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All (105) (10 to 20 of 105 results)

11. 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
12. 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
13. 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
14. 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
15. 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
16. Author’s response to comments on “Statistical inference with non-probability survey samples”
Articles and reports: 12-001-X202200200008
Description:
This response contains additional remarks on a few selected issues raised by the discussants.

Release date: 2022-12-15
17. Optimal linear estimation in two-phase sampling
Articles and reports: 12-001-X202200200011
Description:
Two-phase sampling is a cost effective sampling design employed extensively in surveys. In this paper a method of most efficient linear estimation of totals in two-phase sampling is proposed, which exploits optimally auxiliary survey information. First, a best linear unbiased estimator (BLUE) of any total is formally derived in analytic form, and shown to be also a calibration estimator. Then, a proper reformulation of such a BLUE and estimation of its unknown coefficients leads to the construction of an “optimal” regression estimator, which can also be obtained through a suitable calibration procedure. A distinctive feature of such calibration is the alignment of estimates from the two phases in an one-step procedure involving the combined first-and-second phase samples. Optimal estimation is feasible for certain two-phase designs that are used often in large scale surveys. For general two-phase designs, an alternative calibration procedure gives a generalized regression estimator as an approximate optimal estimator. The proposed general approach to optimal estimation leads to the most effective use of the available auxiliary information in any two-phase survey. The advantages of this approach over existing methods of estimation in two-phase sampling are shown both theoretically and through a simulation study.
Release date: 2022-12-15
18. Bayesian inference for multinomial data from small areas incorporating uncertainty about order restriction
Articles and reports: 12-001-X202200100004
Description:
When the sample size of an area is small, borrowing information from neighbors is a small area estimation technique to provide more reliable estimates. One of the famous models in small area estimation is a multinomial-Dirichlet hierarchical model for multinomial counts. Due to natural characteristics of the data, making unimodal order restriction assumption to parameter spaces is relevant. In our application, body mass index is more likely at an overweight level, which means the unimodal order restriction may be reasonable. The same unimodal order restriction for all areas may be too strong to be true for some cases. To increase flexibility, we add uncertainty to the unimodal order restriction. Each area will have similar unimodal patterns, but not the same. Since the order restriction with uncertainty increases the inference difficulty, we make comparison with the posterior summaries and approximated log-pseudo marginal likelihood.

Release date: 2022-06-21
19. A generalization of inverse probability weighting
Articles and reports: 12-001-X202200100009
Description:
In finite population estimation, the inverse probability or Horvitz-Thompson estimator is a basic tool. Even when auxiliary information is available to model the variable of interest, it is still used to estimate the model error. Here, the inverse probability estimator is generalized by introducing a positive definite matrix. The usual inverse probability estimator is a special case of the generalized estimator, where the positive definite matrix is the identity matrix. Since calibration estimation seeks weights that are close to the inverse probability weights, it too can be generalized by seeking weights that are close to those of the generalized inverse probability estimator. Calibration is known to be optimal, in the sense that it asymptotically attains the Godambe-Joshi lower bound. That lower bound has been derived under a model where no correlation is present. This too, can be generalized to allow for correlation. With the correct choice of the positive definite matrix that generalizes the calibration estimators, this generalized lower bound can be asymptotically attained. There is often no closed-form formula for the generalized estimators. However, simple explicit examples are given here to illustrate how the generalized estimators take advantage of the correlation. This simplicity is achieved here, by assuming a correlation of one between some population units. Those simple estimators can still be useful, even if the correlation is smaller than one. Simulation results are used to compare the generalized estimators to the ordinary estimators.

Release date: 2022-06-21
20. An alternative jackknife variance estimator when calibrating weights to adjust for unit nonresponse in a complex survey
Articles and reports: 12-001-X202100200003
Description:
Calibration weighting is a statistically efficient way for handling unit nonresponse. Assuming the response (or output) model justifying the calibration-weight adjustment is correct, it is often possible to measure the variance of estimates in an asymptotically unbiased manner. One approach to variance estimation is to create jackknife replicate weights. Sometimes, however, the conventional method for computing jackknife replicate weights for calibrated analysis weights fails. In that case, an alternative method for computing jackknife replicate weights is usually available. That method is described here and then applied to a simple example.
Release date: 2022-01-06

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41. 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
42. 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
43. 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
44. 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
45. 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
46. 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
47. 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
48. 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
49. 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
50. Flexible models for analyzing longitudinal data in population health Archived
Articles and reports: 11-522-X200600110398
Description:
The study of longitudinal data is vital in terms of accurately observing changes in responses of interest for individuals, communities, and larger populations over time. Linear mixed effects models (for continuous responses observed over time) and generalized linear mixed effects models and generalized estimating equations (for more general responses such as binary or count data observed over time) are the most popular techniques used for analyzing longitudinal data from health studies, though, as with all modeling techniques, these approaches have limitations, partly due to their underlying assumptions. In this review paper, we will discuss some advances, including curve-based techniques, which make modeling longitudinal data more flexible. Three examples will be presented from the health literature utilizing these more flexible procedures, with the goal of demonstrating that some otherwise difficult questions can be reasonably answered when analyzing complex longitudinal data in population health studies.
Release date: 2008-03-17

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Date modified:: 2024-09-19