This section describes the methods for multiple imputation that are available in the MI procedure. The method of choice depends on the pattern of missingness in the data and the type of the imputed variable, as summarized in Table 54.3.

To impute missing values for a continuous variable in data sets with monotone missing patterns, you should use either a parametric method that assumes multivariate normality or a nonparametric method that uses propensity scores (Rubin 1987, pp. 124, 158; Lavori, Dawson, and Shera 1995). Parametric methods available include the regression method (Rubin 1987, pp. 166–167) and the predictive mean matching method (Heitjan and Little 1991; Schenker and Taylor 1996).

To impute missing values for a classification variable in data sets with monotone missing patterns, you should use the logistic regression method or the discriminant function method. Use the logistic regression method when the classification variable has a binary or ordinal response, and use the discriminant function method when the classification variable has a binary or nominal response.

For continuous variables in data sets with arbitrary missing patterns, you can use the Markov chain Monte Carlo (MCMC) method (Schafer 1997) to impute either all the 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 imputation models. In addition to the MCMC method, you can implement other methods, such as the regression method, that do not use Markov chains. You can also specify a different set of covariates for each imputed variable.

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 just enough values to make the missing data pattern monotone. Then, you can use a more flexible imputation method. This approach is described in the section Producing Monotone Missingness with the MCMC Method.

Note that all continuous variables are standardized before the imputation process and then are transformed back to the original scale after the imputation process.

Although the regression and MCMC methods assume multivariate normality, inferences based on multiple imputation can be robust to departures from multivariate normality if the amount of missing information is not large, because the imputation model is effectively applied not to the entire data set but only to its missing part (Schafer 1997, pp. 147–148).

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

Li (1988) presents a theoretical argument for convergence of the MCMC method in the continuous case and uses it to create imputations for incomplete multivariate continuous data. In practice, however, it is not easy to check the convergence of a Markov chain, especially for a large number of parameters. PROC MI generates statistics and plots that you can use to check for convergence of the MCMC method. The details are described in the section Checking Convergence in MCMC.