Analysis

Description:

This multivariate statistical analysis, which captures the number of prior police contacts of young people apprehended by the police, uses longitudinally linked records from the Incident-Based Uniform Crime Reporting Survey for 1995 to 2001.

Description:

Linearization (or Taylor series) methods are widely used to estimate standard errors for the co-efficients of linear regression models fit to multi-stage samples. When the number of primary sampling units (PSUs) is large, linearization can produce accurate standard errors under quite general conditions. However, when the number of PSUs is small or a co-efficient depends primarily on data from a small number of PSUs, linearization estimators can have large negative bias.

In this paper, we characterize features of the design matrix that produce large bias in linearization standard errors for linear regression co-efficients. We then propose a new method, bias reduced linearization (BRL), based on residuals adjusted to better approximate the covariance of the true errors. When the errors are independent and identically distributed (i.i.d.), the BRL estimator is unbiased for the variance. Furthermore, a simulation study shows that BRL can greatly reduce the bias, even if the errors are not i.i.d. We also propose using a Satterthwaite approximation to determine the degrees of freedom of the reference distribution for tests and confidence intervals about linear combinations of co-efficients based on the BRL estimator. We demonstrate that the jackknife estimator also tends to be biased in situations where linearization is biased. However, the jackknife's bias tends to be positive. Our bias-reduced linearization estimator can be viewed as a compromise between the traditional linearization and jackknife estimators.

Description:

In this paper, we discuss the analysis of complex health survey data by using multivariate modelling techniques. Main interests are in various design-based and model-based methods that aim at accounting for the design complexities, including clustering, stratification and weighting. Methods covered include generalized linear modelling based on pseudo-likelihood and generalized estimating equations, linear mixed models estimated by restricted maximum likelihood, and hierarchical Bayes techniques using Markov Chain Monte Carlo (MCMC) methods. The methods will be compared empirically, using data from an extensive health interview and examination survey conducted in Finland in 2000 (Health 2000 Study).

The data of the Health 2000 Study were collected using personal interviews, questionnaires and clinical examinations. A stratified two-stage cluster sampling design was used in the survey. The sampling design involved positive intra-cluster correlation for many study variables. For a closer investigation, we selected a small number of study variables from the health interview and health examination phases. In many cases, the different methods produced similar numerical results and supported similar statistical conclusions. Methods that failed to account for the design complexities sometimes led to conflicting conclusions. We also discuss the application of the methods in this paper by using standard statistical software products.

Description:

In this paper, we consider the effect of the interval censoring of cessation time on intensity parameter estimation with regard to smoking cessation and pregnancy. The three waves of the National Population Health Survey allow the methodology of event history analysis to be applied to smoking initiation, cessation and relapse. One issue of interest is the relationship between smoking cessation and pregnancy. If a longitudinal respondent who is a smoker at the first cycle ceases smoking by the second cycle, we know the cessation time to within an interval of length at most a year, since the respondent is asked for the age at which she stopped smoking, and her date of birth is known. We also know whether she is pregnant at the time of the second cycle, and whether she has given birth since the time of the first cycle. For many such subjects, we know the date of conception to within a relatively small interval. If we knew the time of smoking cessation and pregnancy period exactly for each member who experienced one or other of these events between cycles, we could model their temporal relationship through their joint intensities.

Description:

This paper explores the relationship between low income and prevalence of asthma. The genetic and environmental determinants are incompletely understood. It has been observed in a previous study that Canadians with low incomes are at increased risk of asthma. Based on data from 17,605 subjects 12 years of age or older who participated in the first cycle of the National Population Health Survey (NPHS) from 1994 to 1995, males and females with low incomes had 1.44- and 1.33-fold increases, respectively, in the prevalence of asthma compared with their counterparts with high incomes. However, there was no significant difference observed between middle and high income categories. Therefore, it is not clear if there is a more systematic relationship between income adequacy and asthma occurrence. A much larger sample size of the second cycle of the NPHS allowed us to further explore if the prevalence of asthma increases with decreasing income adequacy among Canadians.

Description:

In this highly technical paper, we illustrate the application of the delete-a-group jack-knife variance estimator approach to a particular complex multi-wave longitudinal study, demonstrating its utility for linear regression and other analytic models. The delete-a-group jack-knife variance estimator is proving a very useful tool for measuring variances under complex sampling designs. This technique divides the first-phase sample into mutually exclusive and nearly equal variance groups, deletes one group at a time to create a set of replicates and makes analogous weighting adjustments in each replicate to those done for the sample as a whole. Variance estimation proceeds in the standard (unstratified) jack-knife fashion.

Our application is to the Chicago Health and Aging Project (CHAP), a community-based longitudinal study examining risk factors for chronic health problems of older adults. A major aim of the study is the investigation of risk factors for incident Alzheimer's disease. The current design of CHAP has two components: (1) Every three years, all surviving members of the cohort are interviewed on a variety of health-related topics. These interviews include cognitive and physical function measures. (2) At each of these waves of data collection, a stratified Poisson sample is drawn from among the respondents to the full population interview for detailed clinical evaluation and neuropsychological testing. To investigate risk factors for incident disease, a 'disease-free' cohort is identified at the preceding time point and forms one major stratum in the sampling frame.

We provide proofs of the theoretical applicability of the delete-a-group jack-knife for particular estimators under this Poisson design, paying needed attention to the distinction between finite-population and infinite-population (model) inference. In addition, we examine the issue of determining the 'right number' of variance groups.

Description:

This paper will describe the multiple imputation of income in the National Health Interview Survey and discuss the methodological issues involved. In addition, the paper will present empirical summaries of the imputations as well as results of a Monte Carlo evaluation of inferences based on multiply imputed income items.

Analysts of health data are often interested in studying relationships between income and health. The National Health Interview Survey, conducted by the National Center for Health Statistics of the U.S. Centers for Disease Control and Prevention, provides a rich source of data for studying such relationships. However, the nonresponse rates on two key income items, an individual's earned income and a family's total income, are over 20%. Moreover, these nonresponse rates appear to be increasing over time. A project is currently underway to multiply impute individual earnings and family income along with some other covariates for the National Health Interview Survey in 1997 and subsequent years.

There are many challenges in developing appropriate multiple imputations for such large-scale surveys. First, there are many variables of different types, with different skip patterns and logical relationships. Second, it is not known what types of associations will be investigated by the analysts of multiply imputed data. Finally, some variables, such as family income, are collected at the family level and others, such as earned income, are collected at the individual level. To make the imputations for both the family- and individual-level variables conditional on as many predictors as possible, and to simplify modelling, we are using a modified version of the sequential regression imputation method described in Raghunathan et al. ( Survey Methodology, 2001).

Besides issues related to the hierarchical nature of the imputations just described, there are other methodological issues of interest such as the use of transformations of the income variables, the imposition of restrictions on the values of variables, the general validity of sequential regression imputation and, even more generally, the validity of multiple-imputation inferences for surveys with complex sample designs.

Description:

Missing data are a constant problem in large-scale surveys. Such incompleteness is usually dealt with either by restricting the analysis to the cases with complete records or by imputing, for each missing item, an efficiently estimated value. The deficiencies of these approaches will be discussed in this paper, especially in the context of estimating a large number of quantities. The main part of the paper will describe two examples of analyses using multiple imputation.

In the first, the International Labour Organization (ILO) employment status is imputed in the British Labour Force Survey by a Bayesian bootstrap method. It is an adaptation of the hot-deck method, which seeks to fully exploit the auxiliary information. Important auxiliary information is given by the previous ILO status, when available, and the standard demographic variables.

Missing data can be interpreted more generally, as in the framework of the expectation maximization (EM) algorithm. The second example is from the Scottish House Condition Survey, and its focus is on the inconsistency of the surveyors. The surveyors assess the sampled dwelling units on a large number of elements or features of the dwelling, such as internal walls, roof and plumbing, that are scored and converted to a summarizing 'comprehensive repair cost.' The level of inconsistency is estimated from the discrepancies between the pairs of assessments of doubly surveyed dwellings. The principal research questions concern the amount of information that is lost as a result of the inconsistency and whether the naive estimators that ignore the inconsistency are unbiased. The problem is solved by multiple imputation, generating plausible scores for all the dwellings in the survey.

Description:

In the United States, the National Health and Nutrition Examination Survey (NHANES) is linked to the National Health Interview Survey (NHIS) at the primary sampling unit level (the same counties, but not necessarily the same persons, are in both surveys). The NHANES examines about 5,000 persons per year, while the NHIS samples about 100,000 persons per year. In this paper, we present and develop properties of models that allow NHIS and administrative data to be used as auxiliary information for estimating quantities of interest in the NHANES. The methodology, related to Fay-Herriot (1979) small-area models and to calibration estimators in Deville and Sarndal (1992), accounts for the survey designs in the error structure.

Description:

Cancer surveillance research requires accurate estimates of risk factors at the small area level. These risk factors are often obtained from surveys such as the National Health Interview Survey (NHIS) or the Behavioral Risk Factors Surveillance Survey (BRFSS). Unfortunately, no one population-based survey provides ideal prevalence estimates of such risk factors. One strategy is to combine information from multiple surveys, using the complementary strengths of one survey to compensate for the weakness of the other. The NHIS is a nationally representative, face-to-face survey with a high response rate; however, it cannot produce state or substate estimates of risk factor prevalence because sample sizes are too small. The BRFSS is a state-level telephone survey that excludes non-telephone households and has a lower response rate, but does provide reasonable sample sizes in all states and many counties. Several methods are available for constructing small-area estimators that combine information from both the NHIS and the BRFSS, including direct estimators, estimators under hierarchical Bayes models and model-assisted estimators. In this paper, we focus on the latter, constructing generalized regression (GREG) and 'minimum-distance' estimators and using existing and newly developed small-area smoothing techniques to smooth the resulting estimators.

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: Using data from the Postsecondary Student Information System (PSIS) and the Census of Population, 2021, this infographic provides information on enrolment in Canadian public postsecondary institutions for transgender and non-binary people.

Description: The infographic uses data from the integrated file of the Postsecondary Student Information System, the 2016 Census, the 2021 Census and the T1 Family File to compare the job quality of Indigenous graduates with a bachelor's degree with that of non-racialized and non-Indigenous graduates two years after graduation. Job quality indicators include employment income, unionization rate, and employer pension plan coverage rate.

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: Kennedy, Mercer, and Lau explore misreporting by respondents in non-probability samples and discover a new feature, namely that of deliberate misreporting of demographic characteristics. This finding suggests that the “arms race” between researchers and those determined to disrupt the practice of social science is not over and researchers need to account for such respondents if using high-quality probability surveys to help reduce error in non-probability samples.

Description: Nonprobability samples are quick and low-cost and have become popular for some types of survey research. Kennedy, Mercer and Lau examine data quality issues associated with opt-in nonprobability samples frequently used in the United States. They show that the estimates from these samples have serious problems that go beyond representativeness. A total survey error perspective is important for evaluating all types of surveys.

Description: Since 1984, an annual international symposium on methodological issues has been sponsored by Statistics Canada. Proceedings have been available since 1987.

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: Economic and Social Reports includes in-depth research, brief analyses, and current economic updates on a variety of topics, such as labour, immigration, education and skills, income mobility, well-being, aging, firm dynamics, productivity, economic transitions, and economic geography. All the papers are institutionally reviewed and the research and analytical papers undergo peer review to ensure that they conform to Statistics Canada's mandate as a governmental statistical agency and adhere to generally accepted standards of good professional practice.

Description: Every year, Statistics Canada collects data from hundreds of surveys. As the amount of data gathered increases, Statistics Canada has introduced infographics to help people, business owners, academics, and management at all levels, understand key information derived from the data. Infographics can be used to quickly communicate a message, to simplify the presentation of large amounts of data, to see data patterns and relationships, and to monitor changes in variables over time.

These infographics will provide a quick overview of Statistics Canada survey data.

Description: The journal publishes articles dealing with various aspects of statistical development relevant to a statistical agency, such as design issues in the context of practical constraints, use of different data sources and collection techniques, total survey error, survey evaluation, research in survey methodology, time series analysis, seasonal adjustment, demographic studies, data integration, estimation and data analysis methods, and general survey systems development. The emphasis is placed on the development and evaluation of specific methodologies as applied to data collection or the data themselves.

Description: This report presents the results of the population projections by age group and sex for Canada, the provinces and territories. These projections are based on assumptions that take into account the most recent trends relating to components of population growth, particularly fertility, mortality, immigration, emigration and interprovincial migration.

The detailed data tables are available in CODR: tables 1710005701 and 1710005801.

Description: The papers published in the Analysis in Brief analytical series shed light on current economic issues. Aimed at a general audience, they cover a wide range of topics including National Accounts, business enterprises, trade, transportation, agriculture, the environment, manufacturing, science and technology, services, etc.

Description:

Health Reports, published by the Health Analysis Division of Statistics Canada, is a peer-reviewed journal of population health and health services research. It is designed for a broad audience that includes health professionals, researchers, policymakers, and the general public. The journal publishes articles of wide interest that contain original and timely analyses of national or provincial/territorial surveys or administrative databases. New articles are published electronically each month.

Health Reports had an impact factor of 5.0 for 2022 and a five-year impact factor of 5.6. All articles are indexed in PubMed. Our online catalogue is free and receives more than 700,000 visits per year. External submissions are welcome.

Description: The Prices Analytical Series provides research and analysis pertaining to price indices. The Analytical series is intended to stimulate discussion on a variety of topics related to the analysis of the evolution of prices through time or space.

Description: Labour Statistics at a Glance features short analytical articles on specific topics of interest related to Canada's labour market. The studies examine recent or historical trends using data produced by the Centre for Labour Market Information, i.e., the Labour Force Survey, the Survey of Employment Payrolls and Hours, the Job Vacancy and Wage Survey, the Employment Insurance Coverage Survey and the Employment Insurance Statistics Program.