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
Monotone and FCS Predictive Mean Matching Methods
The predictive mean matching method is also an imputation method available for continuous variables. It is similar to the regression method except that for each missing value, it imputes a value randomly from a set of observed values whose predicted values are closest to the predicted value for the missing value from the simulated regression model (Heitjan and Little, 1991; Schenker and Taylor, 1996).
Following the description of the model in the section Monotone and FCS Regression Methods, the following steps are used to generate imputed values:
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New parameters
and 
are drawn from the posterior predictive distribution of the parameters. That is, they are simulated from 
, 
, and 
. The variance is drawn as
![\[ {\sigma }_{*j}^2 = \hat{\sigma }_{j}^2 (n_{j}-k-1) / g \]](images/statug_mi0111.png)
where g is a
random variate and 
is the number of nonmissing observations for 
. The regression coefficients are drawn as
![\[ \bbeta _{*} = \hat{\bbeta } + {\sigma }_{*j} \mb {V}_{hj}’ \mb {Z} \]](images/statug_mi0113.png)
where
is the upper triangular matrix in the Cholesky decomposition, 
, and 
is a vector of 
independent random normal variates.
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For each missing value, a predicted value
![\[ y_{i*} = {\beta }_{*0} + {\beta }_{*1} \, x_{1} + {\beta }_{*2} \, x_{2} + \ldots + {\beta }_{*(k)} \, x_{k} \]](images/statug_mi0121.png)
is computed with the covariate values
.
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A set of
observations whose corresponding predicted values are closest to 
is generated. You can specify with the K= option.
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The missing value is then replaced by a value drawn randomly from these
observed values.
The predictive mean matching method requires the number of closest observations to be specified. A smaller tends to increase the correlation among the multiple imputations for the missing observation and results in a higher variability
of point estimators in repeated sampling. On the other hand, a larger tends to lessen the effect from the imputation model and results in biased estimators (Schenker and Taylor, 1996, p. 430).
The predictive mean matching method ensures that imputed values are plausible; it might be more appropriate than the regression method if the normality assumption is violated (Horton and Lipsitz, 2001, p. 246).