Imputation of household survey data using linear mixed models

Mixed models are regularly used in the analysis of clustered data, but are only recently

being used for imputation of missing data. In household surveys where multiple people are

selected from each household, imputation of missing values should preserve the structure

pertaining to people within households and should not artificially change the apparent

intracluster correlation (ICC). This paper focuses on the use of multilevel models for

imputation of missing data in household surveys. In particular, the performance of a best

linear unbiased predictor for both stochastic and deterministic imputation using a linear

mixed model is compared to imputation based on a single level linear model, both with

and without information about household respondents.

In this paper an evaluation is carried out in the context of imputing hourly wage rate in the

Household, Income and Labour Dynamics of Australia Survey. Nonresponse is generated

under various assumptions about the missingness mechanism for persons and households,

and with low, moderate and high intra-household correlation to assess the benefits of the

multilevel imputation model under different conditions. The mixed model and single level

model with information about the household respondent lead to clear improvements when

the ICC is moderate or high, and when there is informative missingness.