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- Articles and reports: 12-001-X202400100001Description: 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
- Articles and reports: 12-001-X202400100004Description: 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
Articles and reports (2)
Articles and reports (2) ((2 results))
- Articles and reports: 12-001-X202400100001Description: 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
- Articles and reports: 12-001-X202400100004Description: 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