Fully conditional specification in multivariate imputation

By S. van Buuren, J. Brand, Catharina G. M. Groothuis-Oudshoorn, Donald B. Rubin. 2006

1,197 citations recorded by the source corpus.

The use of the Gibbs sampler with fully conditionally specified models, where the distribution of each variable given the other variables is the starting point, has become a popular method to create imputations in incomplete multivariate data. The theoretical weakness of this approach is that the specified conditional densities can be incompatible, and therefore the stationary distribution to which the Gibbs sampler attempts to converge may not exist. This study investigates practical consequences of this problem by means of simulation. Missing data are created under four different missing data mechanisms. Attention is given to the statistical behavior under compatible and incompatible models. The results indicate that multiple imputation produces essentially unbiased estimates with appropriate coverage in the simple cases investigated, even for the incompatible models. Of particular interest is that these results were produced using only five Gibbs iterations starting from a simple draw from observed marginal distributions. It thus appears that, despite the theoretical weaknesses, the actual performance of conditional model specification for multivariate imputation can be quite good, and therefore deserves further study.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Informing sequential clinical decision-making through reinforcement learning: an empirical study (2010, methodology): “The model for the complete data in FCS is formed via conditional models for each variable v j given v 0 , . . . , v j −1 .”
Cognitive and Noncognitive Peer Effects in Early Education (2008, positive): “…maternal employment, and number of books owned) (3,278), so we impute them using single imputation by chained equations to preserve sample size (Van Buuren et al., 2006).9 For the nonimputed covariates, we use casewise deletion, leaving a final sample of 12,501 with math scores, 11,840 with…”
Multiple imputation using chained equations: Issues and guidance for practice (2011, methodology): “There is little evidence that this matters in practice [49].”
Multiple Imputation by Chained Equations (MICE): Implementation in Stata (2011, methodology): “However, van Buuren et al. (2006) performed some simulations under severely incompatible models and observed that the adverse effects on the estimates following MI were ‘minimal’.”
Multiple imputation for continuous variables using a Bayesian principal component analysis† (2014, methodology): “211–218] The second way to perform multiple imputation is to use chained equations [6]: a model is defined for each variable with missing data and variables are successively imputed using these models.”
A new variable importance measure for random forests with missing data (2012, methodology): “…where observations that contain missing values are entirely omitted from the data—and multiple imputation by chained equations (MICE; cf. Van Buuren et al. 2006; White et al. 2011)—which permits the imputation of data with missing values in several variables—were used to enable the…”
Much Ado About Nothing (2007, methodology): “An alternative approach involves a variable-by-variable approach using chained equations (van Buuren et al. 1999; Raghu-nathan et al. 2001; van Buuren et al. 2006; van Buuren in press).”
Imputation Strategies for the Estimation of Natural Direct and Indirect Effects (2012, background): “Formal descriptions of these assumptions in terms of counterfactuals are for instance given in VanderWeele and Vansteelandt (2009). Under these assumptions, it follows from Pearl (2001, 2011) and Imai, Keele, and Yamamoto (2010b) that E[Y (a,M(a∗))|C = c] can be calculated using the mediation formul”
Machine Learning and Integrative Analysis of Biomedical Big Data (2019, methodology): “MICE can also incorporate methods for imputing data that are not normally distributed [121].”
Multiple imputation using chained equations for missing data in TIMSS: a case study (2013, positive): “…the multivariate normal model (MVN) Despite lacking a theoretical rationale and despite the difficulties encountered when specifying the different imputation models, MICE has several practical advantages (Marchenko, 2011; Van Buuren et al., 2006; Van Buuren & Oudshoorn, 2011; White et al., 2011).”