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Hybrid multiple imputation in a large scale complex survey

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Razzak H., Heumann C.

Statistics in Transition new series

2019

vol. 20

issue 4

33-58

Large-scale complex surveys typically contain a large number of variables measured on an even larger number of respondents. Missing data is a common problem in such surveys. Since usually most of the variables in a survey are categorical, multiple imputation requires robust methods for modelling highdimensional categorical data distributions. This paper introduces the 3-stage Hybrid Multiple Imputation (HMI) approach, computationally efficient and easy to implement, to impute complex survey data sets that contain both continuous and categorical variables. The proposed HMI approach involves the application of sequential regression MI techniques to impute the continuous variables by using information from the categorical variables, already imputed by a non-parametric Bayesian MI approach. The proposed approach seems to be a good alternative to the existing approaches, frequently yielding lower root mean square errors, empirical standard errors and standard errors than the others. The HMI method has proven to be markedly superior to the existing MI methods in terms of computational efficiency. The authors illustrate repeated sampling properties of the hybrid approach using simulated data. The results are also illustrated by child data from the multiple indicator survey (MICS) in Punjab 2014.

Borrowing Information over time in Binomial/Logit Normal Models for Small Area Estimation

75%

Franco C., Bell W. R.

Statistics in Transition new series

2015

vol. 16

issue 4

563-584

Linear area level models for small area estimation, such as the Fay-Herriot model, face challenges when applied to discrete survey data. Such data commonly arise as direct survey estimates of the number of persons possessing some characteristic, such as the number of persons in poverty. For such applications, we examine a binomial/logit normal (BLN) model that assumes a binomial distribution for rescaled survey estimates and a normal distribution with a linear regression mean function for logits of the true proportions. Effective sample sizes are defined so variances given the true proportions equal corresponding sampling variances of the direct survey estimates. We extend the BLN model to bivariate and time series (first order autoregressive) versions to permit borrowing information from past survey estimates, then apply these models to data used by the U.S. Census Bureau’s Small Area Income and Poverty Estimates (SAIPE) program to predict county poverty for school-age children. We compare prediction results from the alternative models to see how much the bivariate and time series models reduce prediction error variances from those of the univariate BLN model. Standard conditional variance calculations for corresponding linear Gaussian models that suggest how much variance reduction will be achieved from borrowing information over time with linear models agree generally with the BLN empirical results.

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2 Statistics in Transition new series

1 2019

1 2015

1 Bell W. R.

1 Franco C.

1 Heumann C.

1 Razzak H.

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Hybrid multiple imputation in a large scale complex survey

Borrowing Information over time in Binomial/Logit Normal Models for Small Area Estimation