Weighting and estimation
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- Articles and reports: 11-522-X202200100001Description: Record linkage aims at identifying record pairs related to the same unit and observed in two different data sets, say A and B. Fellegi and Sunter (1969) suggest each record pair is tested whether generated from the set of matched or unmatched pairs. The decision function consists of the ratio between m(y) and u(y),probabilities of observing a comparison y of a set of k>3 key identifying variables in a record pair under the assumptions that the pair is a match or a non-match, respectively. These parameters are usually estimated by means of the EM algorithm using as data the comparisons on all the pairs of the Cartesian product ?=A×B. These observations (on the comparisons and on the pairs status as match or non-match) are assumed as generated independently of other pairs, assumption characterizing most of the literature on record linkage and implemented in software tools (e.g. RELAIS, Cibella et al. 2012). On the contrary, comparisons y and matching status in ? are deterministically dependent. As a result, estimates on m(y) and u(y) based on the EM algorithm are usually bad. This fact jeopardizes the effective application of the Fellegi-Sunter method, as well as automatic computation of quality measures and possibility to apply efficient methods for model estimation on linked data (e.g. regression functions), as in Chambers et al. (2015). We propose to explore ? by a set of samples, each one drawn so to preserve independence of comparisons among the selected record pairs. Simulations are encouraging.Release date: 2024-03-25
- Articles and reports: 12-001-X202200100002Description:
We consider an intercept only linear random effects model for analysis of data from a two stage cluster sampling design. At the first stage a simple random sample of clusters is drawn, and at the second stage a simple random sample of elementary units is taken within each selected cluster. The response variable is assumed to consist of a cluster-level random effect plus an independent error term with known variance. The objects of inference are the mean of the outcome variable and the random effect variance. With a more complex two stage sampling design, the use of an approach based on an estimated pairwise composite likelihood function has appealing properties. Our purpose is to use our simpler context to compare the results of likelihood inference with inference based on a pairwise composite likelihood function that is treated as an approximate likelihood, in particular treated as the likelihood component in Bayesian inference. In order to provide credible intervals having frequentist coverage close to nominal values, the pairwise composite likelihood function and corresponding posterior density need modification, such as a curvature adjustment. Through simulation studies, we investigate the performance of an adjustment proposed in the literature, and find that it works well for the mean but provides credible intervals for the random effect variance that suffer from under-coverage. We propose possible future directions including extensions to the case of a complex design.
Release date: 2022-06-21 - Articles and reports: 12-001-X202200100009Description:
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 - Articles and reports: 12-001-X202000200003Description:
We combine weighting and Bayesian prediction in a unified approach to survey inference. The general principles of Bayesian analysis imply that models for survey outcomes should be conditional on all variables that affect the probability of inclusion. We incorporate all the variables that are used in the weighting adjustment under the framework of multilevel regression and poststratification, as a byproduct generating model-based weights after smoothing. We improve small area estimation by dealing with different complex issues caused by real-life applications to obtain robust inference at finer levels for subdomains of interest. We investigate deep interactions and introduce structured prior distributions for smoothing and stability of estimates. The computation is done via Stan and is implemented in the open-source R package rstanarm and available for public use. We evaluate the design-based properties of the Bayesian procedure. Simulation studies illustrate how the model-based prediction and weighting inference can outperform classical weighting. We apply the method to the New York Longitudinal Study of Wellbeing. The new approach generates smoothed weights and increases efficiency for robust finite population inference, especially for subsets of the population.
Release date: 2020-12-15 - Articles and reports: 12-001-X202000100004Description:
Cut-off sampling is applied when there is a subset of units from the population from which getting the required information is too expensive or difficult and, therefore, those units are deliberately excluded from sample selection. If those excluded units are different from the sampled ones in the characteristics of interest, naïve estimators may be severely biased. Calibration estimators have been proposed to reduce the design-bias. However, when estimating in small domains, they can be inefficient even in the absence of cut-off sampling. Model-based small area estimation methods may prove useful for reducing the bias due to cut-off sampling if the assumed model holds for the whole population. At the same time, for small domains, these methods provide more efficient estimators than calibration methods. Since model-based properties are obtained assuming that the model holds but no model is exactly true, here we analyze the design properties of calibration and model-based procedures for estimation of small domain characteristics under cut-off sampling. Our results confirm that model-based estimators reduce the bias due to cut-off sampling and perform significantly better in terms of design mean squared error.
Release date: 2020-06-30 - 6. Unequal probability inverse sampling ArchivedArticles and reports: 12-001-X201600214660Description:
In an economic survey of a sample of enterprises, occupations are randomly selected from a list until a number r of occupations in a local unit has been identified. This is an inverse sampling problem for which we are proposing a few solutions. Simple designs with and without replacement are processed using negative binomial distributions and negative hypergeometric distributions. We also propose estimators for when the units are selected with unequal probabilities, with or without replacement.
Release date: 2016-12-20 - Articles and reports: 12-001-X201600214663Description:
We present theoretical evidence that efforts during data collection to balance the survey response with respect to selected auxiliary variables will improve the chances for low nonresponse bias in the estimates that are ultimately produced by calibrated weighting. One of our results shows that the variance of the bias – measured here as the deviation of the calibration estimator from the (unrealized) full-sample unbiased estimator – decreases linearly as a function of the response imbalance that we assume measured and controlled continuously over the data collection period. An attractive prospect is thus a lower risk of bias if one can manage the data collection to get low imbalance. The theoretical results are validated in a simulation study with real data from an Estonian household survey.
Release date: 2016-12-20 - 8. Assessing the impact of potentially influential observations in weighted logistic regression ArchivedArticles and reports: 12-002-X201500114147Description:
Influential observations in logistic regression are those that have a notable effect on certain aspects of the model fit. Large sample size alone does not eliminate this concern; it is still important to examine potentially influential observations, especially in complex survey data. This paper describes a straightforward algorithm for examining potentially influential observations in complex survey data using SAS software. This algorithm was applied in a study using the 2005 Canadian Community Health Survey that examined factors associated with family physician utilization for adolescents.
Release date: 2015-03-25 - Articles and reports: 15-206-X2015039Description:
This paper generates updated estimates of depreciation rates to be used in the Canadian Productivity Accounts for the calculation of capital stock and the user cost of capital. Estimates are derived of depreciation profiles for a diverse set of assets, based on patterns of resale prices and retirement ages.
A maximum likelihood technique is used to jointly estimate changes in the valuation of assets over the course of their service life, as well as the nature of the discard process used to dispose of assets to generate depreciation rates. This method is more efficient than others in producing estimates with less bias and higher efficiency.
The earlier estimates that were derived for the period from 1985 to 2001 are compared with those for the latest period, from 2002 to 2010.
Release date: 2015-01-26 - Articles and reports: 12-001-X201400214090Description:
When studying a finite population, it is sometimes necessary to select samples from several sampling frames in order to represent all individuals. Here we are interested in the scenario where two samples are selected using a two-stage design, with common first-stage selection. We apply the Hartley (1962), Bankier (1986) and Kalton and Anderson (1986) methods, and we show that these methods can be applied conditional on first-stage selection. We also compare the performance of several estimators as part of a simulation study. Our results suggest that the estimator should be chosen carefully when there are multiple sampling frames, and that a simple estimator is sometimes preferable, even if it uses only part of the information collected.
Release date: 2014-12-19
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- Articles and reports: 11-522-X202200100001Description: Record linkage aims at identifying record pairs related to the same unit and observed in two different data sets, say A and B. Fellegi and Sunter (1969) suggest each record pair is tested whether generated from the set of matched or unmatched pairs. The decision function consists of the ratio between m(y) and u(y),probabilities of observing a comparison y of a set of k>3 key identifying variables in a record pair under the assumptions that the pair is a match or a non-match, respectively. These parameters are usually estimated by means of the EM algorithm using as data the comparisons on all the pairs of the Cartesian product ?=A×B. These observations (on the comparisons and on the pairs status as match or non-match) are assumed as generated independently of other pairs, assumption characterizing most of the literature on record linkage and implemented in software tools (e.g. RELAIS, Cibella et al. 2012). On the contrary, comparisons y and matching status in ? are deterministically dependent. As a result, estimates on m(y) and u(y) based on the EM algorithm are usually bad. This fact jeopardizes the effective application of the Fellegi-Sunter method, as well as automatic computation of quality measures and possibility to apply efficient methods for model estimation on linked data (e.g. regression functions), as in Chambers et al. (2015). We propose to explore ? by a set of samples, each one drawn so to preserve independence of comparisons among the selected record pairs. Simulations are encouraging.Release date: 2024-03-25
- Articles and reports: 12-001-X202200100002Description:
We consider an intercept only linear random effects model for analysis of data from a two stage cluster sampling design. At the first stage a simple random sample of clusters is drawn, and at the second stage a simple random sample of elementary units is taken within each selected cluster. The response variable is assumed to consist of a cluster-level random effect plus an independent error term with known variance. The objects of inference are the mean of the outcome variable and the random effect variance. With a more complex two stage sampling design, the use of an approach based on an estimated pairwise composite likelihood function has appealing properties. Our purpose is to use our simpler context to compare the results of likelihood inference with inference based on a pairwise composite likelihood function that is treated as an approximate likelihood, in particular treated as the likelihood component in Bayesian inference. In order to provide credible intervals having frequentist coverage close to nominal values, the pairwise composite likelihood function and corresponding posterior density need modification, such as a curvature adjustment. Through simulation studies, we investigate the performance of an adjustment proposed in the literature, and find that it works well for the mean but provides credible intervals for the random effect variance that suffer from under-coverage. We propose possible future directions including extensions to the case of a complex design.
Release date: 2022-06-21 - Articles and reports: 12-001-X202200100009Description:
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 - Articles and reports: 12-001-X202000200003Description:
We combine weighting and Bayesian prediction in a unified approach to survey inference. The general principles of Bayesian analysis imply that models for survey outcomes should be conditional on all variables that affect the probability of inclusion. We incorporate all the variables that are used in the weighting adjustment under the framework of multilevel regression and poststratification, as a byproduct generating model-based weights after smoothing. We improve small area estimation by dealing with different complex issues caused by real-life applications to obtain robust inference at finer levels for subdomains of interest. We investigate deep interactions and introduce structured prior distributions for smoothing and stability of estimates. The computation is done via Stan and is implemented in the open-source R package rstanarm and available for public use. We evaluate the design-based properties of the Bayesian procedure. Simulation studies illustrate how the model-based prediction and weighting inference can outperform classical weighting. We apply the method to the New York Longitudinal Study of Wellbeing. The new approach generates smoothed weights and increases efficiency for robust finite population inference, especially for subsets of the population.
Release date: 2020-12-15 - Articles and reports: 12-001-X202000100004Description:
Cut-off sampling is applied when there is a subset of units from the population from which getting the required information is too expensive or difficult and, therefore, those units are deliberately excluded from sample selection. If those excluded units are different from the sampled ones in the characteristics of interest, naïve estimators may be severely biased. Calibration estimators have been proposed to reduce the design-bias. However, when estimating in small domains, they can be inefficient even in the absence of cut-off sampling. Model-based small area estimation methods may prove useful for reducing the bias due to cut-off sampling if the assumed model holds for the whole population. At the same time, for small domains, these methods provide more efficient estimators than calibration methods. Since model-based properties are obtained assuming that the model holds but no model is exactly true, here we analyze the design properties of calibration and model-based procedures for estimation of small domain characteristics under cut-off sampling. Our results confirm that model-based estimators reduce the bias due to cut-off sampling and perform significantly better in terms of design mean squared error.
Release date: 2020-06-30 - 6. Unequal probability inverse sampling ArchivedArticles and reports: 12-001-X201600214660Description:
In an economic survey of a sample of enterprises, occupations are randomly selected from a list until a number r of occupations in a local unit has been identified. This is an inverse sampling problem for which we are proposing a few solutions. Simple designs with and without replacement are processed using negative binomial distributions and negative hypergeometric distributions. We also propose estimators for when the units are selected with unequal probabilities, with or without replacement.
Release date: 2016-12-20 - Articles and reports: 12-001-X201600214663Description:
We present theoretical evidence that efforts during data collection to balance the survey response with respect to selected auxiliary variables will improve the chances for low nonresponse bias in the estimates that are ultimately produced by calibrated weighting. One of our results shows that the variance of the bias – measured here as the deviation of the calibration estimator from the (unrealized) full-sample unbiased estimator – decreases linearly as a function of the response imbalance that we assume measured and controlled continuously over the data collection period. An attractive prospect is thus a lower risk of bias if one can manage the data collection to get low imbalance. The theoretical results are validated in a simulation study with real data from an Estonian household survey.
Release date: 2016-12-20 - 8. Assessing the impact of potentially influential observations in weighted logistic regression ArchivedArticles and reports: 12-002-X201500114147Description:
Influential observations in logistic regression are those that have a notable effect on certain aspects of the model fit. Large sample size alone does not eliminate this concern; it is still important to examine potentially influential observations, especially in complex survey data. This paper describes a straightforward algorithm for examining potentially influential observations in complex survey data using SAS software. This algorithm was applied in a study using the 2005 Canadian Community Health Survey that examined factors associated with family physician utilization for adolescents.
Release date: 2015-03-25 - Articles and reports: 15-206-X2015039Description:
This paper generates updated estimates of depreciation rates to be used in the Canadian Productivity Accounts for the calculation of capital stock and the user cost of capital. Estimates are derived of depreciation profiles for a diverse set of assets, based on patterns of resale prices and retirement ages.
A maximum likelihood technique is used to jointly estimate changes in the valuation of assets over the course of their service life, as well as the nature of the discard process used to dispose of assets to generate depreciation rates. This method is more efficient than others in producing estimates with less bias and higher efficiency.
The earlier estimates that were derived for the period from 1985 to 2001 are compared with those for the latest period, from 2002 to 2010.
Release date: 2015-01-26 - Articles and reports: 12-001-X201400214090Description:
When studying a finite population, it is sometimes necessary to select samples from several sampling frames in order to represent all individuals. Here we are interested in the scenario where two samples are selected using a two-stage design, with common first-stage selection. We apply the Hartley (1962), Bankier (1986) and Kalton and Anderson (1986) methods, and we show that these methods can be applied conditional on first-stage selection. We also compare the performance of several estimators as part of a simulation study. Our results suggest that the estimator should be chosen carefully when there are multiple sampling frames, and that a simple estimator is sometimes preferable, even if it uses only part of the information collected.
Release date: 2014-12-19
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- Surveys and statistical programs – Documentation: 11-522-X19980015019Description:
The British Labour Force Survey (LFS) is a quarterly household survey with a rotating sample design that can potentially be used to produce longitudinal data, including estimates of labour force gross flows. However, these estimates may be biased due to the effect of non-response. Weighting adjustments are a commonly used method to account for non-response bias. We find that weighting may not fully account for the effect of non-response bias because non-response may depend on the unobserved labour force flows, i.e., the non-response is non-ignorable. To adjust for the effects of non-ignorable non-response, we propose a model for the complex non-response patterns in the LFS which controls for the correlated within-household non-response behaviour found in the survey. The results of modelling suggest that non-response may be non-ignorable in the LFS, causing the weighting estimates to be biased.
Release date: 1999-10-22
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