Analysis

Description:

In survey sampling, Taylor linearization is often used to obtain variance estimators for calibration estimators of totals and nonlinear finite population (or census) parameters, such as ratios, regression and correlation coefficients, which can be expressed as smooth functions of totals. Taylor linearization is generally applicable to any sampling design, but it can lead to multiple variance estimators that are asymptotically design unbiased under repeated sampling. The choice among the variance estimators requires other considerations such as (i) approximate unbiasedness for the model variance of the estimator under an assumed model, (ii) validity under a conditional repeated sampling framework. In this paper, a new approach to deriving Taylor linearization variance estimators is proposed. It leads directly to a variance estimator which satisfies the above considerations at least in a number of important cases. The method is applied to a variety of problems, covering estimators of a total as well as other estimators defined either explicitly or implicitly as solutions of estimating equations. In particular, estimators of logistic regression parameters with calibration weights are studied. It leads to a new variance estimator for a general class of calibration estimators that includes generalized raking ratio and generalized regression estimators. The proposed method is extended to two-phase sampling to obtain a variance estimator that makes fuller use of the first phase sample data compared to traditional linearization variance estimators.

Description:

In the U.S. Census of Population and Housing, a sample of about one-in-six of the households receives a longer version of the census questionnaire called the long form. All others receive a version called the short form. Raking, using selected control totals from the short form, has been used to create two sets of weights for long form estimation; one for individuals and one for households. We describe a weight construction method based on quadratic programming that produces household weights such that the weighted sum for individual characteristics and for household characteristics agree closely with selected short form totals. The method is broadly applicable to situations where weights are to be constructed to meet both size bounds and sum-to-control restrictions. Application to the situation where the controls are estimates with an estimated covariance matrix is described.

Description:

The weighting cell estimator corrects for unit nonresponse by dividing the sample into homogeneous groups (cells) and applying a ratio correction to the respondents within each cell. Previous studies of the statistical properties of weighting cell estimators have assumed that these cells correspond to known population cells with homogeneous characteristics. In this article, we study the properties of the weighting cell estimator under a response probability model that does not require correct specification of homogeneous population cells. Instead, we assume that the response probabilities are a smooth but otherwise unspecified function of a known auxiliary variable. Under this more general model, we study the robustness of the weighting cell estimator against model misspecification. We show that, even when the population cells are unknown, the estimator is consistent with respect to the sampling design and the response model. We describe the effect of the number of weighting cells on the asymptotic properties of the estimator. Simulation experiments explore the finite sample properties of the estimator. We conclude with some guidance on how to select the size and number of cells for practical implementation of weighting cell estimation when those cells cannot be specified a priori.

Description:

When imputation is used to assign values for missing items in sample surveys, naïve methods of estimating the variances of survey estimates that treat the imputed values as if they were observed give biased variance estimates. This article addresses the problem of variance estimation for a linear estimator in which missing values are assigned by a single hot deck imputation (a form of imputation that is widely used in practice). We propose estimators of the variance of a linear hot deck imputed estimator using a decomposition of the total variance suggested by Särndal (1992). A conditional approach to variance estimation is developed that is applicable to both weighted and unweighted hot deck imputation. Estimation of the variance of a domain estimator is also examined.

Description:

One of the main objectives of a sample survey is the computation of estimates of means and totals for specific domains of interest. Domains are determined either before the survey is carried out (primary domains) or after it has been carried out (secondary domains). The reliability of the associated estimates depends on the variability of the sample size as well as on the y-variables of interest. This variability cannot be controlled in the absence of auxiliary information for subgroups of the population. However, if auxiliary information is available, the estimated reliability of the resulting estimates can be controlled to some extent. In this paper, we study the potential improvements in terms of the reliability of domain estimates that use auxiliary information. The properties (bias, coverage, efficiency) of various estimators that use auxiliary information are compared using a conditional approach.

Description:

This article studies the use of the sample distribution for the prediction of finite population totals under single-stage sampling. The proposed predictors employ the sample values of the target study variable, the sampling weights of the sample units and possibly known population values of auxiliary variables. The prediction problem is solved by estimating the expectation of the study values for units outside the sample as a function of the corresponding expectation under the sample distribution and the sampling weights. The prediction mean square error is estimated by a combination of an inverse sampling procedure and a re-sampling method. An interesting outcome of the present analysis is that several familiar estimators in common use are shown to be special cases of the proposed approach, thus providing them a new interpretation. The performance of the new and some old predictors in common use is evaluated and compared by a Monte Carlo simulation study using a real data set.

Description:

Multilevel models are often fitted to survey data gathered with a complex multistage sampling design. However, if such a design is informative, in the sense that the inclusion probabilities depend on the response variable even after conditioning on the covariates, then standard maximum likelihood estimators are biased. In this paper, following the Pseudo Maximum Likelihood (PML) approach of Skinner (1989), we propose a probability weighted estimation procedure for multilevel ordinal and binary models which eliminates the bias generated by the informativeness of the design. The reciprocals of the inclusion probabilities at each sampling stage are used to weight the log likelihood function and the weighted estimators obtained in this way are tested by means of a simulation study for the simple case of a binary random intercept model with and without covariates. The variance estimators are obtained by a bootstrap procedure. The maximization of the weighted log likelihood of the model is done by the NLMIXED procedure of the SAS, which is based on adaptive Gaussian quadrature. Also the bootstrap estimation of variances is implemented in the SAS environment.

Description:

The Canadian Labour Force Survey (LFS) was not designed to be a longitudinal survey. However, given that respondent households typically remain in the sample for six consecutive months, it is possible to reconstruct six-month fragments of longitudinal data from the monthly records of household members. Such longitudinal micro-data - altogether consisting of millions of person-months of individual and family level data - is useful for analyses of monthly labour market dynamics over relatively long periods of time, 25 years and more.

We make use of these data to estimate hazard functions describing transitions among the labour market states: self-employed, paid employee and not employed. Data on job tenure, for employed respondents, and on the date last worked, for those not employed - together with the date of survey responses - allow the construction of models that include terms reflecting seasonality and macro-economic cycles as well as the duration dependence of each type of transition. In addition, the LFS data permits spouse labour market activity and family composition variables to be included in the hazard models as time-varying covariates. The estimated hazard equations have been incorporated in the LifePaths microsimulation model. In that setting, the equations have been used to simulate lifetime employment activity from past, present and future birth cohorts. Simulation results have been validated by comparison with the age profiles of LFS employment/population ratios for the period 1976 to 2001.

Description:

Combining response data from the Belgian Fertility and Family Survey with individual level and municipality level data from the 1991 Census for both nonrespondents and respondents, multilevel logistic regression models for contact and cooperation propensity are estimated. The covariates introduced are a selection of indirect features, all out of the researchers' direct control. Contrary to previous research, Socio Economic Status is found to be positively related to cooperation. Another unexpected result is the absence of any considerable impact of ecological correlates such as urbanity.

Description:

In this Issue is a column where the Editor biefly presents each paper of the current issue of Survey Methodology. As well, it sometimes contain informations on structure or management changes in the journal.

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: This infographic provides estimates on health care workers' stress, alcohol consumption and positive health behaviours during the COVID-19 pandemic. Estimates are provided across three primary health care worker groups: nurses, physicians, and Personal Support Workers/Care Aides (PSWs/CAs).

Description: Many aspects of Canadian society affect and are affected by climate change. This presentation synthesizes recent research examining the impact of climate change on Canadian society (economy, labour, and health) as well as adaptation and mitigation measures to combat climate change.

Description: StatCan released new analysis into the online culture our kids are growing up in, and it’s far from the best of all possible worlds: misinformation, bullying, violence… and worse.

Analyst Rachel Tsitomeneas joins us to dive into the findings.

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: This infographic explores ecosystem services, which provide many benefits to society. The infographic provides a visual representation of the three main types of ecosystem services – provisioning services, regulating and maintenance services and cultural services.

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: Release published in The Daily – Statistics Canada’s official release bulletin

Description: The Canadian Income Survey (CIS) has introduced improvements to the methods and data sources used to produce income and poverty estimates with the release of its 2022 reference year estimates. Foremost among these improvements is a significant increase in the sample size for a large subset of the CIS content. The weighting methodology was also improved and the target population of the CIS was changed from persons aged 16 years and over to persons aged 15 years and over. This paper describes the changes made and presents the approximate net result of these changes on the income estimates and data quality of the CIS using 2021 data. The changes described in this paper highlight the ways in which data quality has been improved while having little impact on key CIS estimates and trends.

Description: This study examined the impact of federal business innovation and growth support (BIGS) programs on firm financial performance measured using revenue, profit and employment metrics. Using Statistics Canada’s Business Linkable File Environment data, the study observed the effects of BIGS on exporting versus non-exporting firms and Canadian- versus U.S.-owned firms from 2015 to 2020. Unlike previous studies that relied mainly on survey data, one significant aspect of this research was the use of a new dataset, enabling panel data structures and models to be employed. To assess the impact of BIGS and research and development spending on three interrelated measures of firm financial performance, the CDM (Crépon et al., 1998) framework was adopted.

Description: This article provides perspectives on the extent to which recent changes in gross domestic product per capita represent a departure from their long-term trend and discusses factors that have facilitated per capita growth in previous decades.

Description: Many seniors work past their mid-60s for various reasons. Some find it necessary to keep working because of inadequate retirement savings, mortgage payments, unforeseen expenses, or the responsibility to support children and other family members in Canada or abroad. Others choose to work to provide a sense of personal fulfillment, stay active and remain engaged. This article uses data from the Labour Force Survey (LFS) and examines the degree to which Canadian-born and immigrant seniors aged 65 to 74 worked by choice or necessity in 2022.

Description: Since Canada is a vast country with diverse job opportunities available in various locations, some provinces and territories may face challenges and opportunities in retaining and attracting young skilled talent. This article is the first to inform the issue by determining the share of youth who grew up in a certain province or territory and eventually obtained a postsecondary education but left to work in another province or territory. The article also looks at young skilled workers who entered a province or territory to work, as a share of that province or territory’s initial population of homegrown young skilled labour.

Description: This article provides an integrated summary of recent changes in output, consumer prices, employment, and household finances. It highlights changes in the economic data during the second half of 2023 and into the winter months. The article also examines how economic conditions have changed as borrowing costs have risen.

Description: The participation of women-owned businesses in exports is important for policies aiming to ensure that the benefits of international trade reach all groups. Women-owned small and medium-sized enterprises (SMEs) in Canada are as likely to export as those owned by men, and their export intensity (exports as a share of total sales) was not significantly different. This article examines factors related to the exporting success of women-owned small and medium-sized enterprises in Canada.

Description: Social connections and relationships are important, yet often overlooked, indicators of well-being. For immigrants, these networks are also important for integration. This study examines how immigrant women’s sociodemographic characteristics and life-course circumstances are associated with the size and composition of their personal networks and provides comparisons with Canadian-born women.

Description: This study applies small area estimation (SAE) and a new geographic concept called Self-contained Labor Area (SLA) to the Canadian Survey on Business Conditions (CSBC) with a focus on remote work opportunities in rural labor markets. Through SAE modelling, we estimate the proportions of businesses, classified by general industrial sector (service providers and goods producers), that would primarily offer remote work opportunities to their workforce.

Description: The current study uses the 2011 National Household Survey and the 2016 and 2021 Censuses to provide data on the number of Indigenous foster children in private households, foster child rates, and disparity between Indigenous and non-Indigenous foster care rates between 2011 and 2021. Subsequently, select sociodemographic characteristics of Indigenous children in foster care and household characteristics are explored using the 2021 Census.

Description: The papers in this series cover a variety of topics related to labour statistics. The studies are intended to show recent or historical trends observed with the surveys produced by the Centre for Labour Market Information, i.e. the Labour Force Survey, Survey of Employment Payrolls and Hours, Employment insurance Coverage Survey, Employment insurance statistics as well as administrative data sources. All the papers in this analytical series go through institutional and peer review to ensure that they conform to Statistics Canada's mandate as a government statistical agency and adhere to generally accepted standards of good professional practice.

Description: The publication features products and data highlights that focus on rural areas of Canada or that have a rural dimension present. Rural areas are typically areas outside of Canada's Census Metropolitan Areas (CMA) and Census Agglomerations (CA). The publication also includes explanatory notes on key concepts and definitions.

Description: Departmental Plans (DP) are individual expenditure plans for each department and agency. These reports provide increased levels of detail over a three-year period on an organization's main priorities by strategic outcome, program and planned/expected results, including links to related resource requirements presented in the Main Estimates. In conjunction with the Main Estimates, Departmental Plans serve to inform members of Parliament on planned expenditures of departments and agencies, and support Parliament's consideration of supply bills. The DPs are typically tabled soon after the Main Estimates by the President of the Treasury Board.

Description: These short analytical articles, based on data from the Census of Population, provide analysis on specific topics of interest related to the Canadian population. They are available with each Census of Population major release.

Description: This publication presents annual estimates of the total population and annual estimates by age and gender for Canada, provinces and territories. It also presents estimates of the following components of population change: births, deaths, immigration, emigration, returning emigration, net non-permanent residents and inter-provincial migration, the latter by origin and destination. As in the case of population estimates, the components are also available for the total population and by age and gender.

The Annual demographic estimates - Canada, provinces and territories publication contains the most recent estimates as well as an annual historical series. It also contains highlights and analysis of the most current demographic trends, as well as a brief description of the concepts, methods and data quality of the estimates.

Description: The series includes analysis on the characteristics of those with elementary-secondary, postsecondary and apprenticeship training. It also features analysis on students’ pathways through the education system and into the labour market-- including findings for different levels of education and fields of study. This research highlights specific groups of interest such as youth, women, men, immigrants, Indigenous people (First Nations people, Métis and Inuit) and visible minorities, and how intersections between these characteristics influence people’s educational experiences. Other topics include access to education; national and international adult performance assessments; use of technology; lifelong learning; and adult education.

Description: The papers in this series cover a variety of technical topics related to the Centre for Labour Market Information programs, such as the Labour Force Survey, the Survey of Employment Payrolls and Hours, the Employment insurance Coverage Survey, the Employment Insurance Statistics program as well as data from administrative sources.

Description: This publication brings together and analyzes a wide range of data sources in order to provide information on various aspects of Canadian society, including labour, income, education, social, and demographic issues, that affect the lives of Canadians.

Description: These papers provide background information as well as in depth analysis on data reported in any of the following accounts: income and expenditure accounts, provincial economic accounts, financial flow accounts, national balance sheet accounts, estimates of labour income, and national tourism indicators.

Description: Demographic documentsis a series of texts intended for scholars and researchers, published occasionally by the Demography Division of Statistics Canada for their methodological, analytical or descriptive interest in the population field.