Analysis

Description:

Linearization and the jack-knife method are widely used to estimate standard errors for the coefficients of linear regression models fit to multi-stage samples. With few primary sampling units (PSUs) or when a few PSUs have high leverage, linearization estimators can have large negative bias, while the jack-knife method has a correspondingly large positive bias. We characterize the design factors that produce large biases in these standard error estimators. In this technical paper, we propose an alternative estimator, bias reduced linearization (BRL), based on residuals adjusted to better approximate the covariance of the true errors.

When errors are independently and identically distributed (iid), the BRL estimator is unbiased. The BRL method applies to stratified samples with non-constant selection weights and to generalized linear models such as logistic regression. We also discuss BRL standard error estimators for generalized estimating equation models that explicitly model the dependence among observations from the same PSU in data from complex sample designs. Simulation study results show that BRL standard errors are combined with the Satterthwaite approximation to determine the reference distribution yield tests with Type I error rates near nominal values. We contrast our method with alternatives proposed by Kott (1994 and 1996) and Mancl and DeRouen (2001).

Description:

One of the most important advances brought about by life course and event history studies is the use of parallel or interdependent processes as explaining factors in transition rate models. The purpose of this paper is to demonstrate a causal approach to the study of interrelated family events. Various types of interdependent processes are described first, followed by two event history perspectives: the 'system' and 'causal' approaches. The authors assert that the causal approach is more appropriate from an analytical point of view as it provides a straightforward solution to simultaneity, cause-effect lags, and temporal shapes of effects. Based on comparative cross-national applications in West and East Germany, Canada, Latvia and the Netherlands, the usefulness of the causal approach is demonstrated by analysing two highly interdependent family processes: entry into marriage (for individuals who are in a consensual union) as the dependent process, and first pregnancy/childbirth as the explaining one. Both statistical and theoretical explanations are explored emphasizing the need for conceptual reasoning.

Description:

There is much interest in using data from longitudinal surveys to help understand life history processes such as education, employment, fertility, health and marriage. The analysis of data on the durations of spells or sojourns that individuals spend in certain states (e.g., employment, marriage) is a primary tool in studying such processes. This paper examines methods for analysing duration data that address important features associated with longitudinal surveys: the use of complex survey designs in heterogeneous populations; missing or inaccurate information about the timing of events; and the possibility of non-ignorable dropout or censoring mechanisms. Parametric and non-parametric techniques for estimation and for model checking are considered. Both new and existing methodology are proposed and applied to duration data from Canada's Survey of Labour and Income Dynamics (SLID).

Description:

A developmental trajectory describes the course of a behaviour over age or time. This technical paper provides an overview of a semi-parametric, group-based method for analysing developmental trajectories. This methodology provides an alternative to assuming a homogenous population of trajectories as is done in standard growth modelling.

Four capabilities are described: (1) the capability to identify, rather than assume, distinctive groups of trajectories; (2) the capability to estimate the proportion of the population following each such trajectory group; (3) the capability to relate group membership probability to individual characteristics and circumstances; and (4) the capability to use the group membership probabilities for various other purposes, such as creating profiles of group members.

In addition, two important extensions of the method are described: the capability to add time-varying covariates to trajectory models and the capability to estimate joint trajectory models of distinct but related behaviours. The former provides the statistical capacity for testing if a contemporary factor, such as an experimental intervention or a non-experimental event like pregnancy, deflects a pre-existing trajectory. The latter provides the capability to study the unfolding of distinct but related behaviours such as problematic childhood behaviour and adolescent drug abuse.

Description:

The attractiveness of the Regression Discontinuity Design (RDD) rests on its close similarity to a normal experimental design. On the other hand, it is of limited applicability since it is not often the case that units are assigned to the treatment group on the basis of an observable (to the analyst) pre-program measure. Besides, it only allows identification of the mean impact on a very specific subpopulation. In this technical paper, we show that the RDD straightforwardly generalizes to the instances in which the units' eligibility is established on an observable pre-program measure with eligible units allowed to freely self-select into the program. This set-up also proves to be very convenient for building a specification test on conventional non-experimental estimators of the program mean impact. The data requirements are clearly described.

Description:

In 1961, the European Commission launched a harmonized qualitative survey program to the consumers and the heads of companies (industry, services, construction, retail trade, investments) that covers more than 40 countries today. These qualitative surveys are aimed at understanding the economic situation of these companies. Results are available a few days after the end of the reference period, well before the results of the quantitative surveys.

Although qualitative, these surveys have quickly become an essential tool of the cyclical diagnosis and of the short-term economic forecast. This product shows how these surveys are used by the European Commission, in particular by the Directorate-General for economic and financial Affairs (DG ECFIN) and the Statistical Office of the European Communities (EUROSTAT), to evaluate the economic situation of the Euro zone.

The first part of this product briefly presents the harmonized European business and consumer survey program. In the second part, we look at how DG ECFIN calculates a coincident indicator of the economic activity, using a dynamic factorial analysis of the questions of the survey in industry. This type of indicator makes it possible, in addition, to study the convergence of the economic cycles of the member states. The quantitative short-term indicators for the Euro zone are often criticized for the delay with which they are published. In the third part, we look at how EUROSTAT plans to publish flash estimates of the industrial product price index (IPPI) resulting from econometric models integrating the business survey series. Lastly, we show how these surveys can be used to forecast the gross domestic product (GDP) and to define proxies for some non-available key indicators (new orders in industry, etc.).

Description:

This project seeks to shed light not only on the degree to which individuals are stuck in the low-income range, but also on those who have sufficient opportunity to move into the upper part of the income distribution. It also seeks to compare patterns of mobility through the income distribution in North America and Europe, shedding light on the impact of different models of integration. Cross-National Equivalent File data from the British Household Panel Survey (BHPS) for the United Kingdom, the German Socio-Economic Panel (GSOEP) for Germany, the Panel Study of Income Dynamics (PSID) for the United States and the Survey of Labour Income Dynamics (SLID) for Canada offer a comparative analysis of the dynamics of household income during the 1990s, paying particular attention to both low- and high-income dynamics. Canadian administrative data drawn from income tax files are also used. These panel datasets range in length from six years (for the SLID) to almost 20 years (for the PSID and the Canadian administrative data). The analysis focuses on developments during the 1990s, but also explores the sensitivity of the results to changes in the length of the period analysed.

The analysis begins by offering a broad descriptive overview of the major characteristics and events (demographic versus labour market) that determine levels and changes in adjusted household incomes. Attention is paid to movements into and out of low- and high- income ranges. A number of definitions are used, incorporating absolute and relative notions of poverty. The sensitivity of the results to the use of various equivalence scales is examined. An overview offers a broad picture of the state of household income in each country and the relative roles of family structure, the labour market and welfare state in determining income mobility. The paper employs discrete time-hazard methods to model the dynamics of entry to and exit from both low and high income.

Both observed and unobserved heterogeneity are controlled for with the intention of highlighting differences in the determinants of the transition rates between the countries. This is done in a way that assesses the importance of the relative roles of family, market and state. Attention is also paid to important institutional changes, most notably the increasing integration of product and labour markets in North America and Europe.

Description:

Practitioners often use data collected from complex surveys (such as labour force and health surveys involving stratified cluster sampling) to fit logistic regression and other models of interest. A great deal of effort over the last two decades has been spent on developing methods to analyse survey data that take account of design features. This paper looks at an alternative method known as inverse sampling.

Specialized programs, such as SUDAAN and WESVAR, are also available to implement some of the methods developed to take into account the design features. However, these methods require additional information such as survey weights, design effects or cluster identification of microdata and thus, another method is necessary.

Inverse sampling (Hinkins et al., Survey Methodology, 1977) provides an alternative approach by undoing the complex data structures so that standard methods can be applied. Repeated subsamples with simple random structure are drawn and each subsample is analysed by standard methods and is combined to increase the efficiency. Although computer-intensive, this method has the potential to preserve confidentiality of microdata files. A drawback of the method is that it can lead to biased estimates of regression parameters when the subsample sizes are small (as in the case of stratified cluster sampling).

In this paper, we propose using the estimating equation approach that combines the subsamples before estimation and thus leads to nearly unbiased estimates of regression parameters regardless of subsample sizes. This method is computationally less intensive than the original method. We apply the method to cluster-correlated data generated from a nested error linear regression model to illustrate its advantages. A real dataset from a Statistics Canada survey will also be analysed using the estimating equation method.

Description:

Survey sampling is a statistical domain that has been slow to take advantage of flexible regression methods. In this technical paper, two approaches are discussed that could be used to make these regression methods accessible: adapt the techniques to the complex survey design that has been used or sample the survey data so that the standard techniques are applicable.

In following the former route, we introduce techniques that account for the complex survey structure of the data for scatterplot smoothing and additive models. The use of penalized least squares in the sampling context is studied as a tool for the analysis of a general trend in a finite population. We focus on smooth regression with a normal error model. Ties in covariates abound for large scale surveys resulting in the application of scatterplot smoothers to means. The estimation of smooths (for example, smoothing splines) depends on the sampling design only via the sampling weights, meaning that standard software can be used for estimation. Inference for these curves is more challenging, as a result of correlations induced by the sampling design. We propose and illustrate tests that account for the sampling design. Illustrative examples are given using the Ontario health survey, including scatterplot smoothing, additive models and model diagnostics. In an attempt to resolve the problem by appropriate sampling of the survey data file, we discuss some of the hurdles that are faced when using this approach.

Description:

Analyses of data from social and economic surveys sometimes use generalized variance function models to approximate the design variance of point estimators of population means and proportions. Analysts may use the resulting standard error estimates to compute associated confidence intervals or test statistics for the means and proportions of interest. In comparison with design-based variance estimators computed directly from survey microdata, generalized variance function models have several potential advantages, as will be discussed in this paper, including operational simplicity; increased stability of standard errors; and, for cases involving public-use datasets, reduction of disclosure limitation problems arising from the public release of stratum and cluster indicators.

These potential advantages, however, may be offset in part by several inferential issues. First, the properties of inferential statistics based on generalized variance functions (e.g., confidence interval coverage rates and widths) depend heavily on the relative empirical magnitudes of the components of variability associated, respectively, with:

(a) the random selection of a subset of items used in estimation of the generalized variance function model(b) the selection of sample units under a complex sample design (c) the lack of fit of the generalized variance function model (d) the generation of a finite population under a superpopulation model.

Second, under conditions, one may link each of components (a) through (d) with different empirical measures of the predictive adequacy of a generalized variance function model. Consequently, these measures of predictive adequacy can offer us some insight into the extent to which a given generalized variance function model may be appropriate for inferential use in specific applications.

Some of the proposed diagnostics are applied to data from the US Survey of Doctoral Recipients and the US Current Employment Survey. For the Survey of Doctoral Recipients, components (a), (c) and (d) are of principal concern. For the Current Employment Survey, components (b), (c) and (d) receive principal attention, and the availability of population microdata allow the development of especially detailed models for components (b) and (c).

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: 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: This article provides information about population totals in the Labour Force Survey (LFS), including details on who is included in the survey target population, and a description of the methodology used to produce monthly population totals in the LFS. The note also provides guidance on how to interpret population statistics in the LFS, and discusses the extent to which the LFS can be used to examine disaggregated labour market indicators for new immigrants and non-permanent residents.

Description: Active commuting (AC) to and from work is associated with numerous health benefits, through increased physical activity. This study examined whether occupation types and part-time work, by sex, were associated with AC in a population-based sample of Canadian workers. This study examined the associations between occupational classifications, part-time work, and AC (i.e., walking, cycling) and public transit use, in a nationally representative sample of Canadian adults, while controlling for other relevant sociodemographic characteristics (e.g., education, income, urbanity). This study also explored how associations between occupational classifications and AC differed by sex and how AC rates may have changed over time.

Description: Physical and sexual childhood abuse are associated with suicidal ideation and mental health disorders. However, less is known about non-physical types of maltreatment. This study examined associations between non-physical types of child maltreatment (e.g., emotional abuse, interpersonal aggression, exposure to physical intimate partner violence, emotional and physical neglect) and suicidal ideation, and mental health disorders.

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: This study uses data from multiple waves of the Canadian Social Survey (CSS) to examine trends in three key Quality of Life indicators, namely life satisfaction, experiences of financial hardship, and future outlook. Monitoring these well-being indicators following periods of considerable social and economic change is particularly important. Beginning in the summer of 2021, the CSS, a new quarterly survey, captured the latter part of the COVID-19 pandemic as well as the rising cost of living in Canada, allowing for an understanding of how Canadians are coping with these challenges.

Description: This article explores how businesses plan to use AI over the next 12 months and the types of AI they intend to use when producing goods or delivering services. It also explores how businesses expect AI to affect their employment levels, what operational changes they anticipate over the next 12 months and why some are choosing not to use AI. It involves an examination of the data produced by the Canadian Survey on Business Conditions.

Description: Using data from the Labour Force Survey, this study assesses the degree to which employment and hourly wage rates of unpartnered mothers with young children have caught up to their partnered peers between 1997 and 2023. Focusing on mothers aged 18 to 49 with at least one child aged 5 or younger, the analysis examines differences between partnered (i.e., currently married or living common law) and unpartnered mothers, with disaggregation by unpartnered mothers who have never been married and those who were previously married. The study also examines employment and wage gaps by various diverse groups, such as the experiences of immigrant mothers, as well as Indigenous mothers.

Description: The concept of innovation ecosystems has recently gained increasing interest among researchers, practitioners and policy makers. This article uses a systematic literature review approach by drawing on studies that bring together the most recent knowledge on innovation ecosystem performance indicators.

Description: This study provides experimental estimates of the number and percentage of workers in Canada potentially susceptible to AI-related job transformation based on the complementarity-adjusted AI occupational exposure index.

Description: Investing in a postsecondary education is an important decision in the lives of young people, because it may lead to significantly higher lifetime earnings, which may vary substantially across different disciplines. The purpose of this short article is to present results for master’s degree graduates aged 25 to 34 collected on the 2021 Census of Population. Only individuals who worked during the census reference week (May 2 to 8, 2021) and who completed a Canadian master’s degree program are included.

Description:

As Statistics Canada celebrates a significant milestone in 2018, it is time to take a look back at our history to see where we have been and what we have done over the past century. At the same time, it is a chance to reflect on where the agency is headed in the future. This series of articles shows how our work has evolved since 1918: where we started, how we have evolved and what we do now.

Description:

This series of analytical reports provides an overview of the Canadian labour market experiences of immigrants to Canada, based on data from the Labour Force Survey. These reports examine the labour force characteristics of immigrants, by reporting on employment and unemployment at the Canada level, for the provinces and large metropolitan areas. They also provide more detailed analysis by region of birth, as well as in-depth analysis of other specific aspects of the immigrant labour market.

Description:

Historical works allow readers to peer into the past, not only to satisfy our curiosity about “the way things were,” but also to see how far we’ve come, and to learn from the past. For Statistics Canada, such works are also opportunities to commemorate the agency’s contributions to Canada and its people, and serve as a reminder that an institution such as this continues to evolve each and every day.

On the occasion of Statistics Canada’s 100th anniversary in 2018, Standing on the shoulders of giants: History of Statistics Canada: 1970 to 2008, builds on the work of two significant publications on the history of the agency, picking up the story in 1970 and carrying it through the next 36 years, until 2008. To that end, when enough time has passed to allow for sufficient objectivity, it will again be time to document the agency’s next chapter as it continues to tell Canada’s story in numbers.

Description: This publication presents an overview of recent economic developments in the provinces and territories. The overview covers several broad areas: 1) gross domestic product (GDP) by income and by expenditure, 2) GDP by industry, 3) labour productivity and other related variables.

The publication examines trends in the major aggregates that comprise GDP, both income- and expenditure-based, as well as prices and the financing of economic activity by institutional sector. GDP is also examined by industry. The productivity estimates are meant to assist in the analysis of the short-run relationship among the fluctuations of output, employment, compensation and hours worked. Some issues also contain more technical articles, explaining national accounts methodology or analysing a particular aspect of the economy.

This publication carries the detailed analyses, charts and statistical tables that, prior to its first issue, were released in The Daily (11-001-XIE) under the headings Provincial Economic Accounts and Provincial Gross Domestic Product by industry.

Description:

Understanding the role of women in Canadian society and how it has changed over time is dependent on having information that can begin to shed light on the diverse circumstances and experiences of women. Women in Canada provides an unparalleled compilation of data related to women's family status, education, employment, economic well-being, unpaid work, health, and more.

Women in Canada allows readers to better understand the experience of women compared to that of men. Recognizing that women are not a homogenous group and that experiences differ not only across gender but also within gender groups, Women in Canada includes chapters on immigrant women, women in a visible minority, Aboriginal women, senior women, and women with participation and activity limitations.

Description:

The publication provides data users, health professionals and individual Canadians with geometric means and selected percentiles of blood and urine concentrations of selected environmental chemicals for the Canadian population by sex and age group. The results presented in this publication were collected during cycle 4 of the Canadian Health Measures Survey from January 2014 to December 2015.

Description: In 2018, Statistics Canada will celebrate its 100th anniversary. As we count down to this important milestone, we would like to use our data to highlight some of the sweeping changes that have had a lasting impact on Canadian society and economy.

Description:

The Record Linkage Project Process Model (RLPPM) was developed by Statistics Canada to identify the processes and activities involved in record linkage. The RLPPM applies to linkage projects conducted at the individual and enterprise level using diverse data sources to create new data sources to meet analytical and operational needs.

Description:

Each issue of Health at a Glance consists of a short non-technical article on topics that feature statistics from health-related surveys and administrative data.

Description:

The National Apprenticeship Survey (NAS) looks at factors affecting the completion, certification and transition of apprentices to the labour market. The survey was a collaborative effort on the part of Employment and Social Development Canada (ESDC) and Statistics Canada. It is hoped that the findings will contribute to the ongoing dialogue by governments, industry and unions to ensure that the apprenticeship systems in Canada continue to respond to the demands of the 21st Century.