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 and FCS Discriminant Function MethodsMonotone and FCS Logistic Regression MethodsMonotone Propensity Score MethodFCS 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 ImputationSensitivity Analysis for the MAR AssumptionMultiple Imputation with Pattern-Mixture ModelsSpecifying Sets of Observations for Imputation in Pattern-Mixture ModelsAdjusting Imputed Values in Pattern-Mixture ModelsSummary 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 ImputationCreating Control-Based Pattern Imputation in Sensitivity AnalysisAdjusting Imputed Continuous Values in Sensitivity AnalysisAdjusting Imputed Classification Levels in Sensitivity AnalysisAdjusting Imputed Values with Parameters in a Data Set
- References
You can specify the output data set of imputed values with the OUT= option in the PROC MI statement. When an EM statement is used, you can specify the data set that contains the original data set with missing values being replaced by the expected values from the EM algorithm by using the OUT= option in the EM statement. You can also specify the data set that contains MLE computed with the EM algorithm by using the OUTEM= option.
When an MCMC method is used, you can specify the data set that contains parameter estimates used in each imputation with the OUTEST= option in the MCMC statement, and you can specify the data set that contains parameters used in the imputation step for each iteration with the OUTITER option in the MCMC statement.
The OUT= data set contains all the variables in the original data set and a new variable named _Imputation_ that identifies the imputation. For each imputation, the data set contains all variables in the input DATA= data set with
missing values being replaced by imputed values. Note that when the NIMPUTE=1 option is specified, the variable _Imputation_ is not created.
The OUT= data set contains the original data set with missing values being replaced by expected values from the EM algorithm.
The OUTEM= data set is a TYPE=COV data set and contains the MLE computed with the EM algorithm. The observations with _TYPE_=‘MEAN’ contain the estimated mean and the observations with _TYPE_=‘COV’ contain the estimated covariances.
The OUTEST= data set is a TYPE=EST data set and contains parameter estimates used in each imputation in the MCMC method.
It also includes an index variable named _Imputation_, which identifies the imputation.
The observations with _TYPE_=‘SEED’ contain the seed information for the random number generator. The observations with _TYPE_=‘PARM’ or _TYPE_=‘PARMS’ contain the point estimate, and the observations with _TYPE_=‘COV’ or _TYPE_=‘COVB’ contain the associated covariances. These estimates are used as the parameters of the reference distribution to impute
values for observations in the DATA= dataset.
Note that these estimates are the values used in the I-step before each imputation. These are not the parameter values simulated from the P-step in the same iteration. See Example 63.12 for a usage of this option.
The OUTITER= data set in an EM statement is a TYPE=COV data set and contains parameters for each iteration. It also includes
a variable _Iteration_ that provides the iteration number.
The parameters in the output data set depend on the options specified. You can specify the MEAN and COV options for OUTITER.
With the MEAN option, the output data set contains the mean parameters in observations with the variable _TYPE_=‘MEAN’. Similarly, with the COV option, the output data set contains the covariance parameters in observations with the variable
_TYPE_=‘COV’. When no options are specified, the output data set contains the mean parameters for each iteration.
The OUTITER= data set in an FCS statement is a TYPE=COV data set and contains parameters for each iteration. It also includes
variables named _Imputation_ and _Iteration_, which provide the imputation number and iteration number.
The parameters in the output data set depend on the options specified. You can specify the MEAN and STD options for OUTITER.
With the MEAN option, the output data set contains the mean parameters used in the imputation in observations with the variable
_TYPE_=‘MEAN’. Similarly, with the STD option, the output data set contains the standard deviation parameters used in the imputation
in observations with the variable _TYPE_=‘STD’. When no options are specified, the output data set contains the mean parameters for each iteration.
The OUTITER= data set in an MCMC statement is a TYPE=COV data set and contains parameters used in the imputation step for
each iteration. It also includes variables named _Imputation_ and _Iteration_, which provide the imputation number and iteration number.
The parameters in the output data set depend on the options specified. Table 63.6 summarizes the options available for OUTITER and the corresponding values for the output variable _TYPE_.
Table 63.6: Summary of Options for OUTITER in an MCMC statement
|
Option |
Output Parameters |
|
|---|---|---|
|
MEAN |
mean parameters |
MEAN |
|
STD |
standard deviations |
STD |
|
COV |
covariances |
COV |
|
LR |
–2 log LR statistic |
LOG_LR |
|
LR_POST |
–2 log LR statistic of the posterior mode |
LOG_POST |
|
WLF |
worst linear function |
WLF |
When no options are specified, the output data set contains the mean parameters used in the imputation step for each iteration. For a detailed description of the worst linear function and LR statistics, see the section Checking Convergence in MCMC.