The MI Procedure

Example 75.2 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;
run;

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 75.2.1 describes the method and options used in the multiple imputation process. By default, 25 imputations are created for the missing data.

Output 75.2.1: Model Information

The MI Procedure

Model Information
Data Set WORK.FISH1
Method Monotone
Number of Imputations 25
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 75.2.2 displays the detailed model specification. By default, the observations are sorted into five groups based on their propensity scores.

Output 75.2.2: 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 75.2.3 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 75.2.3: 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 75.2.4 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 75.2.4: Variance Information

Variance Information (25 Imputations)
Variable Variance DF Relative
Increase
in Variance
Fraction
Missing
Information
Relative
Efficiency
Between Within Total
Length2 0.003228 0.457211 0.460568 31.925 0.007343 0.007294 0.999708
Length3 0.037617 0.542147 0.581269 29.829 0.072161 0.067656 0.997301



The "Parameter Estimates" table in Output 75.2.5 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 0 by default.

Output 75.2.5: Parameter Estimates

Parameter Estimates (25 Imputations)
Variable Mean Std Error 95% Confidence Limits DF Minimum Maximum Mu0 t for H0:
Mean=Mu0
Pr > |t|
Length2 33.040343 0.678652 31.65785 34.42284 31.925 32.957143 33.122857 0 48.69 <.0001
Length3 38.325143 0.762410 36.76772 39.88257 29.829 37.808571 38.614286 0 50.27 <.0001



The following statements list the first 10 observations of the data set Outex2, as shown in Output 75.2.6. 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';
run;

Output 75.2.6: 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