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The MI Procedure

Example 54.5 Discriminant Function Method for CLASS Variables

This example uses discriminant monotone methods to impute values of a CLASS variable from the observed observation values in a data set with a monotone missing pattern.

The following statements impute the continuous variables Height and Width with the regression method and the classification variable Species with the discriminant function method:

proc mi data=Fish2 seed=7545417 nimpute=3 out=outex5;
   class Species;
   monotone reg( Height Width)
            discrim( Species= Length3 Height Width/ details);
   var Length3 Height Width Species;
run;

The "Model Information"  table in Output 54.5.1 describes the method and options used in the multiple imputation process.

Output 54.5.1 Model Information
The MI Procedure

Model Information
Data Set WORK.FISH2
Method Monotone
Number of Imputations 3
Seed for random number generator 7545417

The "Monotone Model Specification"  table in Output 54.5.2 describes methods and imputed variables in the imputation model. The procedure uses the regression method to impute the variables Height and Width, and uses the logistic regression method to impute the variable Species in the model.

Output 54.5.2 Monotone Model Specification
Monotone Model Specification
Method Imputed Variables
Regression Height Width
Discriminant Function Species

The "Missing Data Patterns" table in Output 54.5.3 lists distinct missing data patterns with corresponding frequencies and percents. The table confirms a monotone missing pattern for these variables.

Output 54.5.3 Missing Data Patterns
Missing Data Patterns
Group Length3 Height Width Species Freq Percent Group Means
Length3 Height Width
1 X X X X 47 85.45 33.497872 12.097645 4.808204
2 X X X . 6 10.91 32.366667 11.411050 4.567050
3 X X . . 2 3.64 36.600000 14.126350 .

When you use the DETAILS option, the parameters estimated from the observed data and the parameters used in each imputation are displayed in Output 54.5.4.

Output 54.5.4 Discriminant Model
Group Means for Monotone Discriminant Method
Species Variable Obs-Data Imputation
1 2 3
Gp1 Length3 0.68104 0.766779 0.724277 0.577304
Gp1 Height 0.74011 0.809770 0.794103 0.671612
Gp1 Width 0.63865 0.700122 0.725179 0.579870
Gp2 Length3 -1.00022 -0.809466 -0.999101 -0.908734
Gp2 Height -1.09007 -0.965672 -1.089324 -1.024453
Gp2 Width -0.88135 -0.710969 -0.827099 -0.746598

The following statements list the first 10 observations of the data set outex5 in Output 54.5.5. Note that all missing values of the variables Width and Species are imputed.

proc print data=outex5(obs=10);
   title 'First 10 Observations of the Imputed Data Set';
run;

Output 54.5.5 Imputed Data Set
First 10 Observations of the Imputed Data Set

Obs _Imputation_ Species Length3 Height Width
1 1 Gp1 30.0 11.5200 4.02000
2 1 Gp1 31.2 12.4800 4.30560
3 1 Gp1 31.1 12.3778 4.69610
4 1 Gp1 33.5 12.7300 4.67966
5 1 Gp2 34.0 12.4440 5.13400
6 1 Gp1 34.7 13.6024 4.92740
7 1 Gp1 34.5 14.1795 5.27850
8 1 Gp1 35.0 12.6700 4.69000
9 1 Gp1 35.1 14.0049 4.84380
10 1 Gp1 36.2 14.2266 4.95940

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