Analysis

Description:

Nearly all surveys use complex sampling designs to collect data and these data are frequently used for statistical analyses beyond the estimation of simple descriptive parameters of the target population. Many procedures available in popular statistical software packages are not appropriate for this purpose because the analyses are based on the assumption that the sample has been drawn with simple random sampling. Therefore, the results of the analyses conducted using these software packages would not be valid when the sample design incorporates multistage sampling, stratification, or clustering. Two commonly used methods for analysing data from complex surveys are replication and Taylor linearization techniques. We discuss the use of WESVAR software to compute estimates and replicate variance estimates by properly reflecting complex sampling and estimation procedures. We also illustrate the WESVAR features by using data from two Westat surveys that employ complex survey designs: the Third International Mathematics and Science Study (TIMSS) and the National Health and Nutrition Examination Survey (NHANES).

Description:

For most survey samples, if not all, we have to deal with the problem of missing values. Missing values are usually caused by nonresponse (such as refusal of participant or interviewer was unable to contact respondent) but can also be produced at the editing step of the survey in an attempt to resolve problems of inconsistent or suspect responses. The presence of missing values (nonresponse) generally leads to bias and uncertainty in the estimates. To treat this problem, the appropriate use of all available auxiliary information permits the maximum reduction of nonresponse bias and variance. During this presentation, we will define the problem, describe the methodology that SEVANI is based on and discuss potential uses of the system. We will end the discussion by presenting some examples based on real data to illustrate the theory in practice.

In practice, it is very difficult to estimate the nonresponse bias. However, it is possible to estimate the nonresponse variance by assuming that the bias is negligible. In the last decade, many methods were indeed proposed to estimate this variance, and some of these have been implemented in the System for Estimation of Variance due to Nonresponse and Imputation (SEVANI).

The methodology used to develop SEVANI is based on the theory of two-phase sampling where we assume that the second phase of selection is nonresponse. However, contrary to two-phase sampling, an imputation or nonresponse model is required for variance estimation. SEVANI also assumes that nonresponse is treated by reweighting respondent units or by imputing their missing values. Three imputation methods are considered: the imputation of an auxiliary variable, regression imputation (deterministic or random) and nearest-neighbour imputation.

Description:

A wide class of models of interest in social and economic research can be represented by specifying a parametric structure for the covariances of observed variables. The availability of software, such as LISREL (Jöreskog and Sörbom 1988) and EQS (Bentler 1995), has enabled these models to be fitted to survey data in many applications. In this paper, we consider approaches to inference about such models using survey data derived by complex sampling schemes. We consider evidence of finite sample biases in parameter estimation and ways to reduce such biases (Altonji and Segal 1996) and associated issues of efficiency of estimation, standard error estimation and testing. We use longitudinal data from the British Household Panel Survey for illustration. As these data are subject to attrition, we also consider the issue of how to use nonresponse weights in the modelling.

Description:

Behavioural researchers use a variety of techniques to predict respondent scores on constructs that are not directly observable. Examples of such constructs include job satisfaction, work stress, aptitude for graduate study, children's mathematical ability, etc. The techniques commonly used for modelling and predicting scores on such constructs include factor analysis, classical psychometric scaling and item response theory (IRT), and for each technique there are often several different strategies that can be used to generate individual scores. However, researchers are seldom satisfied with simply measuring these constructs. They typically use the derived scores in multiple regression, analysis of variance and numerous multivariate procedures. Though using predicted scores in this way can result in biased estimates of model parameters, not all researchers are aware of this difficulty. The paper will review the literature on this issue, with particular emphasis on IRT methods. Problems will be illustrated, some remedies suggested, and areas for further research will be identified.

Description:

Analysis of dose-response relationships has long been important in toxicology. More recently, this type of analysis has been employed to evaluate public education campaigns. The data that are collected in such evaluations are likely to come from standard household survey designs with all the usual complexities of multiple stages, stratification and variable selection probabilities. On a recent evaluation, a system was developed with the following features: categorization of doses into three or four levels, propensity scoring of dose selection and a new jack-knifed Jonckheere-Terpstra test for a monotone dose-response relationship. This system allows rapid production of tests for monotone dose-response relationships that are corrected both for sample design and for confounding. The focus of this paper will be the results of a Monte-Carlo simulation of the properties of the jack-knifed Jonckheere-Terpstra.

Moreover, there is no experimental control over dosages and the possibility of confounding variables must be considered. Standard regressions in WESVAR and SUDAAN could be used to determine if there is a linear dose-response relationship while controlling on confounders, but such an approach obviously has low power to detect nonlinear but monotone dose-response relationships and is time-consuming to implement if there are a large number of possible outcomes of interest.

Description:

While censuses and surveys are often said to measure populations as they are, most reflect information about individuals as they were at the time of measurement, or even at some prior time point. Inferences from such data therefore should take into account change over time at both the population and individual levels. In this paper, we provide a unifying framework for such inference problems, illustrating it through a diverse series of examples including: (1) estimating residency status on Census Day using multiple administrative records, (2) combining administrative records for estimating the size of the US population, (3) using rolling averages from the American Community Survey, and (4) estimating the prevalence of human rights abuses.

Specifically, at the population level, the estimands of interest, such as the size or mean characteristics of a population, might be changing. At the same time, individual subjects might be moving in and out of the frame of the study or changing their characteristics. Such changes over time can affect statistical studies of government data that combine information from multiple data sources, including censuses, surveys and administrative records, an increasingly common practice. Inferences from the resulting merged databases often depend heavily on specific choices made in combining, editing and analysing the data that reflect assumptions about how populations of interest change or remain stable over time.

Description:

According to recent literature, the calibration method has gained much popularity on survey sampling and calibration estimators are routinely computed by many survey organizations. The choice of calibration variables for all existing approaches, however, remains ad hoc. In this article, we show that the model-calibration estimator for the finite population mean, which was proposed by Wu and Sitter (2001) through an intuitive argument, is indeed optimal among a class of calibration estimators. We further present optimal calibration estimators for the finite population distribution function, the population variance, variance of a linear estimator and other quadratic finite population functions under a unified framework. A limited simulation study shows that the improvement of these optimal estimators over the conventional ones can be substantial. The question of when and how auxiliary information can be used for both the estimation of the population mean using a generalized regression estimator and the estimation of its variance through calibration is addressed clearly under the proposed general methodology. Constructions of proposed estimators under two-phase sampling and some fundamental issues in using auxiliary information from survey data are also addressed under the context of optimal estimation.

Description:

In the 2001 Canadian Census of Population, calibration or regression estimation was used to calculate a single set of household level weights to be used for all census estimates based on a one in five national sample of more than two million households. Because many auxiliary variables were available, only a subset of them could be used. Otherwise, some of the weights would have been smaller than the number one or even negative. In this technical paper, a forward selection procedure was used to discard auxiliary variables that caused weights to be smaller than one or that caused a large condition number for the calibration weight matrix being inverted. Also, two calibration adjustments were done to achieve close agreement between auxiliary population counts and estimates for small areas. Prior to 2001, the projection generalized regression (GREG) estimator was used and the weights were required to be greater than zero. For the 2001 Census, a switch was made to a pseudo-optimal regression estimator that kept more auxiliary variables and, at the same time, required that the weights be one or more.

Description:

The US Census Bureau supports research into an optimal design program as an alternative to its current decennial redesign of demographic surveys. The optimal design program seeks to optimize redesign samples annually and reduce deterioration of the precision of survey estimates.

Initial research has focussed on the use of multi-agent systems (also known as distributed artificial intelligence) to produce optimal annual samples for all demographic surveys. The first multi-agent system optimizes redesign inputs. It represents each housing unit as an autonomous agent and solves the distributed constrain satisfaction problem (DCSP) to forecast household characteristics that are consistent with recent survey data and estimates. The second multi-agent system selects optimal samples for all demographic surveys. It represents each survey-state pair as a deliberative agent and applies the Bayesian optimization algorithm (BOA) at each design stage to partition the sampling units into sample and non-sample subsets. Thus, sampling units are selected directly, without the need for initial stratification.

Description:

If the dataset available to machine learning results from cluster sampling (e.g., patients from a sample of hospital wards), the usual cross-validation error rate estimate can lead to biased and misleading results. In this technical paper, an adapted cross-validation is described for this case. Using a simulation, the sampling distribution of the generalization error rate estimate, under cluster or simple random sampling hypothesis, is compared with the true value. The results highlight the impact of the sampling design on inference: clearly, clustering has a significant impact; the repartition between learning set and test set should result from a random partition of the clusters, not from a random partition of the examples. With cluster sampling, standard cross-validation underestimates the generalization error rate, and is deficient for model selection. These results are illustrated with a real application of automatic identification of spoken language.

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 details the prevalence of vitamin D inadequacy among the Canadian population aged 3 to 79 by focusing on risk factors as well as behaviours that can reduce the likelihood of low vitamin D.

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

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

Description: A series of articles on various subjects which explore the impact of COVID-19 on the socio-economic landscape. New articles will be released periodically.

Description: This article provides insights into the rates of COVID-19 mortality among First Nations peoples and Métis living in private dwellings and the social determinants of COVID-19 mortality among these populations using data from the 2016 Canadian Census Health and Environment Cohorts linked to the Canadian Vital Statistics – Death Database from 2016 to 2021.

Description: This article uses 12 months of data from the Labour Force Survey (LFS) and LFS supplement for 2022, and the 2016 General Social Survey on Canadians at Work and Home to explore several quality of employment indicators based on Statistics Canada's Statistical Framework on Quality of Employment among the core working age First Nations people living off reserve and Métis (18 to 64 years), in the 10 provinces.

Description: This Juristat article explores recent trends in police-reported sexual assault and other selected types of violent crime, following the implementation of changes to the Uniform Crime Reporting Survey in 2018. Analysis includes a focus on clearance status and victim, accused person and incident characteristics, comparing results from 2017 to the years that followed the changes.

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 demolinguistic portrait of the French-speaking population in Canada was undertaken with the financial support of Canadian Heritage's Official Languages Secretariat, prepared by the Statistics Canada's Language Statistics Section.

This study paints a general statistical portrait of the official-language minority in Canada based on data from the Census of Population and the Survey on the Vitality of Official-language Minorities in Canada, conducted in 2006. The purpose of such a portrait is to present a set of characteristics, behaviours and perceptions of the official-language minority population, exploiting the analytical opportunities contained in the data.

Description:

The Canadian Economy in Transition is a series of new analytical reports that investigate the dynamics of industrial change in the Canadian economy. Many of these studies focus on the growth and development of industries that are often described as vanguards of the new economy, such as information and communications technology industries and science-based industries (heavy investors in research and development and human capital). Other studies examine the role that knowledge workers play in Canada's industrial evolution. In addition, future studies will investigate productivity performance in different industrial sectors.

This new series brings together a coherent set of research reports that provide users with a wide variety of empirical perspectives on the economy's changing industrial structure. These perspectives include the dynamics of productivity, profitability, employment, output, investment, occupational structure and industrial geography.

Description:

The Economic Analysis Research Paper Series provides the circulation of research conducted by the staff of National Accounts and Analytical Studies, visiting fellows and academic associates. The research paper series is meant to stimulate discussion on a range of topics including the impact of the new economy; productivity issues; firm profitability; technology usage; the effect of financing on firm growth; depreciation functions; the use of satellite accounts; savings rates; leasing; firm dynamics; hedonic estimations; diversification patterns; investment patterns; the differences in the performance of small and large, or domestic and multinational firms; and purchasing power parity estimates. Readers of the series are encouraged to contact the authors with comments, criticisms and suggestions.

The primary distribution medium for the papers is the Internet. These papers can be downloaded from the Internet at www.statcan.gc.ca for free. Papers in the series are distributed to Statistics Canada Regional Offices and provincial statistical focal points.

All papers in the Economic Analysis 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.

The papers in the series often include results derived from multivariate analysis or other statistical techniques. It should be recognized that the results of these analyses are subject to uncertainty in the reported estimates.

The level of uncertainty will depend on several factors: the nature of the functional form used in the multivariate analysis; the type of econometric technique employed; the appropriateness of the statistical assumptions embedded in the model or technique; the comprehensiveness of the variables included in the analysis; and the accuracy of the data that are utilized. The peer group review process is meant to ensure that the papers in the series have followed accepted standards to minimize problems in each of these areas.

Description:

This topic presents data on the income of individuals, families, and households of Canada for the year 2010, including the composition of income, earnings and low-income prevalence data. The data also include the family and household incomes of Canadians by characteristics, family structure, household type and geography, as well as the total income and earnings levels of certain population groups (e.g., immigrants). The composition of income includes market income and income from government sources, and presents detailed components.

This topic also presents data on dwelling characteristics, including number of rooms and bedrooms, condition of dwelling, period of construction, condominium status, value of dwelling, and structural type of dwelling. Data on households are also presented, including household maintainer, housing tenure, housing subsidy, housing suitability and shelter costs.

Analytical products

Two analytical documents provide analysis on the key findings in the data, and are complemented with the short articles found in NHS in Brief and the data in the NHS Focus on Geography Series.

Data products

The NHS Profile is one data product that provides a statistical overview of user selected geographic areas based on several detailed variables and/or groups of variables. Other data products include data tables which represent a series of cross tabulations ranging in complexity and are available for various levels of geography.

Description:

This on-line report summarizes research and development (R&D) activities performed and funded by Canadian business enterprises and industrial research institutes and associations. The data are used, for instance, to plan and evaluate R&D tax incentive programs, to provide indicators of the state of industrial innovation and to complement national aggregates for scientific R&D expenditures and personnel. Among the topics covered are current and capital expenditures on research and development, energy R&D expenditures by area of technology, R&D expenditures as a percentage of company revenues, sources of funds for intramural R&D, personnel engaged in R&D, and foreign payments made and received for technological services. Most historical tables are presented for the latest five years and disaggregated by 46 industrial groupings, size of R&D program, employment size, revenue size, country of control, and by province.

Description:

This paper surveys the history of Statistics Canada's Consumer Price Index (CPI) from its origins to today. It discusses changes in the construction, scope and uses of the CPI within the context of historical events.

Description:

This reference publication on productivity in Canada shows how productivity trends affect Canadian living standards and measures the relative productivity performance of Canada and other countries. Its articles cover productivity and related issues, and it illuminates the sources underlying economic growth in Canada.

Description:

The Canadian Income Survey (CIS) is a cross-sectional survey developed to assess the economic well-being of individuals and families in Canada. It provides a portrait of the income and income sources of Canadians, with their individual and household characteristics.

Description:

Many of the 60 or so Aboriginal languages in Canada are considered endangered to varying degrees for their long-term survival. Assessing language vitality or endangerment through the measurement of various factors can provide useful information to help ensure the continuity of a language. This paper illustrates how the 2011 Census of Population and the 2011 National Household Survey (NHS) can be used to measure some of the factors that provide information related to the vitality of Aboriginal languages.

Description:

Canadian Demographics at a glance is designed to gather a maximum of demographic information in a single document, giving users an easily and quickly accessible up-to-date picture of the Canadian population. It presents data on demographic growth, fertility, mortality, migratory movements, aging and ethno-cultural diversity of the population in the form of tables and graphs accompanied by a brief analytical commentary.