### Example 61.4 Monotone Logistic Regression Method for CLASS Variables

This example uses logistic regression method to impute values for a binary variable in a data set with a monotone missing pattern.

In the following statements, the logistic regression method is used for the binary CLASS variable `Species`:

```proc mi data=Fish2 seed=1305417 out=outex4;
class Species;
monotone reg( Width/ details)
logistic( Species= Length Width Length*Width/ details);
var Length Width Species;
run;
```

The Model Information  table in Output 61.4.1 describes the method and options used in the multiple imputation process.

Output 61.4.1: Model Information

The MI Procedure

Model Information
Data Set WORK.FISH2
Method Monotone
Number of Imputations 5
Seed for random number generator 1305417

The Monotone Model Specification  table in Output 61.4.2 describes methods and imputed variables in the imputation model. The procedure uses the logistic regression method to impute the variable `Species` in the model. Missing values in other variables are not imputed.

Output 61.4.2: Monotone Model Specification

Monotone Model Specification
Method Imputed Variables
Regression Width
Logistic Regression Species

The Missing Data Patterns table in Output 61.4.3 lists distinct missing data patterns with corresponding frequencies and percentages. The table confirms a monotone missing pattern for these variables.

Output 61.4.3: Missing Data Patterns

Missing Data Patterns
Group Length Width Species Freq Percent Group Means
Length Width
1 X X X 49 73.13 28.595918 4.482518
2 X X . 9 13.43 27.533333 4.444844
3 X . . 9 13.43 28.633333 .

When you use the DETAILS option, parameters estimated from the observed data and the parameters used in each imputation are displayed in the Logistic Models for Monotone Method table in Output 61.4.4.

Output 61.4.4: Regression Model

Regression Models for Monotone Method
Imputed
Variable
Effect Obs-Data Imputation
1 2 3 4 5
Width Intercept 0.00284 -0.029987 0.049363 -0.015273 -0.064915 0.059375
Width Length 0.96212 0.981287 0.906104 0.962814 0.978103 0.952034

Output 61.4.5: Logistic Regression Model

Logistic Models for Monotone Method
Imputed
Variable
Effect Obs-Data Imputation
1 2 3 4 5
Species Intercept -3.93577 -5.016163 -3.422209 -4.706398 -2.049090 -4.568278
Species Length 10.41940 16.262215 6.082966 9.832246 4.992717 11.886805
Species Width -14.56630 -21.856472 -8.653119 -15.534802 -7.401465 -15.621272
Species Length*Width -0.48936 -0.208880 0.795883 -0.011135 -0.461227 0.080406

The following statements list the first 10 observations of the data set `Outex4` in Output 61.4.6:

```proc print data=outex4(obs=10);
title 'First 10 Observations of the Imputed Data Set';
run;
```

Output 61.4.6: Imputed Data Set

 First 10 Observations of the Imputed Data Set

Obs _Imputation_ Species Length Width
1 1 Parkki 16.5 2.32650
2 1 Parkki 17.4 2.31420
3 1 Parkki 19.8 2.20482
4 1 Parkki 21.3 2.91810
5 1 Parkki 22.4 3.29280
6 1 Perch 23.2 3.29440
7 1 Parkki 23.2 3.41040
8 1 Parkki 24.1 3.15710
9 1 Perch 25.8 3.66360
10 1 Parkki 28.0 4.14400

Note that a missing value of the variable `Species` is not imputed if the corresponding covariates are missing and not imputed, as shown by observation 4 in the table.