Multiple imputation and other resampling schemes for imputing missing observations

Abstract

Multiple and single imputation Regression model Resampling Comparison of confidence intervals a b s t r a c tThe problem of imputing missing observations under the linear regression model is considered. It is assumed that observations are missing at random and all the observations on the auxiliary or independent variables are available. Estimates of the regression parameters based on singly and multiply imputed values are given. Jackknife as well as bootstrap estimates of the variance of the singly imputed estimator of the regression parameters are given. These estimators are shown to be consistent estimators. The asymptotic distributions of the imputed estimators are also given to obtain interval estimates of the parameters of interest. These interval estimates are then compared with the interval estimates obtained from multiple imputation. It is shown that singly imputed estimators perform at least as good as multiply imputed estimators. A new nonparametric multiply imputed estimator is proposed and shown to perform as good as a multiply imputed estimator under normality. The singly imputed estimator, however, still remains at least as good as a multiply imputed estimator.

Tests of Homoscedasticity, Normality, and Missing Completely at Random for Incomplete Multivariate Data

“…In this section we consider an imputation method that only assumes independence of the observations from case to case and the continuity of their cumulative distribution function; no specific distributional assumptions are required. This method is in the spirit of a method given by Srivastava and Dolatabadi (2009) and described in Srivastava (2002). To obtain appropriate imputation values, the best linear predictors of the missing observations are obtained first, and then random errors are added to them to obtain imputation values.…”

“…Recall that in the method of Section 3.2, we obtain the best linear estimator for Y mis, ij based on the completely observed data and add a random component e j that is a function of a sample from the residuals e j . To extend this method for multiple imputation, Srivastava (2002) and Srivastava and Dolatabadi (2009) recommend re-sampling the e j , computing ${\mathrm{bold-italic\eta }}_{\text{italicij}}^{*}$ for each instance of multiple imputation, and using (7) to form the imputations. Variations to this method are discussed in Srivastava and Dolatabadi (2009).…”

Imputação múltipla livre de distribuição em tabelas incompletas de dupla entrada

“…Para realizar a imputação múltipla a partir do algoritmo descrito, sugerem-se duas aproximações que estão de acordo com os trabalhos de Bergamo et al (2008) e Srivastava & Dolatabadi (2009). Srivastava & Dolatabadi (2009) propuseram IM com uso dos resíduos simples do modelo de regressão linear clássico Y=Qβ+E, em que o vetor Y (n × 1) representa a variável dependente; Q (n × p) é a matriz de delineamento que contém as variáveis independentes; β (p × 1) é o vetor desconhecido de parâmetros de regressão; e E (n × 1) é o vetor de erros aleatórios independentes e identicamente distribuídos.…”

“…Srivastava & Dolatabadi (2009) propuseram IM com uso dos resíduos simples do modelo de regressão linear clássico Y=Qβ+E, em que o vetor Y (n × 1) representa a variável dependente; Q (n × p) é a matriz de delineamento que contém as variáveis independentes; β (p × 1) é o vetor desconhecido de parâmetros de regressão; e E (n × 1) é o vetor de erros aleatórios independentes e identicamente distribuídos. Assume-se que os dados ausentes somente podem ocorrer no vetor Y e que todas as observações das variáveis independentes são disponíveis e completas.…”

Multiple imputations and the missing censoring indicator model

“…The approach of multiple imputations is useful when there are missing data [10,11,26,8,23,13,21]. In this approach, the missing components are filled in with imputed values and parameter estimates are obtained from the completed data set, treating the imputed values as though they were actually observed.…”