The MI Procedure

 

Example 56.4 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 56.4.1 describes the method and options used in the multiple imputation process.

Output 56.4.1 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 56.4.2 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 56.4.2 Monotone Model Specification
Monotone Model Specification
Method Imputed Variables
Regression Height Width
Logistic Regression Species

The "Missing Data Patterns" table in Output 56.4.3 lists distinct missing data patterns with corresponding frequencies and percentages. The table confirms a monotone missing pattern for these variables.

Output 56.4.3 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 56.4.4.

Output 56.4.4 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 56.4.5 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 56.4.5:

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

Output 56.4.6 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.