## Example 56.5 Monotone 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= Length Height Width/ details);
var Length Height Width Species;
run;
```

The "Model Information"  table in Output 56.5.1 describes the method and options used in the multiple imputation process.

Output 56.5.1 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 56.5.2 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 56.5.2 Monotone Model Specification
Monotone Model Specification
Method Imputed Variables
Regression Height Width
Discriminant Function Species

The "Missing Data Patterns" table in Output 56.5.3 lists distinct missing data patterns with corresponding frequencies and percentages. The table confirms a monotone missing pattern for these variables.

Output 56.5.3 Missing Data Patterns
Missing Data Patterns
Group Length Height Width Species Freq Percent Group Means
Length Height Width
1 X X X X 43 82.69 41.997674 12.819512 5.359860
2 X X X . 3 5.77 38.433333 11.797667 4.587667
3 X X . . 4 7.69 42.275000 13.346750 .
4 X . . . 2 3.85 40.150000 . .

When you use the DETAILS option, the parameters estimated from the observed data and the parameters used in each imputation are displayed in Output 56.5.4.

Output 56.5.4 Discriminant Model
Group Means for Monotone Discriminant Method
Species Variable Obs-Data Imputation
1 2 3
Bream Length -0.36712 -0.198907 -0.375696 -0.307771
Bream Height 0.64051 0.756448 0.684845 0.658337
Bream Width 0.20882 0.465034 0.254438 0.252637
Pike Length 0.85554 0.656521 0.677957 1.024069
Pike Height -1.31185 -1.431954 -1.436355 -1.119520
Pike Width -0.25768 -0.381503 -0.420441 -0.136188

The following statements list the first 10 observations of the data set outex5 in Output 56.5.5. 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 56.5.5 Imputed Data Set
 First 10 Observations of the Imputed Data Set

Obs _Imputation_ Species Length Height Width
1 1 Bream 30.0 11.520 4.02000
2 1 Bream 31.2 12.480 4.30600
3 1 Bream 31.1 12.378 4.69600
4 1 Bream 33.5 12.730 4.45600
5 1 Bream 34.0 12.444 4.46687
6 1 Bream 34.7 13.602 4.92700
7 1 Bream 34.5 14.180 5.27900
8 1 Bream 35.0 12.670 4.69000
9 1 Bream 35.1 14.005 4.84400
10 1 Bream 36.2 14.227 4.95900