The MI Procedure

Example 57.2 Monotone Propensity Score Method

This example uses the propensity score method to impute missing values for variables in a data set with a monotone missing pattern. The following statements invoke the MI procedure and request the propensity score method. The resulting data set is named outex2.

proc mi data=Fish1 seed=899603 out=outex2;
   monotone propensity;
   var Length1 Length2 Length3;

Note that the VAR statement is required and the data set must have a monotone missing pattern with variables as ordered in the VAR statement.

The Model Information  table in Output 57.2.1 describes the method and options used in the multiple imputation process. By default, five imputations are created for the missing data.

Output 57.2.1: Model Information

The MI Procedure

Model Information
Method Monotone
Number of Imputations 5
Seed for random number generator 899603

When monotone methods are used in the imputation, MONOTONE is displayed as the method. The Monotone Model Specification table in Output 57.2.2 displays the detailed model specification. By default, the observations are sorted into five groups based on their propensity scores.

Output 57.2.2: Monotone Model Specification

Monotone Model Specification
Method Imputed Variables
Propensity( Groups= 5) Length2 Length3

Without covariates specified for imputed variables Length2 and Length3, the variable Length1 is used as the covariate for Length2, and the variables Length1 and Length2 are used as covariates for Length3.

The Missing Data Patterns table in Output 57.2.3 lists distinct missing data patterns with corresponding frequencies and percentages. Here, values of X and . indicate that the variable is observed or missing, respectively, in the corresponding group. The table confirms a monotone missing pattern for these three variables.

Output 57.2.3: Missing Data Patterns

Missing Data Patterns
Group Length1 Length2 Length3 Freq Percent Group Means
Length1 Length2 Length3
1 X X X 30 85.71 30.603333 33.436667 38.720000
2 X X . 3 8.57 29.033333 31.666667 .
3 X . . 2 5.71 27.750000 . .

For the imputation process, first, missing values of Length2 in group 3 are imputed using observed values of Length1. Then the missing values of Length3 in group 2 are imputed using observed values of Length1 and Length2. And finally, the missing values of Length3 in group 3 are imputed using observed values of Length1 and imputed values of Length2.

After the completion of m imputations, the Variance Information table in Output 57.2.4 displays the between-imputation variance, within-imputation variance, and total variance for combining complete-data inferences. It also displays the degrees of freedom for the total variance. The relative increase in variance due to missingness, the fraction of missing information, and the relative efficiency for each variable are also displayed. A detailed description of these statistics is provided in the section Combining Inferences from Multiply Imputed Data Sets.

Output 57.2.4: Variance Information

Variance Information
Variable Variance DF Relative
in Variance
Between Within Total
Length2 0.001500 0.465422 0.467223 32.034 0.003869 0.003861 0.999228
Length3 0.049725 0.547434 0.607104 27.103 0.108999 0.102610 0.979891

The Parameter Estimates table in Output 57.2.5 displays the estimated mean and standard error of the mean for each variable. The inferences are based on the t distributions. For each variable, the table also displays a 95% mean confidence interval and a t statistic with the associated p-value for the hypothesis that the population mean is equal to the value specified in the MU0= option, which is zero by default.

Output 57.2.5: Parameter Estimates

Parameter Estimates
Variable Mean Std Error 95% Confidence Limits DF Minimum Maximum Mu0 t for H0:
Pr > |t|
Length2 33.006857 0.683537 31.61460 34.39912 32.034 32.957143 33.060000 0 48.29 <.0001
Length3 38.361714 0.779169 36.76328 39.96015 27.103 38.080000 38.545714 0 49.23 <.0001

The following statements list the first 10 observations of the data set outex2, as shown in Output 57.2.6. The missing values are imputed from observed values with similar propensity scores.

proc print data=outex2(obs=10);
   title 'First 10 Observations of the Imputed Data Set';

Output 57.2.6: Imputed Data Set

First 10 Observations of the Imputed Data Set

Obs _Imputation_ Length1 Length2 Length3
1 1 23.2 25.4 30.0
2 1 24.0 26.3 31.2
3 1 23.9 26.5 31.1
4 1 26.3 29.0 33.5
5 1 26.5 29.0 38.6
6 1 26.8 29.7 34.7
7 1 26.8 29.0 35.0
8 1 27.6 30.0 35.0
9 1 27.6 30.0 35.1
10 1 28.5 30.7 36.2