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 Logistic Regression Methods |
The logistic regression method is another imputation method available for classification variables. In the logistic regression method, a logistic regression model is fitted for a classification variable with a set of covariates constructed from the effects. For a binary classification variable, based on the fitted regression model, a new logistic 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. 169–170).
For a binary variable 
with responses 1 and 2, a logistic regression model is fitted using observations with observed values for the imputed variable and its covariates 
, 
, ..., 
:
 |
where 
are covariates for , 
, and 
The fitted model includes the regression parameter estimates 
and the associated covariance matrix 
.
The following steps are used to generate imputed values for a binary variable with responses 1 and 2:
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New parameters
are drawn from the posterior predictive distribution of the parameters. 
where
is the upper triangular matrix in the Cholesky decomposition, 
, and 
is a vector of 
independent random normal variates. -
For an observation with missing
and covariates 
, compute the expected probability that 
: 
where
. Draw a random uniform variate,
, between 0 and 1. If the value of is less than 
, impute ; otherwise impute 
.
The preceding logistic regression method can be extended to include the ordinal classification variables with more than two levels of responses. The options ORDER= and DESCENDING can be used to specify the sorting order for the levels of the imputed variables.