Analysis

Composite imputation is often used in business surveys. The term "composite" means that more than a single imputation method is used to impute missing values for a variable of interest. The literature on variance estimation in the presence of composite imputation is rather limited. To deal with this problem, we consider an extension of the methodology developed by Särndal (1992). Our extension is quite general and easy to implement provided that linear imputation methods are used to fill in the missing values. This class of imputation methods contains linear regression imputation, donor imputation and auxiliary value imputation, sometimes called cold-deck or substitution imputation. It thus covers the most common methods used by national statistical agencies for the imputation of missing values. Our methodology has been implemented in the System for the Estimation of Variance due to Nonresponse and Imputation (SEVANI) developed at Statistics Canada. Its performance is evaluated in a simulation study.

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.

Composite imputation is often used in business surveys. The term "composite" means that more than a single imputation method is used to impute missing values for a variable of interest. The literature on variance estimation in the presence of composite imputation is rather limited. To deal with this problem, we consider an extension of the methodology developed by Särndal (1992). Our extension is quite general and easy to implement provided that linear imputation methods are used to fill in the missing values. This class of imputation methods contains linear regression imputation, donor imputation and auxiliary value imputation, sometimes called cold-deck or substitution imputation. It thus covers the most common methods used by national statistical agencies for the imputation of missing values. Our methodology has been implemented in the System for the Estimation of Variance due to Nonresponse and Imputation (SEVANI) developed at Statistics Canada. Its performance is evaluated in a simulation study.

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.