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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: We provide comparisons among three parametric methods for the estimation of participation probabilities and some brief comments on homogeneous groups and post-stratification.

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.

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 rejoinder, I address the comments from the discussants, Dr. Takumi Saegusa, Dr. Jae-Kwang Kim and Ms. Yonghyun Kwon. Dr. Saegusa’s comments about the differences between the conditional exchangeability (CE) assumption for causal inferences versus the CE assumption for finite population inferences using nonprobability samples, and the distinction between design-based versus model-based approaches for finite population inference using nonprobability samples, are elaborated and clarified in the context of my paper. Subsequently, I respond to Dr. Kim and Ms. Kwon’s comprehensive framework for categorizing existing approaches for estimating propensity scores (PS) into conditional and unconditional approaches. I expand their simulation studies to vary the sampling weights, allow for misspecified PS models, and include an additional estimator, i.e., scaled adjusted logistic propensity estimator (Wang, Valliant and Li (2021), denoted by sWBS). In my simulations, it is observed that the sWBS estimator consistently outperforms or is comparable to the other estimators under the misspecified PS model. The sWBS, as well as WBS or ABS described in my paper, do not assume that the overlapped units in both the nonprobability and probability reference samples are negligible, nor do they require the identification of overlap units as needed by the estimators proposed by Dr. Kim and Ms. Kwon.

Description: In some of non-probability sample literature, the conditional exchangeability assumption is considered to be necessary for valid statistical inference. This assumption is rooted in causal inference though its potential outcome framework differs greatly from that of non-probability samples. We describe similarities and differences of two frameworks and discuss issues to consider when adopting the conditional exchangeability assumption in non-probability sample setups. We also discuss the role of finite population inference in different approaches of propensity scores and outcome regression modeling to non-probability samples.

Description: Pseudo weight construction for data integration can be understood in the two-phase sampling framework. Using the two-phase sampling framework, we discuss two approaches to the estimation of propensity scores and develop a new way to construct the propensity score function for data integration using the conditional maximum likelihood method. Results from a limited simulation study are also presented.

Description: Nonprobability samples emerge rapidly to address time-sensitive priority topics in different areas. These data are timely but subject to selection bias. To reduce selection bias, there has been wide literature in survey research investigating the use of propensity-score (PS) adjustment methods to improve the population representativeness of nonprobability samples, using probability-based survey samples as external references. Conditional exchangeability (CE) assumption is one of the key assumptions required by PS-based adjustment methods. In this paper, I first explore the validity of the CE assumption conditional on various balancing score estimates that are used in existing PS-based adjustment methods. An adaptive balancing score is proposed for unbiased estimation of population means. The population mean estimators under the three CE assumptions are evaluated via Monte Carlo simulation studies and illustrated using the NIH SARS-CoV-2 seroprevalence study to estimate the proportion of U.S. adults with COVID-19 antibodies from April 01-August 04, 2020.

Description: Our comments respond to discussion from Sen, Brick, and Elliott. We weigh the potential upside and downside of Sen’s suggestion of using machine learning to identify bogus respondents through interactions and improbable combinations of variables. We join Brick in reflecting on bogus respondents’ impact on the state of commercial nonprobability surveys. Finally, we consider Elliott’s discussion of solutions to the challenge raised in our study.

Description: This discussion summarizes the interesting new findings around measurement errors in opt-in surveys by Kennedy, Mercer and Lau (KML). While KML enlighten readers about “bogus responding” and possible patterns in them, this discussion suggests combining these new-found results with other avenues of research in nonprobability sampling, such as improvement of representativeness.

Description: This web application provides access to data on the sales of food services and drinking places for Canada, provinces and territories. This dynamic application allows users to compare provincial and territorial data with interactive maps and charts. All data in this release are seasonally adjusted and expressed in current dollars.

Description: This interactive dashboard provides access to current and historical Consumer Price Index (CPI) data in a dynamic and customizable format. Key indicators such as the 12-month and 1-month inflation rates and price trends are presented in interactive charts, allowing users to compare and analyze price changes of all the goods and services in the CPI basket over time as well as across geography (national, provincial and territorial levels).

Other CPI indicators available in this tool include the Bank of Canada’s core measures of inflation, seasonally adjusted inflation rates, and CPI basket weights.

This web-based application is updated monthly, as soon as the data for the latest reference month is released in The Daily.

Description: Statistics Canada produces a variety of interactive visualization tools that present data in a graphical form. These tools provide a useful way of interpreting trends behind our data on various social and economic topics.

Description: Quarterly data by level of government.

Description: This table contains 39 series, with data for starting from 1991 (not all combinations necessarily have data for all years). This table contains data described by the following dimensions (Not all combinations are available): Geography (1 item: Canada); Financial market statistics (39 items: Government of Canada Treasury Bills, 1-month (composite rates); Government of Canada Treasury Bills, 2-month (composite rates); Government of Canada Treasury Bills, 3-month (composite rates);Government of Canada Treasury Bills, 6-month (composite rates); ...).

Description:

Monthly average retail prices for gasoline and fuel oil for Canada, selected provincial cities, Whitehorse and Yellowknife. Prices are presented for the current month and previous four months. Includes fuel type and the price in cents per litre.

Description:

Monthly indexes for major components and special aggregates of the Consumer Price Index (CPI), not seasonally adjusted, for Canada, provinces, Whitehorse, Yellowknife and Iqaluit. Data are presented for the current month and previous four months. The base year for the index is 2002=100.

Description:

Monthly indexes and percentage changes for all components and special aggregates of the Consumer Price Index (CPI), not seasonally adjusted, for Canada, provinces, Whitehorse, Yellowknife and Iqaluit. Data are presented for the corresponding month of the previous year, the previous month and the current month. The base year for the index is 2002=100. 

Description: Monthly indexes and percentage changes for selected sub-groups of the food component of the Consumer Price Index (CPI), not seasonally adjusted, for Canada, provinces, Whitehorse and Yellowknife. Data are presented for the corresponding month of the previous year, the previous month and the current month. The base year for the index is 2002=100.

Description: Monthly indexes and percentage changes for selected sub-groups of the shelter component of the Consumer Price Index (CPI), not seasonally adjusted, for Canada, provinces, Whitehorse and Yellowknife. Data are presented for the corresponding month of the previous year, the previous month and the current month. The base year for the index is 2002=100.

Description:

A Hot Deck imputation procedure is defined to be one where an incomplete response is completed by using values from one or more other records on the same file and the choice of these records varies with the record requiring imputation.

General approaches to Hot Deck imputation are outlined, with emphasis on the interaction between the edit constraints and the imputation procedures. Distance functions can be constructed on a mixture of categorical and numeric fields, can be modified to take account of the relative importance of fields and can discriminate against less desirable donors. Matching fields may be correlated with missing fields, may be linked with missing fields by edits or may be natural stratification variables; but increasing the number of matching fields does not necessarily result in a better match. It is important to audit the imputation process and to summarize its performance.

Hot Deck procedures should be evaluated to study the bias and reliability of the estimates, donor usage and frequency of imputation failure in terms of a variety of conditions of the data and variations of the imputation procedure. It appears that the only generally available approach to evaluation is by simulation.

Description:

This paper looks at the current state of development of social statistics in Canada. Some key concepts related to statistics and social information are defined and discussed. The availability and analysis of administrative data is highlighted, along with the need for social surveys. Suggestions are made about the types of data analysis needed for the development of social decision models to meet policy requirements. Finally, an outline of priorities for future work toward the effective use of social statistics is given.

Description: This paper discusses the management of information within the context of the information industry and indicates some likely future trends related thereto. The information industry itself is first briefly described. Then the process used in producing information, the organizational structure required for such production, and the legislation relating to the information industry are discussed in turn. Finally, some approaches to solving the problems of the future are suggested.

Description: This paper includes a description of interviewer techniques and procedures used to minimize non-response, an outline of methods used to monitor and control non-response, and a discussion of how non-respondents are treated in the data processing and estimation stages of the Canadian Labour Force Survey. Recent non-response rates as well as data on the characteristics of non-respondents are also given. It is concluded that a yearly non-response rate of approximately 5 percent is probably the best that can be achieved in the Labour Force Survey.

Description: Two methods for estimating the correlated response variance of a survey estimator are studied by way of both theoretical comparison and empirical investigation. The variance of these estimators is discussed and the effects of outliers examined. Finally, an improved estimator is developed and evaluated.

Description: Let U = {1, 2, …, i, …, N} be a finite population of N identifiable units. A known “size measure” x_i is associated with unit i; i = 1, 2, ..., N. A sampling procedure for selecting a sample of size n (2 < n < N) with probability proportional to size (PPS) and without replacement (WOR) from the population is proposed. With this method, the inclusion probability is proportional to size (IPPS) for each unit in the population.

Description: Approximate cutoff rules for stratifying a population into a take-all and take-some universe have been given by Dalenius (1950) and Glasser (1962). They expressed the cutoff value (that value which delineates the boundary of the take-all and take-some) as a function of the mean, the sampling weight and the population variance. Their cutoff values were derived on the assumption that a single random sample of size n was to be drawn without replacement from the population of size N.

In the present context, exact and approximate cutoff rules have been worked out for a similar situation. Rather than providing the sample size of the sample, the precision (coefficient of variation) is given. Note that in many sampling situations, the sampler is given a set of objectives in terms of reliability and not sample size. The result is particularly useful for determining the take-all - take-some boundary for samples drawn from a known population. The procedure is also extended to ratio estimation.

Description: Under a sequential sampling plan, the proportion defective in the sample is generally a biased estimator of the population value. In this paper, an unbiased estimator is given. Also, an unbiased estimator of its variance is derived. These results are applied to an estimation problem from the 1976 Canadian Census.

Description: I.P. Fellegi and D. Holt proposed a systematic approach to automatic edit and imputation. An implementation of this proposal was a Generalized Edit and Imputation System by the Hot-Deck Approach, that was utilized in the edit and imputation of the 1976 Canadian Census of Population and Housing. This paper discusses that application, evaluating the strengths and weaknesses of the methodology with some empirical evidence. The system will be considered in relation to the general issues of the edit and imputation of survey data. Some directions for future developments will also be considered.

Description: Owners of small businesses complain about the quantity of forms they are required to collectors of statistics. Administrative data are an alternative source but do not usually include all the information required by the survey takers.

The “Tax Data Imputation System” makes use of tax data collected from a large number of businesses by Revenue Canada and data obtained by sample survey for a small subset of these businesses. Survey data is imputed (estimated) for all the businesses not actually surveyed using a “hot-deck” technique, with adjustments made to ensure certain edit rules are satisfied. The results of a simulation study suggest that this procedure has reasonable statistical properties. Estimators (of means or totals) are unbiased with variances of comparable size to the corresponding ratio estimators.

Description: This is not a survey. The Business Integrated Databse (BID) is a joint Industry Canada and Statistics Canada project.

Description: This is not a survey. The DLI Collection contains geography files from 1971 - 2006.

Description: The area, production and value data for the Mexican potato crop in this table are provided by the Servicio de Información Agroalimentaria y Pesquera. For further details, please refer to: Servicio de Información Agroalimentaria y Pesquera Av. Benjamin Franklin 146, Col Escandón Delegación Miquel Hidalgo C.P. 11800 México, D.F. E-mail: aclaradatos@siap.gob.mx Telephone: (01552) 55 3871-8500 ext 120-173 Websites: http://www.siap.gob.mx or http://www.siap.sagarpa.gob.mx

Description: This is non-Statistics Canada information.

Description: This is non-Statistics Canada information.

Description: This is non-Statistics Canada information.

Description: The survey objective is to validate industry classification codes, and to obtain information required to efficiently select samples for Statistics Canada's economic survey programs. Topics studied include business activity, research and development, and capital expenditures.

Description: The Historical Database gathers the data from existing cycles of the General Social Survey (GSS) together in an easily accessed form so that researchers may follow trends in Canadian society over time.

Description: These data sets are developed for the purpose of longitudinal analysis of the Census of Agriculture for both Soil Landscapes of Canada and Drainage Area (Watershed) spatial frameworks.

Description: The Longitudinal Employment Analysis Program (LEAP) is a database that contains annual employment information for each employer business in Canada, starting with the 1983 reference year.