The MI Procedure
- Overview
- Getting Started
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Syntax
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DetailsDescriptive StatisticsEM Algorithm for Data with Missing ValuesStatistical Assumptions for Multiple ImputationMissing Data PatternsImputation MethodsMonotone Methods for Data Sets with Monotone Missing PatternsMonotone and FCS Regression MethodsMonotone and FCS Predictive Mean Matching MethodsMonotone Propensity Score MethodMonotone and FCS Discriminant Function MethodsMonotone and FCS Logistic Regression MethodsFCS Methods for Data Sets with Arbitrary Missing PatternsChecking Convergence in FCS MethodsMCMC Method for Arbitrary Missing Multivariate Normal DataProducing Monotone Missingness with the MCMC MethodMCMC Method SpecificationsChecking Convergence in MCMCInput Data SetsOutput Data SetsCombining Inferences from Multiply Imputed Data SetsMultiple Imputation EfficiencyImputer’s Model Versus Analyst’s ModelParameter Simulation versus Multiple ImputationSummary of Issues in Multiple ImputationODS Table NamesODS Graphics
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ExamplesEM Algorithm for MLEMonotone Propensity Score MethodMonotone Regression MethodMonotone Logistic Regression Method for CLASS VariablesMonotone Discriminant Function Method for CLASS VariablesFCS Method for Continuous VariablesFCS Method for CLASS VariablesFCS Method with Trace PlotMCMC MethodProducing Monotone Missingness with MCMCChecking Convergence in MCMCSaving and Using Parameters for MCMCTransforming to NormalityMultistage Imputation
- References
Multiple Imputation Efficiency
The relative efficiency (RE) of using the finite m imputation estimator, rather than using an infinite number for the fully efficient imputation, in units of variance, is approximately
a function of m and 
(Rubin, 1987, p. 114):
![\[ \mr {RE} = { \left( 1 + \frac{\lambda }{m} \right) }^{-1} \]](images/statug_mi0336.png){kind=small} |
Table 57.7 shows relative efficiencies with different values of m and .
Table 57.7: Relative Efficiencies
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|
||||||
|---|---|---|---|---|---|---|
|
m |
10% |
20% |
30% |
50% |
70% |
|
|
3 |
0.9677 |
0.9375 |
0.9091 |
0.8571 |
0.8108 |
|
|
5 |
0.9804 |
0.9615 |
0.9434 |
0.9091 |
0.8772 |
|
|
10 |
0.9901 |
0.9804 |
0.9709 |
0.9524 |
0.9346 |
|
|
20 |
0.9950 |
0.9901 |
0.9852 |
0.9756 |
0.9662 |
|
The table shows that for situations with little missing information, only a small number of imputations are necessary. In practice, the number of imputations needed can be informally verified by replicating sets of m imputations and checking whether the estimates are stable between sets (Horton and Lipsitz, 2001, p. 246).