paradigm of inference in the social and economic sciences. This paper discusses alternative ways forward at this moment in history. "
Release date: 2016-03-24 - Articles and reports: 11-522-X201700014738Description:
In the standard design approach to missing observations, the construction of weight classes and calibration are used to adjust the design weights for the respondents in the sample. Here we use these adjusted weights to define a Dirichlet distribution which can be used to make inferences about the population. Examples show that the resulting procedures have better performance properties than the standard methods when the population is skewed.
Release date: 2016-03-24 - Articles and reports: 11-522-X201700014759Description:
Many of the challenges and opportunities of modern data science have to do with dynamic aspects: evolving populations, the growing volume of administrative and commercial data on individuals and establishments, continuous flows of data and the capacity to analyze and summarize them in real time, and the deterioration of data absent the resources to maintain them. With its emphasis on data quality and supportable results, the domain of Official Statistics is ideal for highlighting statistical and data science issues in a variety of contexts. The messages of the talk include the importance of population frames and their maintenance; the potential for use of multi-frame methods and linkages; how the use of large scale non-survey data as auxiliary information shapes the objects of inference; the complexity of models for large data sets; the importance of recursive methods and regularization; and the benefits of sophisticated data visualization tools in capturing change.
Release date: 2016-03-24 - Articles and reports: 11-522-X201300014251Description:
I present a modeller's perspective on the current status quo in official statistics surveys-based inference. In doing so, I try to identify the strengths and weaknesses of the design and model-based inferential positions that survey sampling, at least as far as the official statistics world is concerned, finds itself at present. I close with an example from adaptive survey design that illustrates why taking a model-based perspective (either frequentist or Bayesian) represents the best way for official statistics to avoid the debilitating 'inferential schizophrenia' that seems inevitable if current methodologies are applied to the emerging information requirements of today's world (and possibly even tomorrow's).
Release date: 2014-10-31 - Articles and reports: 11-522-X201300014252Description:
Although estimating finite populations characteristics from probability samples has been very successful for large samples, inferences from non-probability samples may also be possible. Non-probability samples have been criticized due to self-selection bias and the lack of methods for estimating the precision of the estimates. The wide spread access to the Web and the ability to do very inexpensive data collection on the Web has reinvigorated interest in this topic. We review of non-probability sampling strategies and summarize some of the key issues. We then propose conditions under which non-probability sampling may be a reasonable approach. We conclude with ideas for future research.
Release date: 2014-10-31
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