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- Articles and reports: 11-536-X200900110811Description:
Composite imputation is often used in business surveys. It occurs when several imputation methods are used to impute a single variable of interest. The choice of one method instead of another depends on the availability or not of some auxiliary variables. For instance, ratio imputation could be used to impute a missing value when an auxiliary variable is available and, otherwise, mean imputation could be used.
Although composite imputation is frequent in practice, the literature on variance estimation when composite imputation is used is limited. We consider the general methodology proposed by Särndal et al. (1992), which requires the validity of an imputation model i.e., a model for the variable being imputed. At first glance, the extension of this methodology to composite imputation seems quite tedious until we notice that most imputation methods used in practice lead to imputed estimators that are linear in the observed values of the variable of interest. This considerably simplifies the derivation of a variance estimator even when there is a single imputation method. Regarding the estimation of the sampling portion of the total variance, we use a methodology slightly different than the one proposed by Särndal et al. (1992). Our methodology is similar to the sampling variance estimator under multiple imputation with an infinite number of imputations.
This methodology is the central part of version 2.0 of the System for Estimation of Variance due to Nonresponse and Imputation (SEVANI), which is being developed at Statistics Canada. Using SEVANI, we will illustrate our method through an example based on real data.
Release date: 2009-08-11 - Articles and reports: 12-001-X200900110882Description:
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.
Release date: 2009-06-22
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- Articles and reports: 11-536-X200900110811Description:
Composite imputation is often used in business surveys. It occurs when several imputation methods are used to impute a single variable of interest. The choice of one method instead of another depends on the availability or not of some auxiliary variables. For instance, ratio imputation could be used to impute a missing value when an auxiliary variable is available and, otherwise, mean imputation could be used.
Although composite imputation is frequent in practice, the literature on variance estimation when composite imputation is used is limited. We consider the general methodology proposed by Särndal et al. (1992), which requires the validity of an imputation model i.e., a model for the variable being imputed. At first glance, the extension of this methodology to composite imputation seems quite tedious until we notice that most imputation methods used in practice lead to imputed estimators that are linear in the observed values of the variable of interest. This considerably simplifies the derivation of a variance estimator even when there is a single imputation method. Regarding the estimation of the sampling portion of the total variance, we use a methodology slightly different than the one proposed by Särndal et al. (1992). Our methodology is similar to the sampling variance estimator under multiple imputation with an infinite number of imputations.
This methodology is the central part of version 2.0 of the System for Estimation of Variance due to Nonresponse and Imputation (SEVANI), which is being developed at Statistics Canada. Using SEVANI, we will illustrate our method through an example based on real data.
Release date: 2009-08-11 - Articles and reports: 12-001-X200900110882Description:
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.
Release date: 2009-06-22
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