Weighting and estimation
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- Articles and reports: 12-001-X201200211754Description:
The propensity-scoring-adjustment approach is commonly used to handle selection bias in survey sampling applications, including unit nonresponse and undercoverage. The propensity score is computed using auxiliary variables observed throughout the sample. We discuss some asymptotic properties of propensity-score-adjusted estimators and derive optimal estimators based on a regression model for the finite population. An optimal propensity-score-adjusted estimator can be implemented using an augmented propensity model. Variance estimation is discussed and the results from two simulation studies are presented.
Release date: 2012-12-19 - 2. Confidence interval estimation of small area parameters shrinking both means and variances ArchivedArticles and reports: 12-001-X201200211756Description:
We propose a new approach to small area estimation based on joint modelling of means and variances. The proposed model and methodology not only improve small area estimators but also yield "smoothed" estimators of the true sampling variances. Maximum likelihood estimation of model parameters is carried out using EM algorithm due to the non-standard form of the likelihood function. Confidence intervals of small area parameters are derived using a more general decision theory approach, unlike the traditional way based on minimizing the squared error loss. Numerical properties of the proposed method are investigated via simulation studies and compared with other competitive methods in the literature. Theoretical justification for the effective performance of the resulting estimators and confidence intervals is also provided.
Release date: 2012-12-19 - Articles and reports: 12-001-X201200211757Description:
Collinearities among explanatory variables in linear regression models affect estimates from survey data just as they do in non-survey data. Undesirable effects are unnecessarily inflated standard errors, spuriously low or high t-statistics, and parameter estimates with illogical signs. The available collinearity diagnostics are not generally appropriate for survey data because the variance estimators they incorporate do not properly account for stratification, clustering, and survey weights. In this article, we derive condition indexes and variance decompositions to diagnose collinearity problems in complex survey data. The adapted diagnostics are illustrated with data based on a survey of health characteristics.
Release date: 2012-12-19 - Articles and reports: 75F0002M2012003Description:
The release of the 2010 Survey of Labour and Income Dynamics (SLID) data coincided with a historical revision of the 2006 to 2009 results. The survey weights were updated to take into account new population estimates based on the 2006 Census rather than the 2001 Census. This paper presents a summary of the impact of this revision on the 2006-2009 survey estimates.
Release date: 2012-11-01 - Articles and reports: 12-002-X201200111642Description:
It is generally recommended that weighted estimation approaches be used when analyzing data from a long-form census microdata file. Since such data files are now available in the RDC's, there is a need to provide researchers there with more information about doing weighted estimation with these files. The purpose of this paper is to provide some of this information - in particular, how the weight variables were derived for the census microdata files and what weight should be used for different units of analysis. For the 1996, 2001 and 2006 censuses the same weight variable is appropriate regardless of whether people, families or households are being studied. For the 1991 census, recommendations are more complex: a different weight variable is required for households than for people and families, and additional restrictions apply to obtain the correct weight value for families.
Release date: 2012-10-25 - Articles and reports: 12-001-X201200111682Description:
Sample allocation issues are studied in the context of estimating sub-population (stratum or domain) means as well as the aggregate population mean under stratified simple random sampling. A non-linear programming method is used to obtain "optimal" sample allocation to strata that minimizes the total sample size subject to specified tolerances on the coefficient of variation of the estimators of strata means and the population mean. The resulting total sample size is then used to determine sample allocations for the methods of Costa, Satorra and Ventura (2004) based on compromise allocation and Longford (2006) based on specified "inferential priorities". In addition, we study sample allocation to strata when reliability requirements for domains, cutting across strata, are also specified. Performance of the three methods is studied using data from Statistics Canada's Monthly Retail Trade Survey (MRTS) of single establishments.
Release date: 2012-06-27 - Articles and reports: 12-001-X201200111683Description:
We consider alternatives to poststratification for doubly classified data in which at least one of the two-way cells is too small to allow the poststratification based upon this double classification. In our study data set, the expected count in the smallest cell is 0.36. One approach is simply to collapse cells. This is likely, however, to destroy the double classification structure. Our alternative approaches allows one to maintain the original double classification of the data. The approaches are based upon the calibration study by Chang and Kott (2008). We choose weight adjustments dependent upon the marginal classifications (but not full cross classification) to minimize an objective function of the differences between the population counts of the two way cells and their sample estimates. In the terminology of Chang and Kott (2008), if the row and column classifications have I and J cells respectively, this results in IJ benchmark variables and I + J - 1 model variables. We study the performance of these estimators by constructing simulation simple random samples from the 2005 Quarterly Census of Employment and Wages which is maintained by the Bureau of Labor Statistics. We use the double classification of state and industry group. In our study, the calibration approaches introduced an asymptotically trivial bias, but reduced the MSE, compared to the unbiased estimator, by as much as 20% for a small sample.
Release date: 2012-06-27 - Articles and reports: 12-001-X201200111684Description:
Many business surveys provide estimates for the monthly turnover for the major Standard Industrial Classification codes. This includes estimates for the change in the level of the monthly turnover compared to 12 months ago. Because business surveys often use overlapping samples, the turnover estimates in consecutive months are correlated. This makes the variance calculations for a change less straightforward. This article describes a general variance estimation procedure. The procedure allows for yearly stratum corrections when establishments move into other strata according to their actual sizes. The procedure also takes into account sample refreshments, births and deaths. The paper concludes with an example of the variance for the estimated yearly growth rate of the monthly turnover of Dutch Supermarkets.
Release date: 2012-06-27 - Articles and reports: 12-001-X201200111685Description:
Survey data are often used to fit linear regression models. The values of covariates used in modeling are not controlled as they might be in an experiment. Thus, collinearity among the covariates is an inevitable problem in the analysis of survey data. Although many books and articles have described the collinearity problem and proposed strategies to understand, assess and handle its presence, the survey literature has not provided appropriate diagnostic tools to evaluate its impact on regression estimation when the survey complexities are considered. We have developed variance inflation factors (VIFs) that measure the amount that variances of parameter estimators are increased due to having non-orthogonal predictors. The VIFs are appropriate for survey-weighted regression estimators and account for complex design features, e.g., weights, clusters, and strata. Illustrations of these methods are given using a probability sample from a household survey of health and nutrition.
Release date: 2012-06-27 - Articles and reports: 12-001-X201200111686Description:
We present a generalized estimating equations approach for estimating the concordance correlation coefficient and the kappa coefficient from sample survey data. The estimates and their accompanying standard error need to correctly account for the sampling design. Weighted measures of the concordance correlation coefficient and the kappa coefficient, along with the variance of these measures accounting for the sampling design, are presented. We use the Taylor series linearization method and the jackknife procedure for estimating the standard errors of the resulting parameter estimates. Body measurement and oral health data from the Third National Health and Nutrition Examination Survey are used to illustrate this methodology.
Release date: 2012-06-27
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- Articles and reports: 12-001-X201200211754Description:
The propensity-scoring-adjustment approach is commonly used to handle selection bias in survey sampling applications, including unit nonresponse and undercoverage. The propensity score is computed using auxiliary variables observed throughout the sample. We discuss some asymptotic properties of propensity-score-adjusted estimators and derive optimal estimators based on a regression model for the finite population. An optimal propensity-score-adjusted estimator can be implemented using an augmented propensity model. Variance estimation is discussed and the results from two simulation studies are presented.
Release date: 2012-12-19 - 2. Confidence interval estimation of small area parameters shrinking both means and variances ArchivedArticles and reports: 12-001-X201200211756Description:
We propose a new approach to small area estimation based on joint modelling of means and variances. The proposed model and methodology not only improve small area estimators but also yield "smoothed" estimators of the true sampling variances. Maximum likelihood estimation of model parameters is carried out using EM algorithm due to the non-standard form of the likelihood function. Confidence intervals of small area parameters are derived using a more general decision theory approach, unlike the traditional way based on minimizing the squared error loss. Numerical properties of the proposed method are investigated via simulation studies and compared with other competitive methods in the literature. Theoretical justification for the effective performance of the resulting estimators and confidence intervals is also provided.
Release date: 2012-12-19 - Articles and reports: 12-001-X201200211757Description:
Collinearities among explanatory variables in linear regression models affect estimates from survey data just as they do in non-survey data. Undesirable effects are unnecessarily inflated standard errors, spuriously low or high t-statistics, and parameter estimates with illogical signs. The available collinearity diagnostics are not generally appropriate for survey data because the variance estimators they incorporate do not properly account for stratification, clustering, and survey weights. In this article, we derive condition indexes and variance decompositions to diagnose collinearity problems in complex survey data. The adapted diagnostics are illustrated with data based on a survey of health characteristics.
Release date: 2012-12-19 - Articles and reports: 75F0002M2012003Description:
The release of the 2010 Survey of Labour and Income Dynamics (SLID) data coincided with a historical revision of the 2006 to 2009 results. The survey weights were updated to take into account new population estimates based on the 2006 Census rather than the 2001 Census. This paper presents a summary of the impact of this revision on the 2006-2009 survey estimates.
Release date: 2012-11-01 - Articles and reports: 12-002-X201200111642Description:
It is generally recommended that weighted estimation approaches be used when analyzing data from a long-form census microdata file. Since such data files are now available in the RDC's, there is a need to provide researchers there with more information about doing weighted estimation with these files. The purpose of this paper is to provide some of this information - in particular, how the weight variables were derived for the census microdata files and what weight should be used for different units of analysis. For the 1996, 2001 and 2006 censuses the same weight variable is appropriate regardless of whether people, families or households are being studied. For the 1991 census, recommendations are more complex: a different weight variable is required for households than for people and families, and additional restrictions apply to obtain the correct weight value for families.
Release date: 2012-10-25 - Articles and reports: 12-001-X201200111682Description:
Sample allocation issues are studied in the context of estimating sub-population (stratum or domain) means as well as the aggregate population mean under stratified simple random sampling. A non-linear programming method is used to obtain "optimal" sample allocation to strata that minimizes the total sample size subject to specified tolerances on the coefficient of variation of the estimators of strata means and the population mean. The resulting total sample size is then used to determine sample allocations for the methods of Costa, Satorra and Ventura (2004) based on compromise allocation and Longford (2006) based on specified "inferential priorities". In addition, we study sample allocation to strata when reliability requirements for domains, cutting across strata, are also specified. Performance of the three methods is studied using data from Statistics Canada's Monthly Retail Trade Survey (MRTS) of single establishments.
Release date: 2012-06-27 - Articles and reports: 12-001-X201200111683Description:
We consider alternatives to poststratification for doubly classified data in which at least one of the two-way cells is too small to allow the poststratification based upon this double classification. In our study data set, the expected count in the smallest cell is 0.36. One approach is simply to collapse cells. This is likely, however, to destroy the double classification structure. Our alternative approaches allows one to maintain the original double classification of the data. The approaches are based upon the calibration study by Chang and Kott (2008). We choose weight adjustments dependent upon the marginal classifications (but not full cross classification) to minimize an objective function of the differences between the population counts of the two way cells and their sample estimates. In the terminology of Chang and Kott (2008), if the row and column classifications have I and J cells respectively, this results in IJ benchmark variables and I + J - 1 model variables. We study the performance of these estimators by constructing simulation simple random samples from the 2005 Quarterly Census of Employment and Wages which is maintained by the Bureau of Labor Statistics. We use the double classification of state and industry group. In our study, the calibration approaches introduced an asymptotically trivial bias, but reduced the MSE, compared to the unbiased estimator, by as much as 20% for a small sample.
Release date: 2012-06-27 - Articles and reports: 12-001-X201200111684Description:
Many business surveys provide estimates for the monthly turnover for the major Standard Industrial Classification codes. This includes estimates for the change in the level of the monthly turnover compared to 12 months ago. Because business surveys often use overlapping samples, the turnover estimates in consecutive months are correlated. This makes the variance calculations for a change less straightforward. This article describes a general variance estimation procedure. The procedure allows for yearly stratum corrections when establishments move into other strata according to their actual sizes. The procedure also takes into account sample refreshments, births and deaths. The paper concludes with an example of the variance for the estimated yearly growth rate of the monthly turnover of Dutch Supermarkets.
Release date: 2012-06-27 - Articles and reports: 12-001-X201200111685Description:
Survey data are often used to fit linear regression models. The values of covariates used in modeling are not controlled as they might be in an experiment. Thus, collinearity among the covariates is an inevitable problem in the analysis of survey data. Although many books and articles have described the collinearity problem and proposed strategies to understand, assess and handle its presence, the survey literature has not provided appropriate diagnostic tools to evaluate its impact on regression estimation when the survey complexities are considered. We have developed variance inflation factors (VIFs) that measure the amount that variances of parameter estimators are increased due to having non-orthogonal predictors. The VIFs are appropriate for survey-weighted regression estimators and account for complex design features, e.g., weights, clusters, and strata. Illustrations of these methods are given using a probability sample from a household survey of health and nutrition.
Release date: 2012-06-27 - Articles and reports: 12-001-X201200111686Description:
We present a generalized estimating equations approach for estimating the concordance correlation coefficient and the kappa coefficient from sample survey data. The estimates and their accompanying standard error need to correctly account for the sampling design. Weighted measures of the concordance correlation coefficient and the kappa coefficient, along with the variance of these measures accounting for the sampling design, are presented. We use the Taylor series linearization method and the jackknife procedure for estimating the standard errors of the resulting parameter estimates. Body measurement and oral health data from the Third National Health and Nutrition Examination Survey are used to illustrate this methodology.
Release date: 2012-06-27
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