### Example 57.4 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( Length Width/ details)
logistic( Species= Length Height Width Height*Width/ details);
var Length Height Width Species;
run;
```

The Model Information  table in Output 57.4.1 describes the method and options used in the multiple imputation process.

Output 57.4.1: 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 57.4.2 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 57.4.2: Monotone Model Specification

Monotone Model Specification
Method Imputed Variables
Regression Height Width
Logistic Regression Species

The Missing Data Patterns table in Output 57.4.3 lists distinct missing data patterns with corresponding frequencies and percentages. The table confirms a monotone missing pattern for these variables.

Output 57.4.3: 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, 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 57.4.4.

Output 57.4.4: Regression Model

Regression Models for Monotone Method
Imputed
Variable
Effect Obs-Data Imputation
1 2 3 4 5
Width Intercept 0.00682 0.054140 0.018049 -0.015137 0.024027 0.084643
Width Length 0.75519 0.838485 0.768945 0.789577 0.728779 0.631217
Width Height 0.73890 0.832117 0.831748 0.809482 0.747734 0.745232

Output 57.4.5: Logistic Regression Model

Logistic Models for Monotone Method
Imputed
Variable
Effect Obs-Data Imputation
1 2 3 4 5
Species Intercept 22.80713 22.807129 22.807129 22.807129 22.807129 22.807129
Species Length -14.44698 -14.446980 -14.446980 -14.446980 -14.446980 -14.446980
Species Height 43.11236 43.112363 43.112363 43.112363 43.112363 43.112363
Species Width -9.64352 -9.643524 -9.643524 -9.643524 -9.643524 -9.643524
Species Height*Width -9.73015 -9.730154 -9.730154 -9.730154 -9.730154 -9.730154

The following statements list the first 10 observations of the data set `outex4` in Output 57.4.5:

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

Output 57.4.6: 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 4.62964
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

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.