Parameter Simulation Versus Multiple Imputation

The MI Procedure

Parameter Simulation Versus Multiple Imputation

For many incomplete-data problems, simulation-based methods of parameter simulation and multiple imputation can be used to analyze the data. In parameter simulation, you simulate random values of parameters from the observed-data posterior distribution and make simple inferences about these parameters (Schafer 1997, p. 89).

When a set of well-defined population parameters ${{\theta}}$ are of interest, parameter simulation can be used to directly examine and summarize simulated values of ${{\theta}}$ .This usually requires a large number of iterations, and involves calculating appropriate summaries of the resulting dependent sample of the iterates of the ${{\theta}}$ .If only a small set of parameters are involved, parameter simulation can be suitable (Schafer 1997).

In multiple imputation, the unknown missing data are replaced by multiple sets of simulated values. Each complete data set is then analyzed by standard complete-data methods. The variability among the results from these repeated analyses provides a measure of the uncertainty due to missing data. Combining this between-imputation variation with the ordinary within-imputation sample variation provides statistical inference for the parameters of interest. Multiple imputation is suitable for analyses that are more exploratory in nature.

Multiple imputation only requires a small number of imputations. Generating and storing a few imputations can be more efficient than generating and storing a large number of iterations for parameter simulation.

When fractions of missing information are low, methods that average over simulated values of the missing data, as in multiple imputation, can be much more efficient than methods that average over simulated values of ${{\theta}}$ as in parameter simulation (Schafer 1997).

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