Quartagno, M;
Carpenter, J;
(2018)
Multilevel Multiple Imputation in presence of interactions, non-linearities and random slopes.
In:
SIS2018: 49th Scientific Meeting of the Italian Statistical Society.
(pp. pp. 175-182).
: Palermo, Italy.
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Abstract
Multiple Imputation is a flexible tool to handle missing data that has been increasingly used in recent years. One of the conditions for its validity is that the two models used for (i) imputing and (ii) analysing the data need to be compatible. For example, when the partially observed data have a multilevel structure, both models need to reflect this. Choosing an appropriate imputation model is more complicated when data are missing in a variable included in the substantive multilevel analysis model as a covariate with a random slope, an interaction or a non-linear term. We propose an imputation method based on joint modelling of the partially observed variables. We factor this joint model in two parts: a joint distribution for the covariates, and a conditional distribution for the outcome given the covariates. We guarantee compatibility by using as second term the substantive analysis model. We fit this model with a Gibbs sampler, and we use a Metropolis-Hastings step to accept/reject the proposed draws for the missing values, to guarantee that they are actual random draws from the desired distribution. We show with simulations how this method is up to the job and overcomes competing imputation strategies.
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