The MI Procedure
- Overview
- Getting Started
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Syntax
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Details
Descriptive Statistics EM Algorithm for Data with Missing Values Statistical Assumptions for Multiple Imputation Missing Data Patterns Imputation Methods Monotone Methods for Data Sets with Monotone Missing Patterns Monotone and FCS Regression Methods Monotone and FCS Predictive Mean Matching Methods Monotone Propensity Score Method Monotone and FCS Discriminant Function Methods Monotone and FCS Logistic Regression Methods FCS Methods for Data Sets with Arbitrary Missing Patterns Checking Convergence in FCS Methods MCMC Method for Arbitrary Missing Multivariate Normal Data Producing Monotone Missingness with the MCMC Method MCMC Method Specifications Checking Convergence in MCMC Input Data Sets Output Data Sets Combining Inferences from Multiply Imputed Data Sets Multiple Imputation Efficiency Imputer’s Model Versus Analyst’s Model Parameter Simulation versus Multiple Imputation Summary of Issues in Multiple Imputation ODS Table Names ODS Graphics
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Examples
EM Algorithm for MLE Monotone Propensity Score Method Monotone Regression Method Monotone Logistic Regression Method for CLASS Variables Monotone Discriminant Function Method for CLASS Variables FCS Method for Continuous Variables FCS Method for CLASS Variables FCS Method with Trace Plot MCMC Method Producing Monotone Missingness with MCMC Checking Convergence in MCMC Saving and Using Parameters for MCMC Transforming to Normality Multistage Imputation
- References
| Monotone and FCS Regression Methods |
The regression method is the default imputation method in the MONOTONE and FCS statements for continuous variables.
In the regression method, a regression model is fitted for a continuous variable with the covariates constructed from a set of effects. Based on the fitted regression model, a new regression model is simulated from the posterior predictive distribution of the parameters and is used to impute the missing values for each variable (Rubin 1987, pp. 166–167). That is, for a continuous variable 
with missing values, a model
 |
is fitted using observations with observed values for the variable and its covariates 
, 
, ..., 
.
The fitted model includes the regression parameter estimates 
and the associated covariance matrix 
, where 
is the usual 
inverse matrix derived from the intercept and covariates , , ..., .
The following steps are used to generate imputed values for each imputation:
-
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 
where
is a 
random variate and 
is the number of nonmissing observations for . The regression coefficients are drawn as 
where
is the upper triangular matrix in the Cholesky decomposition, 
, and 
is a vector of 
independent random normal variates. -
The missing values are then replaced by
where
are the values of the covariates and 
is a simulated normal deviate.