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All (105) (40 to 50 of 105 results)

41. Bayesian inference for finite population quantiles from unequal probability samples Archived
Articles and reports: 12-001-X201200211758
Description:
This paper develops two Bayesian methods for inference about finite population quantiles of continuous survey variables from unequal probability sampling. The first method estimates cumulative distribution functions of the continuous survey variable by fitting a number of probit penalized spline regression models on the inclusion probabilities. The finite population quantiles are then obtained by inverting the estimated distribution function. This method is quite computationally demanding. The second method predicts non-sampled values by assuming a smoothly-varying relationship between the continuous survey variable and the probability of inclusion, by modeling both the mean function and the variance function using splines. The two Bayesian spline-model-based estimators yield a desirable balance between robustness and efficiency. Simulation studies show that both methods yield smaller root mean squared errors than the sample-weighted estimator and the ratio and difference estimators described by Rao, Kovar, and Mantel (RKM 1990), and are more robust to model misspecification than the regression through the origin model-based estimator described in Chambers and Dunstan (1986). When the sample size is small, the 95% credible intervals of the two new methods have closer to nominal confidence coverage than the sample-weighted estimator.
Release date: 2012-12-19
42. A hierarchical Bayesian nonresponse model for two-way categorical data from small areas with uncertainty about ignorability Archived
Articles and reports: 12-001-X201200111688
Description:
We study the problem of nonignorable nonresponse in a two dimensional contingency table which can be constructed for each of several small areas when there is both item and unit nonresponse. In general, the provision for both types of nonresponse with small areas introduces significant additional complexity in the estimation of model parameters. For this paper, we conceptualize the full data array for each area to consist of a table for complete data and three supplemental tables for missing row data, missing column data, and missing row and column data. For nonignorable nonresponse, the total cell probabilities are allowed to vary by area, cell and these three types of "missingness". The underlying cell probabilities (i.e., those which would apply if full classification were always possible) for each area are generated from a common distribution and their similarity across the areas is parametrically quantified. Our approach is an extension of the selection approach for nonignorable nonresponse investigated by Nandram and Choi (2002a, b) for binary data; this extension creates additional complexity because of the multivariate nature of the data coupled with the small area structure. As in that earlier work, the extension is an expansion model centered on an ignorable nonresponse model so that the total cell probability is dependent upon which of the categories is the response. Our investigation employs hierarchical Bayesian models and Markov chain Monte Carlo methods for posterior inference. The models and methods are illustrated with data from the third National Health and Nutrition Examination Survey.
Release date: 2012-06-27
43. Modelling of complex survey data: Why model? Why is it a problem? How can we approach it? Archived
Articles and reports: 12-001-X201100211602
Description:
This article attempts to answer the three questions appearing in the title. It starts by discussing unique features of complex survey data not shared by other data sets, which require special attention but suggest a large variety of diverse inference procedures. Next a large number of different approaches proposed in the literature for handling these features are reviewed with discussion on their merits and limitations. The approaches differ in the conditions underlying their use, additional data required for their application, goodness of fit testing, the inference objectives that they accommodate, statistical efficiency, computational demands, and the skills required from analysts fitting the model. The last part of the paper presents simulation results, which compare the approaches when estimating linear regression coefficients from a stratified sample in terms of bias, variance, and coverage rates. It concludes with a short discussion of pending issues.
Release date: 2011-12-21
44. A Bayesian analysis of small area probabilities under a constraint Archived
Articles and reports: 12-001-X201100211603
Description:
In many sample surveys there are items requesting binary response (e.g., obese, not obese) from a number of small areas. Inference is required about the probability for a positive response (e.g., obese) in each area, the probability being the same for all individuals in each area and different across areas. Because of the sparseness of the data within areas, direct estimators are not reliable, and there is a need to use data from other areas to improve inference for a specific area. Essentially, a priori the areas are assumed to be similar, and a hierarchical Bayesian model, the standard beta-binomial model, is a natural choice. The innovation is that a practitioner may have much-needed additional prior information about a linear combination of the probabilities. For example, a weighted average of the probabilities is a parameter, and information can be elicited about this parameter, thereby making the Bayesian paradigm appropriate. We have modified the standard beta-binomial model for small areas to incorporate the prior information on the linear combination of the probabilities, which we call a constraint. Thus, there are three cases. The practitioner (a) does not specify a constraint, (b) specifies a constraint and the parameter completely, and (c) specifies a constraint and information which can be used to construct a prior distribution for the parameter. The griddy Gibbs sampler is used to fit the models. To illustrate our method, we use an example on obesity of children in the National Health and Nutrition Examination Survey in which the small areas are formed by crossing school (middle, high), ethnicity (white, black, Mexican) and gender (male, female). We use a simulation study to assess some of the statistical features of our method. We have shown that the gain in precision beyond (a) is in the order with (b) larger than (c).
Release date: 2011-12-21
45. Small area estimation under transformation to linearity Archived
Articles and reports: 12-001-X201100111446
Description:
Small area estimation based on linear mixed models can be inefficient when the underlying relationships are non-linear. In this paper we introduce SAE techniques for variables that can be modelled linearly following a non-linear transformation. In particular, we extend the model-based direct estimator of Chandra and Chambers (2005, 2009) to data that are consistent with a linear mixed model in the logarithmic scale, using model calibration to define appropriate weights for use in this estimator. Our results show that the resulting transformation-based estimator is both efficient and robust with respect to the distribution of the random effects in the model. An application to business survey data demonstrates the satisfactory performance of the method.
Release date: 2011-06-29
46. The use of estimating equations to perform a calibration on complex parameters Archived
Articles and reports: 12-001-X201100111451
Description:
In the calibration method proposed by Deville and Särndal (1992), the calibration equations take only exact estimates of auxiliary variable totals into account. This article examines other parameters besides totals for calibration. Parameters that are considered complex include the ratio, median or variance of auxiliary variables.
Release date: 2011-06-29
47. Bayesian penalized spline model-based inference for finite population proportion in unequal probability sampling Archived
Articles and reports: 12-001-X201000111250
Description:
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
48. Pseudo empirical likelihood inference for multiple surveys and multiple-frame surveys Archived
Articles and reports: 11-536-X200900110806
Description:
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
49. A Bayesian allocation of undecided voters Archived
Articles and reports: 12-001-X200800110606
Description:
Data from election polls in the US are typically presented in two-way categorical tables, and there are many polls before the actual election in November. For example, in the Buckeye State Poll in 1998 for governor there are three polls, January, April and October; the first category represents the candidates (e.g., Fisher, Taft and other) and the second category represents the current status of the voters (likely to vote and not likely to vote for governor of Ohio). There is a substantial number of undecided voters for one or both categories in all three polls, and we use a Bayesian method to allocate the undecided voters to the three candidates. This method permits modeling different patterns of missingness under ignorable and nonignorable assumptions, and a multinomial-Dirichlet model is used to estimate the cell probabilities which can help to predict the winner. We propose a time-dependent nonignorable nonresponse model for the three tables. Here, a nonignorable nonresponse model is centered on an ignorable nonresponse model to induce some flexibility and uncertainty about ignorabilty or nonignorability. As competitors we also consider two other models, an ignorable and a nonignorable nonresponse model. These latter two models assume a common stochastic process to borrow strength over time. Markov chain Monte Carlo methods are used to fit the models. We also construct a parameter that can potentially be used to predict the winner among the candidates in the November election.
Release date: 2008-06-26
50. Robust Bayesian predictive inference for the finite population quantile of a small area Archived
Articles and reports: 11-522-X200600110392
Description:
We use a robust Bayesian method to analyze data with possibly nonignorable nonresponse and selection bias. A robust logistic regression model is used to relate the response indicators (Bernoulli random variable) to the covariates, which are available for everyone in the finite population. This relationship can adequately explain the difference between respondents and nonrespondents for the sample. This robust model is obtained by expanding the standard logistic regression model to a mixture of Student's distributions, thereby providing propensity scores (selection probability) which are used to construct adjustment cells. The nonrespondents' values are filled in by drawing a random sample from a kernel density estimator, formed from the respondents' values within the adjustment cells. Prediction uses a linear spline rank-based regression of the response variable on the covariates by areas, sampling the errors from another kernel density estimator; thereby further robustifying our method. We use Markov chain Monte Carlo (MCMC) methods to fit our model. The posterior distribution of a quantile of the response variable is obtained within each sub-area using the order statistic over all the individuals (sampled and nonsampled). We compare our robust method with recent parametric methods
Release date: 2008-03-17

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Analysis (97)

Analysis (97) (0 to 10 of 97 results)

1. Authors’ response to comments on “Handling non-probability samples through inverse probability weighting with an application to Statistics Canada’s crowdsourcing data”: Some new developments on likelihood approaches to estimation of participation probabilities for non-probability samples
Articles and reports: 12-001-X202400100001
Description: Inspired by the two excellent discussions of our paper, we offer some new insights and developments into the problem of estimating participation probabilities for non-probability samples. First, we propose an improvement of the method of Chen, Li and Wu (2020), based on best linear unbiased estimation theory, that more efficiently leverages the available probability and non-probability sample data. We also develop a sample likelihood approach, similar in spirit to the method of Elliott (2009), that properly accounts for the overlap between both samples when it can be identified in at least one of the samples. We use best linear unbiased prediction theory to handle the scenario where the overlap is unknown. Interestingly, our two proposed approaches coincide in the case of unknown overlap. Then, we show that many existing methods can be obtained as a special case of a general unbiased estimating function. Finally, we conclude with some comments on nonparametric estimation of participation probabilities.
Release date: 2024-06-25
2. Comments by Changbao Wu on “Handling non-probability samples through inverse probability weighting with an application to Statistics Canada’s crowdsourcing data”
Articles and reports: 12-001-X202400100002
Description: We provide comparisons among three parametric methods for the estimation of participation probabilities and some brief comments on homogeneous groups and post-stratification.
Release date: 2024-06-25
3. Comments by Julie Gershunskaya and Vladislav Beresovsky on “Handling non-probability samples through inverse probability weighting with an application to Statistics Canada’s crowdsourcing data”
Articles and reports: 12-001-X202400100003
Description: Beaumont, Bosa, Brennan, Charlebois and Chu (2024) propose innovative model selection approaches for estimation of participation probabilities for non-probability sample units. We focus our discussion on the choice of a likelihood and parameterization of the model, which are key for the effectiveness of the techniques developed in the paper. We consider alternative likelihood and pseudo-likelihood based methods for estimation of participation probabilities and present simulations implementing and comparing the AIC based variable selection. We demonstrate that, under important practical scenarios, the approach based on a likelihood formulated over the observed pooled non-probability and probability samples performed better than the pseudo-likelihood based alternatives. The contrast in sensitivity of the AIC criteria is especially large for small probability sample sizes and low overlap in covariates domains.
Release date: 2024-06-25
4. Handling non-probability samples through inverse probability weighting with an application to Statistics Canada’s crowdsourcing data
Articles and reports: 12-001-X202400100004
Description: Non-probability samples are being increasingly explored in National Statistical Offices as an alternative to probability samples. However, it is well known that the use of a non-probability sample alone may produce estimates with significant bias due to the unknown nature of the underlying selection mechanism. Bias reduction can be achieved by integrating data from the non-probability sample with data from a probability sample provided that both samples contain auxiliary variables in common. We focus on inverse probability weighting methods, which involve modelling the probability of participation in the non-probability sample. First, we consider the logistic model along with pseudo maximum likelihood estimation. We propose a variable selection procedure based on a modified Akaike Information Criterion (AIC) that properly accounts for the data structure and the probability sampling design. We also propose a simple rank-based method of forming homogeneous post-strata. Then, we extend the Classification and Regression Trees (CART) algorithm to this data integration scenario, while again properly accounting for the probability sampling design. A bootstrap variance estimator is proposed that reflects two sources of variability: the probability sampling design and the participation model. Our methods are illustrated using Statistics Canada’s crowdsourcing and survey data.
Release date: 2024-06-25
5. Preface to the special issue for papers presented at the 29th Morris Hansen Lecture on the use of nonprobability samples
Articles and reports: 12-001-X202400100014
Description: This paper is an introduction to the special issue on the use of nonprobability samples featuring three papers that were presented at the 29^th Morris Hansen Lecture by Courtney Kennedy, Yan Li and Jean-François Beaumont.
Release date: 2024-06-25
6. 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
7. 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
8. 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
9. 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
10. 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

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Date modified:: 2024-09-18