# Inference and foundations

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- Articles and reports: 12-001-X201800254956Description:
In Italy, the Labor Force Survey (LFS) is conducted quarterly by the National Statistical Institute (ISTAT) to produce estimates of the labor force status of the population at different geographical levels. In particular, ISTAT provides LFS estimates of employed and unemployed counts for local Labor Market Areas (LMAs). LMAs are 611 sub-regional clusters of municipalities and are unplanned domains for which direct estimates have overly large sampling errors. This implies the need of Small Area Estimation (SAE) methods. In this paper, we develop a new area level SAE method that uses a Latent Markov Model (LMM) as linking model. In LMMs, the characteristic of interest, and its evolution in time, is represented by a latent process that follows a Markov chain, usually of first order. Therefore, areas are allowed to change their latent state across time. The proposed model is applied to quarterly data from the LFS for the period 2004 to 2014 and fitted within a hierarchical Bayesian framework using a data augmentation Gibbs sampler. Estimates are compared with those obtained by the classical Fay-Herriot model, by a time-series area level SAE model, and on the basis of data coming from the 2011 Population Census.

Release date: 2018-12-20 - Articles and reports: 12-001-X201800154928Description:
A two-phase process was used by the Substance Abuse and Mental Health Services Administration to estimate the proportion of US adults with serious mental illness (SMI). The first phase was the annual National Survey on Drug Use and Health (NSDUH), while the second phase was a random subsample of adult respondents to the NSDUH. Respondents to the second phase of sampling were clinically evaluated for serious mental illness. A logistic prediction model was fit to this subsample with the SMI status (yes or no) determined by the second-phase instrument treated as the dependent variable and related variables collected on the NSDUH from all adults as the model’s explanatory variables. Estimates were then computed for SMI prevalence among all adults and within adult subpopulations by assigning an SMI status to each NSDUH respondent based on comparing his (her) estimated probability of having SMI to a chosen cut point on the distribution of the predicted probabilities. We investigate alternatives to this standard cut point estimator such as the probability estimator. The latter assigns an estimated probability of having SMI to each NSDUH respondent. The estimated prevalence of SMI is the weighted mean of those estimated probabilities. Using data from NSDUH and its subsample, we show that, although the probability estimator has a smaller mean squared error when estimating SMI prevalence among all adults, it has a greater tendency to be biased at the subpopulation level than the standard cut point estimator.

Release date: 2018-06-21 - Articles and reports: 12-001-X201700254872Description:
This note discusses the theoretical foundations for the extension of the Wilson two-sided coverage interval to an estimated proportion computed from complex survey data. The interval is shown to be asymptotically equivalent to an interval derived from a logistic transformation. A mildly better version is discussed, but users may prefer constructing a one-sided interval already in the literature.

Release date: 2017-12-21 - Articles 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 - 7. 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 - 8. Big Data: A Survey Research PerspectiveArchivedArticles 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

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## Analysis (69)

## Analysis (69) (0 to 10 of 69 results)

- Articles and reports: 12-001-X201800254956Description:
In Italy, the Labor Force Survey (LFS) is conducted quarterly by the National Statistical Institute (ISTAT) to produce estimates of the labor force status of the population at different geographical levels. In particular, ISTAT provides LFS estimates of employed and unemployed counts for local Labor Market Areas (LMAs). LMAs are 611 sub-regional clusters of municipalities and are unplanned domains for which direct estimates have overly large sampling errors. This implies the need of Small Area Estimation (SAE) methods. In this paper, we develop a new area level SAE method that uses a Latent Markov Model (LMM) as linking model. In LMMs, the characteristic of interest, and its evolution in time, is represented by a latent process that follows a Markov chain, usually of first order. Therefore, areas are allowed to change their latent state across time. The proposed model is applied to quarterly data from the LFS for the period 2004 to 2014 and fitted within a hierarchical Bayesian framework using a data augmentation Gibbs sampler. Estimates are compared with those obtained by the classical Fay-Herriot model, by a time-series area level SAE model, and on the basis of data coming from the 2011 Population Census.

Release date: 2018-12-20 - Articles and reports: 12-001-X201800154928Description:
A two-phase process was used by the Substance Abuse and Mental Health Services Administration to estimate the proportion of US adults with serious mental illness (SMI). The first phase was the annual National Survey on Drug Use and Health (NSDUH), while the second phase was a random subsample of adult respondents to the NSDUH. Respondents to the second phase of sampling were clinically evaluated for serious mental illness. A logistic prediction model was fit to this subsample with the SMI status (yes or no) determined by the second-phase instrument treated as the dependent variable and related variables collected on the NSDUH from all adults as the model’s explanatory variables. Estimates were then computed for SMI prevalence among all adults and within adult subpopulations by assigning an SMI status to each NSDUH respondent based on comparing his (her) estimated probability of having SMI to a chosen cut point on the distribution of the predicted probabilities. We investigate alternatives to this standard cut point estimator such as the probability estimator. The latter assigns an estimated probability of having SMI to each NSDUH respondent. The estimated prevalence of SMI is the weighted mean of those estimated probabilities. Using data from NSDUH and its subsample, we show that, although the probability estimator has a smaller mean squared error when estimating SMI prevalence among all adults, it has a greater tendency to be biased at the subpopulation level than the standard cut point estimator.

Release date: 2018-06-21 - Articles and reports: 12-001-X201700254872Description:
This note discusses the theoretical foundations for the extension of the Wilson two-sided coverage interval to an estimated proportion computed from complex survey data. The interval is shown to be asymptotically equivalent to an interval derived from a logistic transformation. A mildly better version is discussed, but users may prefer constructing a one-sided interval already in the literature.

Release date: 2017-12-21 - Articles 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 - 7. 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 - 8. Big Data: A Survey Research PerspectiveArchivedArticles 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

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## Reference (3)

## Reference (3) ((3 results))

- 1. Inverse sampling design algorithmsArchivedSurveys and statistical programs – Documentation: 12-001-X19970013101Description:
In the main body of statistics, sampling is often disposed of by assuming a sampling process that selects random variables such that they are independent and identically distributed (IID). Important techniques, like regression and contingency table analysis, were developed largely in the IID world; hence, adjustments are needed to use them in complex survey settings. Rather than adjust the analysis, however, what is new in the present formulation is to draw a second sample from the original sample. In this second sample, the first set of selections are inverted, so as to yield at the end a simple random sample. Of course, to employ this two-step process to draw a single simple random sample from the usually much larger complex survey would be inefficient, so multiple simple random samples are drawn and a way to base inferences on them developed. Not all original samples can be inverted; but many practical special cases are discussed which cover a wide range of practices.

Release date: 1997-08-18 - Surveys and statistical programs – Documentation: 12-001-X19970013102Description:
The selection of auxiliary variables is considered for regression estimation in finite populations under a simple random sampling design. This problem is a basic one for model-based and model-assisted survey sampling approaches and is of practical importance when the number of variables available is large. An approach is developed in which a mean squared error estimator is minimised. This approach is compared to alternative approaches using a fixed set of auxiliary variables, a conventional significance test criterion, a condition number reduction approach and a ridge regression approach. The proposed approach is found to perform well in terms of efficiency. It is noted that the variable selection approach affects the properties of standard variance estimators and thus leads to a problem of variance estimation.

Release date: 1997-08-18 - 3. A transformation method for finite population sampling calibrated with empirical likelihoodArchivedSurveys and statistical programs – Documentation: 12-001-X19960022980Description:
In this paper, we study a confidence interval estimation method for a finite population average when some auxiliairy information is available. As demonstrated by Royall and Cumberland in a series of empirical studies, naive use of existing methods to construct confidence intervals for population averages may result in very poor conditional coverage probabilities, conditional on the sample mean of the covariate. When this happens, we propose to transform the data to improve the precision of the normal approximation. The transformed data are then used to make inference on the original population average, and the auxiliary information is incorporated into the inference directly, or by calibration with empirical likelihood. Our approach is design-based. We apply our approach to six real populations and find that when transformation is needed, our approach performs well compared to the usual regression method.

Release date: 1997-01-30

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