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All (92)

All (92) (0 to 10 of 92 results)

1. Dealing with undercoverage for non-probability survey samples
Articles and reports: 12-001-X202300200005
Description: Population undercoverage is one of the main hurdles faced by statistical analysis with non-probability survey samples. We discuss two typical scenarios of undercoverage, namely, stochastic undercoverage and deterministic undercoverage. We argue that existing estimation methods under the positivity assumption on the propensity scores (i.e., the participation probabilities) can be directly applied to handle the scenario of stochastic undercoverage. We explore strategies for mitigating biases in estimating the mean of the target population under deterministic undercoverage. In particular, we examine a split population approach based on a convex hull formulation, and construct estimators with reduced biases. A doubly robust estimator can be constructed if a followup subsample of the reference probability survey with measurements on the study variable becomes feasible. Performances of six competing estimators are investigated through a simulation study and issues which require further investigation are briefly discussed.
Release date: 2024-01-03
2. QR prediction for statistical data integration
Articles and reports: 12-001-X202300200009
Description: In this paper, we investigate how a big non-probability database can be used to improve estimates of finite population totals from a small probability sample through data integration techniques. In the situation where the study variable is observed in both data sources, Kim and Tam (2021) proposed two design-consistent estimators that can be justified through dual frame survey theory. First, we provide conditions ensuring that these estimators are more efficient than the Horvitz-Thompson estimator when the probability sample is selected using either Poisson sampling or simple random sampling without replacement. Then, we study the class of QR predictors, introduced by Särndal and Wright (1984), to handle the less common case where the non-probability database contains no study variable but auxiliary variables. We also require that the non-probability database is large and can be linked to the probability sample. We provide conditions ensuring that the QR predictor is asymptotically design-unbiased. We derive its asymptotic design variance and provide a consistent design-based variance estimator. We compare the design properties of different predictors, in the class of QR predictors, through a simulation study. This class includes a model-based predictor, a model-assisted estimator and a cosmetic estimator. In our simulation setups, the cosmetic estimator performed slightly better than the model-assisted estimator. These findings are confirmed by an application to La Poste data, which also illustrates that the properties of the cosmetic estimator are preserved irrespective of the observed non-probability sample.
Release date: 2024-01-03
3. The missing information principle ‒ A paradigm for analysis of messy sample survey data
Articles and reports: 12-001-X202300200018
Description: Sample surveys, as a tool for policy development and evaluation and for scientific, social and economic research, have been employed for over a century. In that time, they have primarily served as tools for collecting data for enumerative purposes. Estimation of these characteristics has been typically based on weighting and repeated sampling, or design-based, inference. However, sample data have also been used for modelling the unobservable processes that gave rise to the finite population data. This type of use has been termed analytic, and often involves integrating the sample data with data from secondary sources.
Alternative approaches to inference in these situations, drawing inspiration from mainstream statistical modelling, have been strongly promoted. The principal focus of these alternatives has been on allowing for informative sampling. Modern survey sampling, though, is more focussed on situations where the sample data are in fact part of a more complex set of data sources all carrying relevant information about the process of interest. When an efficient modelling method such as maximum likelihood is preferred, the issue becomes one of how it should be modified to account for both complex sampling designs and multiple data sources. Here application of the Missing Information Principle provides a clear way forward.
In this paper I review how this principle has been applied to resolve so-called “messy” data analysis issues in sampling. I also discuss a scenario that is a consequence of the rapid growth in auxiliary data sources for survey data analysis. This is where sampled records from one accessible source or register are linked to records from another less accessible source, with values of the response variable of interest drawn from this second source, and where a key output is small area estimates for the response variable for domains defined on the first source.
Release date: 2024-01-03
4. Bayes, buttressed by design-based ideas, is the best overarching paradigm for sample survey inference
Articles and reports: 12-001-X202200200001
Description:
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
5. Statistical inference with non-probability survey samples
Articles and reports: 12-001-X202200200002
Description:
We provide a critical review and some extended discussions on theoretical and practical issues with analysis of non-probability survey samples. We attempt to present rigorous inferential frameworks and valid statistical procedures under commonly used assumptions, and address issues on the justification and verification of assumptions in practical applications. Some current methodological developments are showcased, and problems which require further investigation are mentioned. While the focus of the paper is on non-probability samples, the essential role of probability survey samples with rich and relevant information on auxiliary variables is highlighted.
Release date: 2022-12-15
6. Comments by Michael A. Bailey on “Statistical inference with non-probability survey samples” – Non-probability samples: An assessment and way forward
Articles and reports: 12-001-X202200200003
Description:
Non-probability surveys play an increasing role in survey research. Wu’s essay ably brings together the many tools available when assuming the non-response is conditionally independent of the study variable. In this commentary, I explore how to integrate Wu’s insights in a broader framework that encompasses the case in which non-response depends on the study variable, a case that is particularly dangerous in non-probabilistic polling.

Release date: 2022-12-15
7. Comments by Michael R. Elliott on “Statistical inference with non-probability survey samples”
Articles and reports: 12-001-X202200200004
Description:
This discussion attempts to add to Wu’s review of inference from non-probability samples, as well as to highlighting aspects that are likely avenues for useful additional work. It concludes with a call for an organized stable of high-quality probability surveys that will be focused on providing adjustment information for non-probability surveys.

Release date: 2022-12-15
8. Comments by Sharon L. Lohr on “Statistical inference with non-probability survey samples”
Articles and reports: 12-001-X202200200005
Description:
Strong assumptions are required to make inferences about a finite population from a nonprobability sample. Statistics from a nonprobability sample should be accompanied by evidence that the assumptions are met and that point estimates and confidence intervals are fit for use. I describe some diagnostics that can be used to assess the model assumptions, and discuss issues to consider when deciding whether to use data from a nonprobability sample.

Release date: 2022-12-15
9. Comments by Xiao-Li Meng on “Statistical inference with non-probability survey samples” – Miniaturizing data defect correlation: A versatile strategy for handling non-probability samples
Articles and reports: 12-001-X202200200006
Description:
Non-probability samples are deprived of the powerful design probability for randomization-based inference. This deprivation, however, encourages us to take advantage of a natural divine probability that comes with any finite population. A key metric from this perspective is the data defect correlation (ddc), which is the model-free finite-population correlation between the individual’s sample inclusion indicator and the individual’s attribute being sampled. A data generating mechanism is equivalent to a probability sampling, in terms of design effect, if and only if its corresponding ddc is of N-1/2 (stochastic) order, where N is the population size (Meng, 2018). Consequently, existing valid linear estimation methods for non-probability samples can be recast as various strategies to miniaturize the ddc down to the N-1/2 order. The quasi design-based methods accomplish this task by diminishing the variability among the N inclusion propensities via weighting. The super-population model-based approach achieves the same goal through reducing the variability of the N individual attributes by replacing them with their residuals from a regression model. The doubly robust estimators enjoy their celebrated property because a correlation is zero whenever one of the variables being correlated is constant, regardless of which one. Understanding the commonality of these methods through ddc also helps us see clearly the possibility of “double-plus robustness”: a valid estimation without relying on the full validity of either the regression model or the estimated inclusion propensity, neither of which is guaranteed because both rely on device probability. The insight generated by ddc also suggests counterbalancing sub-sampling, a strategy aimed at creating a miniature of the population out of a non-probability sample, and with favorable quality-quantity trade-off because mean-squared errors are much more sensitive to ddc than to the sample size, especially for large populations.

Release date: 2022-12-15
10. Comments by Zhonglei Wang and Jae Kwang Kim on “Statistical inference with non-probability survey samples”
Articles and reports: 12-001-X202200200007
Description:
Statistical inference with non-probability survey samples is a notoriously challenging problem in statistics. We introduce two new methods of nonparametric propensity score technique for weighting in the non-probability samples. One is the information projection approach and the other is the uniform calibration in the reproducing kernel Hilbert space.

Release date: 2022-12-15

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Analysis (92)

Analysis (92) (80 to 90 of 92 results)

81. Design effects for correlated (P_i - P_j) Archived
Articles and reports: 12-001-X199500214398
Description:
We present empirical evidence from 14 surveys in six countries concerning the existence and magnitude of design effects (defts) for five designs of two major types. The first type concerns deft (p_i – p_j), the difference of two proportions from a polytomous variable of three or more categories. The second type uses Chi-square tests for differences from two samples. We find that for all variables in all designs deft (p_i – p_j) \cong [deft (p_i) + deft (p_j)] / 2 are good approximations. These are empirical results, and exceptions disprove the existence of mere analytical inequalities. These results hold despite great variations of defts between variables and also between categories of the same variables. They also show the need for sample survey treatment of survey data even for analytical statistics. Furthermore they permit useful approximations of deft (p_i – p_j) from more accessible deft (p_i) values.
Release date: 1995-12-15
82. Median estimation using auxiliary information Archived
Articles and reports: 12-001-X199500114408
Description:
The problem of estimating the median of a finite population when an auxiliary variable is present is considered. Point and interval estimators based on a non-informative Bayesian approach are proposed. The point estimator is compared to other possible estimators and is seen to perform well in a variety of situations.
Release date: 1995-06-15
83. Robust model-based methods for analytic surveys Archived
Articles and reports: 12-001-X199200214487
Description:
This paper reviews the idea of robustness for randomisation and model-based inference for descriptive and analytic surveys. The lack of robustness for model-based procedures can be partially overcome by careful design. In this paper a robust model-based approach to analysis is proposed based on smoothing methods.
Release date: 1992-12-15
84. Robustness and optimal design under prediction models for finite populations Archived
Articles and reports: 12-001-X199200214488
Description:
In many finite population sampling problems the design that is optimal in the sense of minimizing the variance of the best linear unbiased estimator under a particular working model is bad in the sense of robustness - it leaves the estimator extremely vulnerable to bias if the working model is incorrect. However there are some important models under which one design provides both efficiency and robustness. We present a theorem that identifies such models and their optimal designs.
Release date: 1992-12-15
85. A theory of quota surveys Archived
Articles and reports: 12-001-X199100214504
Description:
Simple or marginal quota surveys are analyzed using two methods: (1) behaviour modelling (superpopulation model) and prediction estimation, and (2) sample modelling (simple restricted random sampling) and estimation derived from the sample distribution. In both cases the limitations of the theory used to establish the variance formulas and estimates when measuring totals are described. An extension of the quota method (non-proportional quotas) is also briefly described and analyzed. In some cases, this may provide a very significant improvement in survey precision. The advantages of the quota method are compared with those of random sampling. The latter remains indispensable in the case of large scale surveys within the framework of Official Statistics.
Release date: 1991-12-16
86. Marginal and approximate conditional likelihoods for sampling on successive occasions Archived
Articles and reports: 12-001-X199100114521
Description:
Marginal and approximate conditional likelihoods are given for the correlation parameters in a normal linear regression model with correlated errors. This general likelihood approach is applied to obtain marginal and approximate conditional likelihoods for the correlation parameters in sampling on successive occasions under both simple random sampling on each occasion and more complex surveys.
Release date: 1991-06-14
87. Comments by Morris H. Hansen on papers in the Special section – History and emerging issues in censuses and surveys Archived
Articles and reports: 12-001-X199000114561
Description:
This note by Morris H. Hansen presents a discussion of the four papers in the special section “History and emerging issues in censuses and surveys” by: i) J.N.K. Rao and D.R. Bellhouse, ii) S.E. Fienberg and J.M. Tanur, iii) B.A. Bailar, and iv) L. Kish.

Release date: 1990-06-15
88. History and development of the theoretical foundations of survey based estimation and analysis Archived
Articles and reports: 12-001-X199000114560
Description:
Early developments in sampling theory and methods largely concentrated on efficient sampling designs and associated estimation techniques for population totals or means. More recently, the theoretical foundations of survey based estimation have also been critically examined, and formal frameworks for inference on totals or means have emerged. During the past 10 years or so, rapid progress has also been made in the development of methods for the analysis of survey data that take account of the complexity of the sampling design. The scope of this paper is restricted to an overview and appraisal of some of these developments.
Release date: 1990-06-15
89. Simultaneous confidence intervals for proportions under cluster sampling Archived
Articles and reports: 12-001-X198900214568
Description:
The paper describes a Monte Carlo study of simultaneous confidence interval procedures for k > 2 proportions, under a model of two-stage cluster sampling. The procedures investigated include: (i) standard multinomial intervals; (ii) Scheffé intervals based on sample estimates of the variances of cell proportions; (iii) Quesenberry-Hurst intervals adapted for clustered data using Rao and Scott’s first and second order adjustments to X^2; (iv) simple Bonferroni intervals; (v) Bonferroni intervals based on transformations of the estimated proportions; (vi) Bonferroni intervals computed using the critical points of Student’s t. In several realistic situations, actual coverage rates of the multinomial procedures were found to be seriously depressed compared to the nominal rate. The best performing intervals, from the point of view of coverage rates and coverage symmetry (an extension of an idea due to Jennings), were the t-based Bonferroni intervals derived using log and logit transformations. Of the Scheffé-like procedures, the best performance was provided by Quesenberry-Hurst intervals in combination with first-order Rao-Scott adjustments.
Release date: 1989-12-15
90. Conditional inference in survey sampling Archived
Articles and reports: 12-001-X198500114364
Description:
Conventional methods of inference in survey sampling are critically examined. The need for conditioning the inference on recognizable subsets of the population is emphasized. A number of real examples involving random sample sizes are presented to illustrate inferences conditional on the realized sample configuration and associated difficulties. The examples include the following: estimation of (a) population mean under simple random sampling; (b) population mean in the presence of outliers; (c) domain total and domain mean; (d) population mean with two-way stratification; (e) population mean in the presence of non-responses; (f) population mean under general designs. The conditional bias and the conditional variance of estimators of a population mean (or a domain mean or total), and the associated confidence intervals, are examined.
Release date: 1985-06-14

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Date modified:: 2024-05-22