Analysis

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:

The Fay-Herriot model is often used to produce small area estimates. These estimates are generally more efficient than standard direct estimates. In order to evaluate the efficiency gains obtained by small area estimation methods, model mean square error estimates are usually produced. However, these estimates do not reflect all the peculiarities of a given domain (or area) because model mean square errors integrate out the local effects. An alternative is to estimate the design mean square error of small area estimators, which is often more attractive from a user point of view. However, it is known that design mean square error estimates can be very unstable, especially for domains with few sampled units. In this paper, we propose two local diagnostics that aim to choose between the empirical best predictor and the direct estimator for a particular domain. We first find an interval for the local effect such that the best predictor is more efficient under the design than the direct estimator. Then, we consider two different approaches to assess whether it is plausible that the local effect falls in this interval. We evaluate our diagnostics using a simulation study. Our preliminary results indicate that our diagnostics are effective for choosing between the empirical best predictor and the direct estimator.

Description:

Statistics Canada continues to use a variety of data sources to provide neighbourhood-level variables across an expanding set of domains, such as sociodemographic characteristics, income, services and amenities, crime, and the environment. Yet, despite these advances, information on the social aspects of neighbourhoods is still unavailable. In this paper, answers to the Canadian Community Health Survey on respondents’ sense of belonging to their local community were pooled over the four survey years from 2016 to 2019. Individual responses were aggregated up to the census tract (CT) level.

Description:

The bootstrap technique is becoming more and more popular in sample surveys conducted by national statistical agencies. In most of its implementations, several sets of bootstrap weights accompany the survey microdata file given to analysts. So far, the use of the technique in practice seems to have been mostly limited to variance estimation problems. In this paper, we propose a bootstrap methodology for testing hypotheses about a vector of unknown model parameters when the sample has been drawn from a finite population. The probability sampling design used to select the sample may be informative or not. Our method uses model-based test statistics that incorporate the survey weights. Such statistics are usually easily obtained using classical software packages. We approximate the distribution under the null hypothesis of these weighted model-based statistics by using bootstrap weights. An advantage of our bootstrap method over existing methods of hypothesis testing with survey data is that, once sets of bootstrap weights are provided to analysts, it is very easy to apply even when no specialized software dealing with complex surveys is available. Also, our simulation results suggest that, overall, it performs similarly to the Rao-Scott procedure and better than the Wald and Bonferroni procedures when testing hypotheses about a vector of linear regression model parameters.

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:

The Fay-Herriot model is often used to produce small area estimates. These estimates are generally more efficient than standard direct estimates. In order to evaluate the efficiency gains obtained by small area estimation methods, model mean square error estimates are usually produced. However, these estimates do not reflect all the peculiarities of a given domain (or area) because model mean square errors integrate out the local effects. An alternative is to estimate the design mean square error of small area estimators, which is often more attractive from a user point of view. However, it is known that design mean square error estimates can be very unstable, especially for domains with few sampled units. In this paper, we propose two local diagnostics that aim to choose between the empirical best predictor and the direct estimator for a particular domain. We first find an interval for the local effect such that the best predictor is more efficient under the design than the direct estimator. Then, we consider two different approaches to assess whether it is plausible that the local effect falls in this interval. We evaluate our diagnostics using a simulation study. Our preliminary results indicate that our diagnostics are effective for choosing between the empirical best predictor and the direct estimator.

Description:

Statistics Canada continues to use a variety of data sources to provide neighbourhood-level variables across an expanding set of domains, such as sociodemographic characteristics, income, services and amenities, crime, and the environment. Yet, despite these advances, information on the social aspects of neighbourhoods is still unavailable. In this paper, answers to the Canadian Community Health Survey on respondents’ sense of belonging to their local community were pooled over the four survey years from 2016 to 2019. Individual responses were aggregated up to the census tract (CT) level.

Description:

The bootstrap technique is becoming more and more popular in sample surveys conducted by national statistical agencies. In most of its implementations, several sets of bootstrap weights accompany the survey microdata file given to analysts. So far, the use of the technique in practice seems to have been mostly limited to variance estimation problems. In this paper, we propose a bootstrap methodology for testing hypotheses about a vector of unknown model parameters when the sample has been drawn from a finite population. The probability sampling design used to select the sample may be informative or not. Our method uses model-based test statistics that incorporate the survey weights. Such statistics are usually easily obtained using classical software packages. We approximate the distribution under the null hypothesis of these weighted model-based statistics by using bootstrap weights. An advantage of our bootstrap method over existing methods of hypothesis testing with survey data is that, once sets of bootstrap weights are provided to analysts, it is very easy to apply even when no specialized software dealing with complex surveys is available. Also, our simulation results suggest that, overall, it performs similarly to the Rao-Scott procedure and better than the Wald and Bonferroni procedures when testing hypotheses about a vector of linear regression model parameters.