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 Propensity Score Method |
The propensity score method is another imputation method available for continuous variables when the data set has a monotone missing pattern.
A propensity score is generally defined as the conditional probability of assignment to a particular treatment given a vector of observed covariates (Rosenbaum and Rubin 1983). In the propensity score method, for a variable with missing values, a propensity score is generated for each observation to estimate the probability that the observation is missing. The observations are then grouped based on these propensity scores, and an approximate Bayesian bootstrap imputation (Rubin 1987, p. 124) is applied to each group (Lavori, Dawson, and Shera 1995).
The propensity score method uses the following steps to impute values for variable 
with missing values:
Creates an indicator variable
with the value 0 for observations with missing and 1 otherwise. -
Fits a logistic regression model
where
are covariates for , 
, and 
Creates a propensity score for each observation to estimate the probability that it is missing.
Divides the observations into a fixed number of groups (typically assumed to be five) based on these propensity scores.
Applies an approximate Bayesian bootstrap imputation to each group. In group
, suppose that 
denotes the 
observations with nonmissing values and 
denotes the 
observations with missing . The approximate Bayesian bootstrap imputation first draws observations randomly with replacement from to create a new data set 
. This is a nonparametric analog of drawing parameters from the posterior predictive distribution of the parameters. The process then draws the values for randomly with replacement from .
Steps 1 through 5 are repeated sequentially for each variable with missing values.
The propensity score method was originally designed for a randomized experiment with repeated measures on the response variables. The goal was to impute the missing values on the response variables. The method uses only the covariate information that is associated with whether the imputed variable values are missing; it does not use correlations among variables. It is effective for inferences about the distributions of individual imputed variables, such as a univariate analysis, but it is not appropriate for analyses that involve relationship among variables, such as a regression analysis (Schafer 1999, p. 11). It can also produce badly biased estimates of regression coefficients when data on predictor variables are missing (Allison 2000).