Analysis

Description: This paper is an introduction to the eleven papers included in this special issue for the celebration of the 50th anniversary of the Survey Methodology Journal.

Description: This document briefly describes the small area estimation methodology developed to produce monthly estimates of employment and unemployment rate for census metropolitan areas, census agglomerations, and self-contained labour areas using data from the Labour Force Survey, Employment Insurance statistics and population projections.

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.

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.

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.

Description:

In the last two decades, survey response rates have been steadily falling. In that context, it has become increasingly important for statistical agencies to develop and use methods that reduce the adverse effects of non-response on the accuracy of survey estimates. Follow-up of non-respondents may be an effective, albeit time and resource-intensive, remedy for non-response bias. We conducted a simulation study using real business survey data to shed some light on several questions about non-response follow-up. For instance, assuming a fixed non-response follow-up budget, what is the best way to select non-responding units to be followed up? How much effort should be dedicated to repeatedly following up non-respondents until a response is received? Should they all be followed up or a sample of them? If a sample is followed up, how should it be selected? We compared Monte Carlo relative biases and relative root mean square errors under different follow-up sampling designs, sample sizes and non-response scenarios. We also determined an expression for the minimum follow-up sample size required to expend the budget, on average, and showed that it maximizes the expected response rate. A main conclusion of our simulation experiment is that this sample size also appears to approximately minimize the bias and mean square error of the estimates.

Description:

The Fay-Herriot model is often used to produce small area estimates. These estimates are generally more efficient than standard direct estimates. In order to evaluate the efficiency gains obtained by small area estimation methods, model mean square error estimates are usually produced. However, these estimates do not reflect all the peculiarities of a given domain (or area) because model mean square errors integrate out the local effects. An alternative is to estimate the design mean square error of small area estimators, which is often more attractive from a user point of view. However, it is known that design mean square error estimates can be very unstable, especially for domains with few sampled units. In this paper, we propose two local diagnostics that aim to choose between the empirical best predictor and the direct estimator for a particular domain. We first find an interval for the local effect such that the best predictor is more efficient under the design than the direct estimator. Then, we consider two different approaches to assess whether it is plausible that the local effect falls in this interval. We evaluate our diagnostics using a simulation study. Our preliminary results indicate that our diagnostics are effective for choosing between the empirical best predictor and the direct estimator.

Description:

Statistics Canada continues to use a variety of data sources to provide neighbourhood-level variables across an expanding set of domains, such as sociodemographic characteristics, income, services and amenities, crime, and the environment. Yet, despite these advances, information on the social aspects of neighbourhoods is still unavailable. In this paper, answers to the Canadian Community Health Survey on respondents’ sense of belonging to their local community were pooled over the four survey years from 2016 to 2019. Individual responses were aggregated up to the census tract (CT) level.

Description:

Non-probability samples are being increasingly explored by National Statistical Offices as a complement to probability samples. We consider the scenario where the variable of interest and auxiliary variables are observed in both a probability and non-probability sample. Our objective is to use data from the non-probability sample to improve the efficiency of survey-weighted estimates obtained from the probability sample. Recently, Sakshaug, Wisniowski, Ruiz and Blom (2019) and Wisniowski, Sakshaug, Ruiz and Blom (2020) proposed a Bayesian approach to integrating data from both samples for the estimation of model parameters. In their approach, non-probability sample data are used to determine the prior distribution of model parameters, and the posterior distribution is obtained under the assumption that the probability sampling design is ignorable (or not informative). We extend this Bayesian approach to the prediction of finite population parameters under non-ignorable (or informative) sampling by conditioning on appropriate survey-weighted statistics. We illustrate the properties of our predictor through a simulation study.

Key Words: Bayesian prediction; Gibbs sampling; Non-ignorable sampling; Statistical data integration.

Description:

For several decades, national statistical agencies around the world have been using probability surveys as their preferred tool to meet information needs about a population of interest. In the last few years, there has been a wind of change and other data sources are being increasingly explored. Five key factors are behind this trend: the decline in response rates in probability surveys, the high cost of data collection, the increased burden on respondents, the desire for access to “real-time” statistics, and the proliferation of non-probability data sources. Some people have even come to believe that probability surveys could gradually disappear. In this article, we review some approaches that can reduce, or even eliminate, the use of probability surveys, all the while preserving a valid statistical inference framework. All the approaches we consider use data from a non-probability source; data from a probability survey are also used in most cases. Some of these approaches rely on the validity of model assumptions, which contrasts with approaches based on the probability sampling design. These design-based approaches are generally not as efficient; yet, they are not subject to the risk of bias due to model misspecification.

Description: This paper is an introduction to the eleven papers included in this special issue for the celebration of the 50th anniversary of the Survey Methodology Journal.

Description: This document briefly describes the small area estimation methodology developed to produce monthly estimates of employment and unemployment rate for census metropolitan areas, census agglomerations, and self-contained labour areas using data from the Labour Force Survey, Employment Insurance statistics and population projections.

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.

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.

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.

Description:

In the last two decades, survey response rates have been steadily falling. In that context, it has become increasingly important for statistical agencies to develop and use methods that reduce the adverse effects of non-response on the accuracy of survey estimates. Follow-up of non-respondents may be an effective, albeit time and resource-intensive, remedy for non-response bias. We conducted a simulation study using real business survey data to shed some light on several questions about non-response follow-up. For instance, assuming a fixed non-response follow-up budget, what is the best way to select non-responding units to be followed up? How much effort should be dedicated to repeatedly following up non-respondents until a response is received? Should they all be followed up or a sample of them? If a sample is followed up, how should it be selected? We compared Monte Carlo relative biases and relative root mean square errors under different follow-up sampling designs, sample sizes and non-response scenarios. We also determined an expression for the minimum follow-up sample size required to expend the budget, on average, and showed that it maximizes the expected response rate. A main conclusion of our simulation experiment is that this sample size also appears to approximately minimize the bias and mean square error of the estimates.

Description:

The Fay-Herriot model is often used to produce small area estimates. These estimates are generally more efficient than standard direct estimates. In order to evaluate the efficiency gains obtained by small area estimation methods, model mean square error estimates are usually produced. However, these estimates do not reflect all the peculiarities of a given domain (or area) because model mean square errors integrate out the local effects. An alternative is to estimate the design mean square error of small area estimators, which is often more attractive from a user point of view. However, it is known that design mean square error estimates can be very unstable, especially for domains with few sampled units. In this paper, we propose two local diagnostics that aim to choose between the empirical best predictor and the direct estimator for a particular domain. We first find an interval for the local effect such that the best predictor is more efficient under the design than the direct estimator. Then, we consider two different approaches to assess whether it is plausible that the local effect falls in this interval. We evaluate our diagnostics using a simulation study. Our preliminary results indicate that our diagnostics are effective for choosing between the empirical best predictor and the direct estimator.

Description:

Statistics Canada continues to use a variety of data sources to provide neighbourhood-level variables across an expanding set of domains, such as sociodemographic characteristics, income, services and amenities, crime, and the environment. Yet, despite these advances, information on the social aspects of neighbourhoods is still unavailable. In this paper, answers to the Canadian Community Health Survey on respondents’ sense of belonging to their local community were pooled over the four survey years from 2016 to 2019. Individual responses were aggregated up to the census tract (CT) level.

Description:

Non-probability samples are being increasingly explored by National Statistical Offices as a complement to probability samples. We consider the scenario where the variable of interest and auxiliary variables are observed in both a probability and non-probability sample. Our objective is to use data from the non-probability sample to improve the efficiency of survey-weighted estimates obtained from the probability sample. Recently, Sakshaug, Wisniowski, Ruiz and Blom (2019) and Wisniowski, Sakshaug, Ruiz and Blom (2020) proposed a Bayesian approach to integrating data from both samples for the estimation of model parameters. In their approach, non-probability sample data are used to determine the prior distribution of model parameters, and the posterior distribution is obtained under the assumption that the probability sampling design is ignorable (or not informative). We extend this Bayesian approach to the prediction of finite population parameters under non-ignorable (or informative) sampling by conditioning on appropriate survey-weighted statistics. We illustrate the properties of our predictor through a simulation study.

Key Words: Bayesian prediction; Gibbs sampling; Non-ignorable sampling; Statistical data integration.

Description:

For several decades, national statistical agencies around the world have been using probability surveys as their preferred tool to meet information needs about a population of interest. In the last few years, there has been a wind of change and other data sources are being increasingly explored. Five key factors are behind this trend: the decline in response rates in probability surveys, the high cost of data collection, the increased burden on respondents, the desire for access to “real-time” statistics, and the proliferation of non-probability data sources. Some people have even come to believe that probability surveys could gradually disappear. In this article, we review some approaches that can reduce, or even eliminate, the use of probability surveys, all the while preserving a valid statistical inference framework. All the approaches we consider use data from a non-probability source; data from a probability survey are also used in most cases. Some of these approaches rely on the validity of model assumptions, which contrasts with approaches based on the probability sampling design. These design-based approaches are generally not as efficient; yet, they are not subject to the risk of bias due to model misspecification.