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- 1. Low Income Lines, 2013-2014: Update ArchivedArticles and reports: 75F0002M2015002Description:
In order to provide a holographic or complete picture of low income, Statistics Canada uses three complementary low income lines: the Low Income Cut-offs (LICOs), the Low Income Measures (LIMs) and the Market Basket Measure (MBM). While the first two lines were developed by Statistics Canada, the MBM is based on concepts developed by Employment and Social Development Canada. Though these measures differ from one another, they give a generally consistent picture of low income status over time. None of these measures is the best. Each contributes its own perspective and its own strengths to the study of low income, so that cumulatively, the three provide a better understanding of the phenomenon of low income as a whole. These measures are not measures of poverty, but strictly measures of low income.
This update presents revised LIMs for 2006 to 2011 resulting from the reweighting of SLID data. This reweighting makes it possible to compare results from CIS to earlier years.
Release date: 2015-12-17 - Articles and reports: 11F0027M2015099Description:
In the aftermath of 9/11, a new security regime was imposed on Canada–U.S. truck-borne trade, raising the question of whether the border has ‘thickened.’ Did the cost of moving goods across the border by truck rise? If so, by how much, and have these additional costs persisted through time? Building on previous work that measured the premium paid by shippers to move goods across the Canada–U.S. border by truck, from the mid- to late 2000s, this paper extends the time series back to 1994, encompassing the pre- and post-9/11 eras.
Release date: 2015-07-24 - 3. Low Income Lines, 2013-2014 ArchivedArticles and reports: 75F0002M2015001Description:
In order to provide a holographic or complete picture of low income, Statistics Canada uses three complementary low income lines: the Low Income Cut-offs (LICOs), the Low Income Measures (LIMs) and the Market Basket Measure (MBM). While the first two lines were developed by Statistics Canada, the MBM is based on concepts developed by Employment and Social Development Canada. Though these measures differ from one another, they give a generally consistent picture of low income status over time. None of these measures is the best. Each contributes its own perspective and its own strengths to the study of low income, so that cumulatively, the three provide a better understanding of the phenomenon of low income as a whole. These measures are not measures of poverty, but strictly measures of low income.
Release date: 2015-07-08 - Articles and reports: 12-001-X201500114160Description:
Composite estimation is a technique applicable to repeated surveys with controlled overlap between successive surveys. This paper examines the modified regression estimators that incorporate information from previous time periods into estimates for the current time period. The range of modified regression estimators are extended to the situation of business surveys with survey frames that change over time, due to the addition of “births” and the deletion of “deaths”. Since the modified regression estimators can deviate from the generalized regression estimator over time, it is proposed to use a compromise modified regression estimator, a weighted average of the modified regression estimator and the generalised regression estimator. A Monte Carlo simulation study shows that the proposed compromise modified regression estimator leads to significant efficiency gains in both the point-in-time and movement estimates.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114172Description:
When a random sample drawn from a complete list frame suffers from unit nonresponse, calibration weighting to population totals can be used to remove nonresponse bias under either an assumed response (selection) or an assumed prediction (outcome) model. Calibration weighting in this way can not only provide double protection against nonresponse bias, it can also decrease variance. By employing a simple trick one can estimate the variance under the assumed prediction model and the mean squared error under the combination of an assumed response model and the probability-sampling mechanism simultaneously. Unfortunately, there is a practical limitation on what response model can be assumed when design weights are calibrated to population totals in a single step. In particular, the choice for the response function cannot always be logistic. That limitation does not hinder calibration weighting when performed in two steps: from the respondent sample to the full sample to remove the response bias and then from the full sample to the population to decrease variance. There are potential efficiency advantages from using the two-step approach as well even when the calibration variables employed in each step is a subset of the calibration variables in the single step. Simultaneous mean-squared-error estimation using linearization is possible, but more complicated than when calibrating in a single step.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114174Description:
Matrix sampling, often referred to as split-questionnaire, is a sampling design that involves dividing a questionnaire into subsets of questions, possibly overlapping, and then administering each subset to one or more different random subsamples of an initial sample. This increasingly appealing design addresses concerns related to data collection costs, respondent burden and data quality, but reduces the number of sample units that are asked each question. A broadened concept of matrix design includes the integration of samples from separate surveys for the benefit of streamlined survey operations and consistency of outputs. For matrix survey sampling with overlapping subsets of questions, we propose an efficient estimation method that exploits correlations among items surveyed in the various subsamples in order to improve the precision of the survey estimates. The proposed method, based on the principle of best linear unbiased estimation, generates composite optimal regression estimators of population totals using a suitable calibration scheme for the sampling weights of the full sample. A variant of this calibration scheme, of more general use, produces composite generalized regression estimators that are also computationally very efficient.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114192Description:
We are concerned with optimal linear estimation of means on subsequent occasions under sample rotation where evolution of samples in time is designed through a cascade pattern. It has been known since the seminal paper of Patterson (1950) that when the units are not allowed to return to the sample after leaving it for certain period (there are no gaps in the rotation pattern), one step recursion for optimal estimator holds. However, in some important real surveys, e.g., Current Population Survey in the US or Labour Force Survey in many countries in Europe, units return to the sample after being absent in the sample for several occasions (there are gaps in rotation patterns). In such situations difficulty of the question of the form of the recurrence for optimal estimator increases drastically. This issue has not been resolved yet. Instead alternative sub-optimal approaches were developed, as K - composite estimation (see e.g., Hansen, Hurwitz, Nisselson and Steinberg (1955)), AK - composite estimation (see e.g., Gurney and Daly (1965)) or time series approach (see e.g., Binder and Hidiroglou (1988)).
In the present paper we overcome this long-standing difficulty, that is, we present analytical recursion formulas for the optimal linear estimator of the mean for schemes with gaps in rotation patterns. It is achieved under some technical conditions: ASSUMPTION I and ASSUMPTION II (numerical experiments suggest that these assumptions might be universally satisfied). To attain the goal we develop an algebraic operator approach which allows to reduce the problem of recursion for the optimal linear estimator to two issues: (1) localization of roots (possibly complex) of a polynomial Qp defined in terms of the rotation pattern (Qp happens to be conveniently expressed through Chebyshev polynomials of the first kind), (2) rank of a matrix S defined in terms of the rotation pattern and the roots of the polynomial Qp. In particular, it is shown that the order of the recursion is equal to one plus the size of the largest gap in the rotation pattern. Exact formulas for calculation of the recurrence coefficients are given - of course, to use them one has to check (in many cases, numerically) that ASSUMPTIONs I and II are satisfied. The solution is illustrated through several examples of rotation schemes arising in real surveys.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114193Description:
Imputed micro data often contain conflicting information. The situation may e.g., arise from partial imputation, where one part of the imputed record consists of the observed values of the original record and the other the imputed values. Edit-rules that involve variables from both parts of the record will often be violated. Or, inconsistency may be caused by adjustment for errors in the observed data, also referred to as imputation in Editing. Under the assumption that the remaining inconsistency is not due to systematic errors, we propose to make adjustments to the micro data such that all constraints are simultaneously satisfied and the adjustments are minimal according to a chosen distance metric. Different approaches to the distance metric are considered, as well as several extensions of the basic situation, including the treatment of categorical data, unit imputation and macro-level benchmarking. The properties and interpretations of the proposed methods are illustrated using business-economic data.
Release date: 2015-06-29 - 9. A method of determining the winsorization threshold, with an application to domain estimation ArchivedArticles and reports: 12-001-X201500114199Description:
In business surveys, it is not unusual to collect economic variables for which the distribution is highly skewed. In this context, winsorization is often used to treat the problem of influential values. This technique requires the determination of a constant that corresponds to the threshold above which large values are reduced. In this paper, we consider a method of determining the constant which involves minimizing the largest estimated conditional bias in the sample. In the context of domain estimation, we also propose a method of ensuring consistency between the domain-level winsorized estimates and the population-level winsorized estimate. The results of two simulation studies suggest that the proposed methods lead to winsorized estimators that have good bias and relative efficiency properties.
Release date: 2015-06-29 - 10. Observed best prediction via nested-error regression with potentially misspecified mean and variance ArchivedArticles and reports: 12-001-X201500114200Description:
We consider the observed best prediction (OBP; Jiang, Nguyen and Rao 2011) for small area estimation under the nested-error regression model, where both the mean and variance functions may be misspecified. We show via a simulation study that the OBP may significantly outperform the empirical best linear unbiased prediction (EBLUP) method not just in the overall mean squared prediction error (MSPE) but also in the area-specific MSPE for every one of the small areas. A bootstrap method is proposed for estimating the design-based area-specific MSPE, which is simple and always produces positive MSPE estimates. The performance of the proposed MSPE estimator is evaluated through a simulation study. An application to the Television School and Family Smoking Prevention and Cessation study is considered.
Release date: 2015-06-29
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- 1. Low Income Lines, 2013-2014: Update ArchivedArticles and reports: 75F0002M2015002Description:
In order to provide a holographic or complete picture of low income, Statistics Canada uses three complementary low income lines: the Low Income Cut-offs (LICOs), the Low Income Measures (LIMs) and the Market Basket Measure (MBM). While the first two lines were developed by Statistics Canada, the MBM is based on concepts developed by Employment and Social Development Canada. Though these measures differ from one another, they give a generally consistent picture of low income status over time. None of these measures is the best. Each contributes its own perspective and its own strengths to the study of low income, so that cumulatively, the three provide a better understanding of the phenomenon of low income as a whole. These measures are not measures of poverty, but strictly measures of low income.
This update presents revised LIMs for 2006 to 2011 resulting from the reweighting of SLID data. This reweighting makes it possible to compare results from CIS to earlier years.
Release date: 2015-12-17 - Articles and reports: 11F0027M2015099Description:
In the aftermath of 9/11, a new security regime was imposed on Canada–U.S. truck-borne trade, raising the question of whether the border has ‘thickened.’ Did the cost of moving goods across the border by truck rise? If so, by how much, and have these additional costs persisted through time? Building on previous work that measured the premium paid by shippers to move goods across the Canada–U.S. border by truck, from the mid- to late 2000s, this paper extends the time series back to 1994, encompassing the pre- and post-9/11 eras.
Release date: 2015-07-24 - 3. Low Income Lines, 2013-2014 ArchivedArticles and reports: 75F0002M2015001Description:
In order to provide a holographic or complete picture of low income, Statistics Canada uses three complementary low income lines: the Low Income Cut-offs (LICOs), the Low Income Measures (LIMs) and the Market Basket Measure (MBM). While the first two lines were developed by Statistics Canada, the MBM is based on concepts developed by Employment and Social Development Canada. Though these measures differ from one another, they give a generally consistent picture of low income status over time. None of these measures is the best. Each contributes its own perspective and its own strengths to the study of low income, so that cumulatively, the three provide a better understanding of the phenomenon of low income as a whole. These measures are not measures of poverty, but strictly measures of low income.
Release date: 2015-07-08 - Articles and reports: 12-001-X201500114160Description:
Composite estimation is a technique applicable to repeated surveys with controlled overlap between successive surveys. This paper examines the modified regression estimators that incorporate information from previous time periods into estimates for the current time period. The range of modified regression estimators are extended to the situation of business surveys with survey frames that change over time, due to the addition of “births” and the deletion of “deaths”. Since the modified regression estimators can deviate from the generalized regression estimator over time, it is proposed to use a compromise modified regression estimator, a weighted average of the modified regression estimator and the generalised regression estimator. A Monte Carlo simulation study shows that the proposed compromise modified regression estimator leads to significant efficiency gains in both the point-in-time and movement estimates.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114172Description:
When a random sample drawn from a complete list frame suffers from unit nonresponse, calibration weighting to population totals can be used to remove nonresponse bias under either an assumed response (selection) or an assumed prediction (outcome) model. Calibration weighting in this way can not only provide double protection against nonresponse bias, it can also decrease variance. By employing a simple trick one can estimate the variance under the assumed prediction model and the mean squared error under the combination of an assumed response model and the probability-sampling mechanism simultaneously. Unfortunately, there is a practical limitation on what response model can be assumed when design weights are calibrated to population totals in a single step. In particular, the choice for the response function cannot always be logistic. That limitation does not hinder calibration weighting when performed in two steps: from the respondent sample to the full sample to remove the response bias and then from the full sample to the population to decrease variance. There are potential efficiency advantages from using the two-step approach as well even when the calibration variables employed in each step is a subset of the calibration variables in the single step. Simultaneous mean-squared-error estimation using linearization is possible, but more complicated than when calibrating in a single step.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114174Description:
Matrix sampling, often referred to as split-questionnaire, is a sampling design that involves dividing a questionnaire into subsets of questions, possibly overlapping, and then administering each subset to one or more different random subsamples of an initial sample. This increasingly appealing design addresses concerns related to data collection costs, respondent burden and data quality, but reduces the number of sample units that are asked each question. A broadened concept of matrix design includes the integration of samples from separate surveys for the benefit of streamlined survey operations and consistency of outputs. For matrix survey sampling with overlapping subsets of questions, we propose an efficient estimation method that exploits correlations among items surveyed in the various subsamples in order to improve the precision of the survey estimates. The proposed method, based on the principle of best linear unbiased estimation, generates composite optimal regression estimators of population totals using a suitable calibration scheme for the sampling weights of the full sample. A variant of this calibration scheme, of more general use, produces composite generalized regression estimators that are also computationally very efficient.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114192Description:
We are concerned with optimal linear estimation of means on subsequent occasions under sample rotation where evolution of samples in time is designed through a cascade pattern. It has been known since the seminal paper of Patterson (1950) that when the units are not allowed to return to the sample after leaving it for certain period (there are no gaps in the rotation pattern), one step recursion for optimal estimator holds. However, in some important real surveys, e.g., Current Population Survey in the US or Labour Force Survey in many countries in Europe, units return to the sample after being absent in the sample for several occasions (there are gaps in rotation patterns). In such situations difficulty of the question of the form of the recurrence for optimal estimator increases drastically. This issue has not been resolved yet. Instead alternative sub-optimal approaches were developed, as K - composite estimation (see e.g., Hansen, Hurwitz, Nisselson and Steinberg (1955)), AK - composite estimation (see e.g., Gurney and Daly (1965)) or time series approach (see e.g., Binder and Hidiroglou (1988)).
In the present paper we overcome this long-standing difficulty, that is, we present analytical recursion formulas for the optimal linear estimator of the mean for schemes with gaps in rotation patterns. It is achieved under some technical conditions: ASSUMPTION I and ASSUMPTION II (numerical experiments suggest that these assumptions might be universally satisfied). To attain the goal we develop an algebraic operator approach which allows to reduce the problem of recursion for the optimal linear estimator to two issues: (1) localization of roots (possibly complex) of a polynomial Qp defined in terms of the rotation pattern (Qp happens to be conveniently expressed through Chebyshev polynomials of the first kind), (2) rank of a matrix S defined in terms of the rotation pattern and the roots of the polynomial Qp. In particular, it is shown that the order of the recursion is equal to one plus the size of the largest gap in the rotation pattern. Exact formulas for calculation of the recurrence coefficients are given - of course, to use them one has to check (in many cases, numerically) that ASSUMPTIONs I and II are satisfied. The solution is illustrated through several examples of rotation schemes arising in real surveys.
Release date: 2015-06-29 - Articles and reports: 12-001-X201500114193Description:
Imputed micro data often contain conflicting information. The situation may e.g., arise from partial imputation, where one part of the imputed record consists of the observed values of the original record and the other the imputed values. Edit-rules that involve variables from both parts of the record will often be violated. Or, inconsistency may be caused by adjustment for errors in the observed data, also referred to as imputation in Editing. Under the assumption that the remaining inconsistency is not due to systematic errors, we propose to make adjustments to the micro data such that all constraints are simultaneously satisfied and the adjustments are minimal according to a chosen distance metric. Different approaches to the distance metric are considered, as well as several extensions of the basic situation, including the treatment of categorical data, unit imputation and macro-level benchmarking. The properties and interpretations of the proposed methods are illustrated using business-economic data.
Release date: 2015-06-29 - 9. A method of determining the winsorization threshold, with an application to domain estimation ArchivedArticles and reports: 12-001-X201500114199Description:
In business surveys, it is not unusual to collect economic variables for which the distribution is highly skewed. In this context, winsorization is often used to treat the problem of influential values. This technique requires the determination of a constant that corresponds to the threshold above which large values are reduced. In this paper, we consider a method of determining the constant which involves minimizing the largest estimated conditional bias in the sample. In the context of domain estimation, we also propose a method of ensuring consistency between the domain-level winsorized estimates and the population-level winsorized estimate. The results of two simulation studies suggest that the proposed methods lead to winsorized estimators that have good bias and relative efficiency properties.
Release date: 2015-06-29 - 10. Observed best prediction via nested-error regression with potentially misspecified mean and variance ArchivedArticles and reports: 12-001-X201500114200Description:
We consider the observed best prediction (OBP; Jiang, Nguyen and Rao 2011) for small area estimation under the nested-error regression model, where both the mean and variance functions may be misspecified. We show via a simulation study that the OBP may significantly outperform the empirical best linear unbiased prediction (EBLUP) method not just in the overall mean squared prediction error (MSPE) but also in the area-specific MSPE for every one of the small areas. A bootstrap method is proposed for estimating the design-based area-specific MSPE, which is simple and always produces positive MSPE estimates. The performance of the proposed MSPE estimator is evaluated through a simulation study. An application to the Television School and Family Smoking Prevention and Cessation study is considered.
Release date: 2015-06-29
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- Surveys and statistical programs – Documentation: 89-648-X2015001Description:
The Longitudinal and International Study of Adults (LISA) has the direct measures of skills from the Program for International Assessment of Adult Competencies (PIAAC) because the two surveys had coordinated collection. The direct measures of skills cover three domains: literacy, numeracy, and problem solving in technology-rich environments. The skills measures are reflected in sets of 10 plausible values (PVs) that were created using a multiple imputation methodology. This paper demonstrates the proper use of the PVs. It also demonstrates that reliable estimates of skills can be produced using LISA and the results are similar to what would be obtained from the PIAAC data.
Release date: 2015-04-22
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