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
The expectation-maximization (EM) algorithm is a technique for maximum likelihood estimation in parametric models for incomplete
data. The EM statement uses the EM algorithm to compute the MLE for 
, the means and covariance matrix, of a multivariate normal distribution from the input data set with missing values. Either
the means and covariances from complete cases or the means and standard deviations from available cases can be used as the
initial estimates for the EM algorithm. You can also specify the correlations for the estimates from available cases.
You can also use the EM statement with the NIMPUTE=0 option in the PROC MI statement to compute the EM estimates without multiple imputation, as shown in Example 63.1.
The following seven options are available with the EM statement (in alphabetical order):
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CONVERGE=p
XCONV=p -
sets the convergence criterion. The value must be between 0 and 1. The iterations are considered to have converged when the change in the parameter estimates between iteration steps is less than p for each parameter—that is, for each of the means and covariances. For each parameter, the change is a relative change if the parameter is greater than 0.01 in absolute value; otherwise, it is an absolute change. By default, CONVERGE=1E–4.
- INITIAL=CC | AC | AC(R=r)
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sets the initial estimates for the EM algorithm. The INITIAL=CC option uses the means and covariances from complete cases; the INITIAL=AC option uses the means and standard deviations from available cases, and the correlations are set to zero; and the INITIAL=AC( R= r) option uses the means and standard deviations from available cases with correlation r, where
and p is the number of variables to be analyzed. The default is INITIAL=AC.
- ITPRINT
- MAXITER=number
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specifies the maximum number of iterations used in the EM algorithm. The default is MAXITER=200.
- OUT=SAS-data-set
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creates an output SAS data set that contains results from the EM algorithm. The data set contains all variables in the input data set, with missing values being replaced by the expected values from the EM algorithm. See the section Output Data Sets for a description of this data set.
- OUTEM=SAS-data-set
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creates an output SAS data set of TYPE=COV that contains the MLE of the parameter vector
. These estimates are computed with the EM algorithm. See the section Output Data Sets for a description of this output data set.
- OUTITER <( options )> =SAS-data-set
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creates an output SAS data set of TYPE=COV that contains parameters for each iteration. The data set includes a variable named
_Iteration_to identify the iteration number. The parameters in the output data set depend on the options specified. You can specify the MEAN and COV options to output the mean and covariance parameters. When no options are specified, the output data set contains the mean parameters for each iteration. See the section Output Data Sets for a description of this data set.