Statistical techniques

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All (208)

All (208) (0 to 10 of 208 results)

1. Quantitative impact analysis: A practical overview
Articles and reports: 36-28-0001202600500003
Description: This spotlight article outlines practical methods for assessing the economic impacts of public programs delivered by federal agencies and Crown corporations. It summarizes key steps in conducting quantitative impact analysis, including data linkage, cohort construction and implementation of quasi causal estimators.
Release date: 2026-05-27
2. Analytical Studies: Methods and References
Journals and periodicals: 11-633-X
Description: Papers in this series provide background discussions of the methods used to develop data for economic, health, and social analytical studies at Statistics Canada. They are intended to provide readers with information on the statistical methods, standards and definitions used to develop databases for research purposes. All papers in this series have undergone peer and institutional review to ensure that they conform to Statistics Canada's mandate and adhere to generally accepted standards of good professional practice.
Release date: 2026-05-27
3. Effects of model misspecification on small area estimators
Articles and reports: 12-001-X202500200001
Description: Nested error regression models are commonly used to incorporate unit specific auxiliary variables to improve small area estimates. When the mean structure of the model is misspecified, the design-based mean squared prediction error (MSPE) of Empirical Best Linear Unbiased Predictors (EBLUP) generally increases. The Observed Best Prediction (OBP) method has been proposed with the intent to improve on the design-based MSPE over EBLUP. In this paper, we conduct a Monte Carlo simulation experiments to understand the effect of misspsecification of mean structures on different small area estimators. Our findings suggest that the OBP using unit-level auxiliary variables does not outperform the EBLUP in terms of design-based MSPE, unless the number of small areas m is extremely large. Conversely, the performance of OBP significantly improves when area-level auxiliary variables are employed. This paper includes both analytical and numerical evidence to demonstrate these observations, providing practical insights for addressing model misspecification in small area estimation (SAE).
Release date: 2025-12-23
4. Integrating probability and non-probability samples through deep learning-based mass imputation
Articles and reports: 12-001-X202500200007
Description: Although probability samples have been regarded as the gold standard to collect information for population-based study, non-probability samples have been used frequently in practice due to low cost, convenience, and the lack of the sampling frame for the survey. Naïve estimates based on non-probability samples without any adjustments may be misleading due to selection bias. Recently, a valid data integration approach that includes mass imputation, propensity score weighting, and calibration has been used to improve the representativeness of non-probability samples. The effectiveness of the mass imputation approach depends on the underlying model assumptions. In this paper, we propose using deep learning for the mass imputation in the combining of probability and non-probability samples and compare it with several modern machine learning-based mass imputation approaches, including generalized additive modeling, regression tree, random forest, and XG-boosting. In the simulation study, deep learning-based approaches have been shown to be more robust and effective than other mass imputation approaches against the failure of underlying model assumptions under non-linearity scenarios.
Release date: 2025-12-23
5. Generalized regression estimation under misspecified sample design
Articles and reports: 12-001-X202500200008
Description: Classical design-based survey estimation relies on a properly specified sampling design for valid inference. We consider the properties of regression estimation under a misspecified sample design, in which the nominal and true inclusion probabilities do not necessarily match. This general misspecified sample design setting encompasses many challenges in the modern survey environment. Under this setting, an asymptotic analysis of the regression estimator, an expression of the bias, and an expression of the variance are presented. Further, a consistent variance estimator is derived and an expression which estimates the bias in-part or in-whole is discussed. This later expression may be used as an indicator of the presence of bias due to misspecification by a practitioner. A simulation study is conducted to support the presented theory.
Release date: 2025-12-23
6. Mapping location and co-location of industries at the neighborhood level: A spatial kernel density approach
Articles and reports: 18-001-X2025001
Description: This paper brings the analysis of business cluster to a more granular geographic scale by developing a methodology for identifying business clusters at the neighborhood level. The proposed method identifies clusters of businesses at the DB level, which is one of the most granular spatial units of analysis defined by Statistics Canada. The method is developed with an application to four census metropolitan areas (CMAs) of different sizes and for different industry cluster specifications, including simple 2-digit North American Industry Classification System (NAICS) groups as well as industry clusters resulting from groupings of NAICS codes, as defined by Delgado et al. (2014).
Release date: 2025-10-10
7. Efficient Record Linkage for Large Datasets by Business Names Archived
Articles and reports: 11-522-X202500100019
Description: Accurate and efficient record linkage is crucial for maintaining a comprehensive and current Statistical Business Register (SBR) at Statistics Canada. Linking external business lists to the SBR by name presents computational and methodological challenges, especially as data volumes grow. This paper describes a scalable methodology that employs blocking techniques to constrain the computational search space and integrates multiple similarity measures—from edit distances and n-gram overlaps to embedding-based methods using Sentence-BERT (SBERT)—to identify likely matches. By combining simple character-level comparisons with more advanced semantic embedding methods, the approach can adapt to various naming conventions and complexities. While it does not guarantee superior accuracy in all circumstances, it offers a pragmatic balance between computational feasibility and linkage quality.
Release date: 2025-09-08
8. Evaluating the Accuracy when Linking Records in Waves Archived
Articles and reports: 11-522-X202500100020
Description: At Statistics Canada, many data sets are linked with quasi-identifiers such as the first name, last name, or address. In such cases, linkage errors are a potential concern and must be measured. In that regard, previous studies have shown that the evaluation may be based on modeling the number of links from a given record while accounting for all the interactions among the linkage variables and dispensing with clerical reviews, so long as the decision to link two records does not involve other records. In this communication, the methodology is adapted for a class of practical strategies, which violate this constraint by linking the records in consecutive waves, where a given wave links a subset of the records that are not linked in previous waves. In particular, the linkage may be based on a deterministic wave followed by a probabilistic one.
Release date: 2025-09-08
9. Model-Based Threshold Selection for Agricultural Linkages Archived
Articles and reports: 11-522-X202500100021
Description: Optimal threshold selection is a critical challenge in probabilistic linkage, with significant implications for the accuracy and reliability of linked datasets. This paper analyzes the performance of the neighbour model, a recently proposed error model which models linkage errors by the number of links from each record. Three threshold selection algorithms utilizing the neighbour model were assessed, highlighting the strengths and limitations of each. Their performance was assessed through simulation studies, which demonstrated that methods using the neighbour model achieved lower relative bias compared to two established methods for threshold selection. Additionally, the practical utility was validated through goodness-of-fit tests conducted on four agricultural datasets, showing the potential of the model for use in real-world applications.
Release date: 2025-09-08
10. T1 Redesign: T1 Partnership Identification Process Archived
Articles and reports: 11-522-X202500100022
Description: In Canada, T1 Tax forms are used to report personal income, whether earned as an employee or through self-employment. Income from self-employment, or "T1 Business Income" is reported by sole proprietorships or partnerships. A T1 partnership involves two or more legal entities jointly filing for a shared business. T1 business data is received as individual filings, meaning partnerships are received separately for each partner. Internal record linkage within the T1 business database is performed to identify partnerships and prevent overcoverage within the final population of T1 businesses. This new T1 partnership identification process takes advantage of newer algorithms, such as DBSCAN numerical clustering fuzzy matching, to identify internal linkages. Graph theory is used to construct the list of partnerships from the row-pairs identified in the linkage process.
Release date: 2025-09-08

Data (1)

Data (1) ((1 result))

1. Income divergence index (D-index) by census tract
Table: 11-10-0074-01
Geography: Census tract
Frequency: Occasional
Description:
The divergence index (D-index) describes the degree that families with different income levels are mixing together in neighbourhoods. It compares neighbourhood (census tract, CT) discrete income distributions to a base distribution, which is the income quintiles of the neighbourhood’s census metropolitan area (CMA).

Release date: 2020-06-22

Analysis (200)

Analysis (200) (80 to 90 of 200 results)

81. Model-assisted sample design is minimax for model-based prediction Archived
Articles and reports: 12-001-X202000100003
Description:
Probability sampling designs are sometimes used in conjunction with model-based predictors of finite population quantities. These designs should minimize the anticipated variance (AV), which is the variance over both the superpopulation and sampling processes, of the predictor of interest. The AV-optimal design is well known for model-assisted estimators which attain the Godambe-Joshi lower bound for the AV of design-unbiased estimators. However, no optimal probability designs have been found for model-based prediction, except under conditions such that the model-based and model-assisted estimators coincide; these cases can be limiting. This paper shows that the Godambe-Joshi lower bound is an upper bound for the AV of the best linear unbiased estimator of a population total, where the upper bound is over the space of all covariate sets. Therefore model-assisted optimal designs are a sensible choice for model-based prediction when there is uncertainty about the form of the final model, as there often would be prior to conducting the survey. Simulations confirm the result over a range of scenarios, including when the relationship between the target and auxiliary variables is nonlinear and modeled using splines. The AV is lowest relative to the bound when an important design variable is not associated with the target variable.
Release date: 2020-06-30
82. Neighbourhood, Dwelling and Apartment Building Income Mixing: Measures and Experimental Estimates Across Census Metropolitan Areas Archived
Articles and reports: 11-633-X2020001
Description:
This paper reviews alternative measures of income mixing within geographic units and applies them using geographically detailed income data derived from tax records. It highlights the characteristics of these measures, particularly their ease of interpretation and their suitability to decomposition across different levels of analysis, from neighbourhoods to individual apartment buildings. The discussion focuses on three measures: the dissimilarity index, the information theory index and the divergence index (D-index). Particular emphasis is placed on the D-index because it most effectively describes how income distributions at the sub-metropolitan level (e.g., neighbourhoods) differ from distributions at the metropolitan level (i.e., how much income sorting occurs across neighbourhoods). Furthermore, the D-index can consistently measure the contributions of income sorting within neighbourhoods (e.g., across individual apartment buildings) to the degree of income mixing at the neighbourhood and metropolitan scales.
Release date: 2020-01-21
83. Cohort profile: The Canadian Census Health and Environment Cohorts (CanCHECs) Archived
Articles and reports: 82-003-X201901200003
Description: This article provides a description of the Canadian Census Health and Environment Cohorts (CanCHECs), a population-based linked datasets of the household population at the time of census collection. The CanCHEC datasets are rich national data resources that can be used to measure and examine health inequalities across socioeconomic and ethnocultural dimensions for different periods and locations. These datasets can also be used to examine the effects of exposure to environmental factors on human health.
Release date: 2019-12-18
84. Canadian Census Health and Environment Cohorts: Creation of a new health surveillance program Archived
Stats in brief: 11-629-X2019006
Description:
This video describes a new health surveillance program at Statistics Canada: The Canadian Census Health and Environment Cohorts (CanCHECs). The video describes the attributes of and the datasets included in the CanCHECs, how the CanCHECs can be used, and their strengths and limitations. Recent examples of research projects based on the CanCHECs are presented along with information about how to apply for access to these data.
Release date: 2019-12-18
85. Estimating the Effect of Changing Canada-US Border Costs on North American Trade Patterns and Expenditures: Detailed Methodology Archived
Articles and reports: 11-633-X2019004
Description:
This paper shows how to estimate the effect of the Canada-United States border on non-energy goods trade at a sub-provincial/state level using Statistics Canada’s Surface Transportation File (STF), augmented with United States domestic trade data. It uses a gravity model framework to compare cross-border to domestic trade flows among 201 Canadian and United States regions in year 2012. It shows that some 25 years after the Canada-United States Free Trade Agreement (the North American Free Trade Agreement’s predecessor) was ratified, the cost of trading goods across the border still amounts to a 30% tariff on bilateral trade between Canadian and United States regions. The paper also demonstrates how these estimates can be used along with general equilibrium Poisson pseudo maximum likelihood (GEPPML) methods to describe the effect of changing border costs on North American trade patterns and regional welfare.
Release date: 2019-09-24
86. Data Literacy: What It Is and How to Measure It in the Public Service Archived
Articles and reports: 11-633-X2019003
Description:
This report provides an overview of the definitions and competency frameworks of data literacy, as well as the assessment tools used to measure it. These are based on the existing literature and current practices around the world. Data literacy, or the ability to derive meaningful information from data, is a relatively new concept. However, it is gaining increasing recognition as a vital skillset in the information age. Existing approaches to measuring data literacy—from self-assessment tools to objective measures, and from individual to organizational assessments—are discussed in this report to inform the development of an assessment tool for data literacy in the Canadian public service.
Release date: 2019-08-14
87. On combining independent probability samples Archived
Articles and reports: 12-001-X201900200003
Description:
Merging available sources of information is becoming increasingly important for improving estimates of population characteristics in a variety of fields. In presence of several independent probability samples from a finite population we investigate options for a combined estimator of the population total, based on either a linear combination of the separate estimators or on the combined sample approach. A linear combination estimator based on estimated variances can be biased as the separate estimators of the population total can be highly correlated to their respective variance estimators. We illustrate the possibility to use the combined sample to estimate the variances of the separate estimators, which results in general pooled variance estimators. These pooled variance estimators use all available information and have potential to significantly reduce bias of a linear combination of separate estimators.
Release date: 2019-06-27
88. An alternative way of estimating a cumulative logistic model with complex survey data Archived
Articles and reports: 12-001-X201900200007
Description:
When fitting an ordered categorical variable with L > 2 levels to a set of covariates onto complex survey data, it is common to assume that the elements of the population fit a simple cumulative logistic regression model (proportional-odds logistic-regression model). This means the probability that the categorical variable is at or below some level is a binary logistic function of the model covariates. Moreover, except for the intercept, the values of the logistic-regression parameters are the same at each level. The conventional “design-based” method used for fitting the proportional-odds model is based on pseudo-maximum likelihood. We compare estimates computed using pseudo-maximum likelihood with those computed by assuming an alternative design-sensitive robust model-based framework. We show with a simple numerical example how estimates using the two approaches can differ. The alternative approach is easily extended to fit a general cumulative logistic model, in which the parallel-lines assumption can fail. A test of that assumption easily follows.
Release date: 2019-06-27
89. An assessment of accuracy improvement by adaptive survey design Archived
Articles and reports: 12-001-X201900200008
Description:
High nonresponse occurs in many sample surveys today, including important surveys carried out by government statistical agencies. An adaptive data collection can be advantageous in those conditions: Lower nonresponse bias in survey estimates can be gained, up to a point, by producing a well-balanced set of respondents. Auxiliary variables serve a twofold purpose: Used in the estimation phase, through calibrated adjustment weighting, they reduce, but do not entirely remove, the bias. In the preceding adaptive data collection phase, auxiliary variables also play a major role: They are instrumental in reducing the imbalance in the ultimate set of respondents. For such combined use of auxiliary variables, the deviation of the calibrated estimate from the unbiased estimate (under full response) is studied in the article. We show that this deviation is a sum of two components. The reducible component can be decreased through adaptive data collection, all the way to zero if perfectly balanced response is realized with respect to a chosen auxiliary vector. By contrast, the resisting component changes little or not at all by a better balanced response; it represents a part of the deviation that adaptive design does not get rid of. The relative size of the former component is an indicator of the potential payoff from an adaptive survey design.
Release date: 2019-06-27
90. An Assessment of Non-probabilistic Online Survey Data: Comparing the Carrot Rewards Mobile App Survey to the Canadian Community Health Survey Archived
Articles and reports: 11-633-X2019002
Description:
Survey data collection through mobile devices, such as tablets and smartphones, is underway in Canada. However, little is known about the representativeness of the data collected through these devices. In March 2017, Statistics Canada commissioned survey data collection through the Carrot Rewards Application and included 11 questions on the Carrot Rewards Mobile App Survey (Carrot) drawn from the 2017 Canadian Community Health Survey (CCHS).
Release date: 2019-06-04

Reference (7)

Reference (7) ((7 results))

1. Methods for Constructing Life Tables for Canada, Provinces and Territories
Surveys and statistical programs – Documentation: 84-538-X
Geography: Canada
Description: This electronic publication presents the methodology underlying the production of the life tables for Canada, provinces and territories.
Release date: 2023-08-28
2. Canadian Cancer Registry System Guide, 2007 Edition Archived
Surveys and statistical programs – Documentation: 82-225-X200701010508
Description:
The Record Linkage Overview describes the process used in annual internal record linkage of the Canadian Cancer Registry. The steps include: preparation; pre-processing; record linkage; post-processing; analysis and resolution; resolution entry; and, resolution processing.
Release date: 2008-01-18
3. Using the postal code as merge key for independent data files: matching data from the Canadian Census and an administrative file of school test scores in Quebec Archived
Surveys and statistical programs – Documentation: 11-522-X20050019476
Description:
The paper will show how, using data published by Statistics Canada and available from member libraries of the CREPUQ, a linkage approach using postal codes makes it possible to link the data from the outcomes file to a set of contextual variables. These variables could then contribute to producing, on an exploratory basis, a better index to explain the varied outcomes of students from schools. In terms of the impact, the proposed index could show more effectively the limitations of ranking students and schools when this information is not given sufficient weight.
Release date: 2007-03-02
4. The Integrated Approach to Economic Surveys in Canada Archived
Surveys and statistical programs – Documentation: 68-514-X
Description:
Statistics Canada's approach to gathering and disseminating economic data has developed over several decades into a highly integrated system for collection and estimation that feeds the framework of the Canadian System of National Accounts.
The key to this approach was creation of the Unified Enterprise Survey, the goal of which was to improve the consistency, coherence, breadth and depth of business survey data.
The UES did so by bringing many of Statistics Canada's individual annual business surveys under a common framework. This framework included a single survey frame, a sample design framework, conceptual harmonization of survey content, means of using relevant administrative data, common data collection, processing and analysis tools, and a common data warehouse.
Release date: 2006-11-20
5. The Longitudinal Administrative Databank (LAD) and the Longitudinal Immigration Database (IMDB): Building the LAD_IMDB - A Technical Paper Archived
Surveys and statistical programs – Documentation: 89-612-X
Description:
This paper describes the structure and linkage of two databases: the Longitudinal Administrative Databank (LAD), and the Longitudinal Immigration Database (IMDB). The combined data associate landed immigrant taxfilers on the LAD with their key characteristics upon immigration. The paper highlights how the combined information, referred to here as the LAD_IMDB, enhances and complements the existing separate databases. The paper compares the full IMDB file with the sample of immigrants to assess the representativeness of the sample file.
Release date: 2004-01-05
6. Linking Provincial Student Assessments with National and International Assessments Archived
Surveys and statistical programs – Documentation: 81-595-M2003005
Geography: Canada
Description:
This paper develops technical procedures that may enable ministries of education to link provincial tests with national and international tests in order to compare standards and report results on a common scale.
Release date: 2003-05-29
7. An Overview of the Issues Related to the Use of Personal Identifiers Archived
Surveys and statistical programs – Documentation: 85-602-X
Description:
The purpose of this report is to provide an overview of existing methods and techniques making use of personal identifiers to support record linkage. Record linkage can be loosely defined as a methodology for manipulating and / or transforming personal identifiers from individual data records from one or more operational databases and subsequently attempting to match these personal identifiers to create a composite record about an individual. Record linkage is not intended to uniquely identify individuals for operational purposes; however, it does provide probabilistic matches of varying degrees of reliability for use in statistical reporting. Techniques employed in record linkage may also be of use for investigative purposes to help narrow the field of search against existing databases when some form of personal identification information exists.
Release date: 2000-12-05

Date modified:: 2026-06-10

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