Imputation Mechanisms

The MI Procedure

Imputation Mechanisms

This section describes the three methods for multiple imputation that are available in the MI procedure. The method of choice depends on the patterns of missingness in the data.

For data sets with monotone missing patterns, either a parametric regression method (Rubin 1987) that assumes multivariate normality or a nonparametric method that uses propensity scores (Rubin 1987; Lavori, Dawson, and Shera 1995) is appropriate.
For data sets with arbitrary missing patterns, a Markov Chain Monte Carlo (MCMC) method (Schafer 1997) that assumes multivariate normality is used to impute either all missing values or just enough missing values to make the imputed data sets have monotone missing patterns.

With a monotone missing data pattern, you have greater flexibility in your choice of strategies. For example, in addition to the MCMC method, you can also implement other methods, such as a regression method, that do not use Markov chains.

With an arbitrary missing data pattern, you can often use the MCMC method, which creates multiple imputations by drawing simulations from a Bayesian predictive distribution for normal data. Another way to handle a data set with an arbitrary missing data pattern is to use the MCMC approach to impute enough values to make the missing data pattern monotone. Then, you can use a more flexible imputation method. This approach is described in the "Producing Monotone Missingness with the MCMC Method" section.

Although the regression and MCMC methods assume multivariate normality, inferences based on multiple imputation can be robust to departures from the multivariate normality if the amount of missing information is not large. It often makes sense to use a normal model to create multiple imputations even when the observed data are somewhat non-normal, as supported by simulation studies described in Schafer (1997) and the original references therein.

You can also use a TRANSFORM statement to transform variables to conform to the multivariate normality assumption. With a TRANSFORM statement, variables are transformed before the imputation process and then are reverse-transformed to create the imputed data set.

Li (1988) presented an argument for convergence of the MCMC method in the continuous case in theory and used it to create imputations for incomplete multivariate continuous data. But in practice, it is not easy to check the convergence of a Markov chain, especially for parameters from a large number of variables. PROC MI generates statistics and plots that you can use to check for convergence of the MCMC process. The details are described in the "Convergence in MCMC" section.

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