The MI Procedure

Example 75.4 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 nimpute=15 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 75.4.1 describes the method and options used in the multiple imputation process.

Output 75.4.1: Model Information

The MI Procedure

Model Information
Data Set WORK.FISH2
Method Monotone
Number of Imputations 15
Seed for random number generator 1305417



The "Monotone Model Specification"  table in Output 75.4.2 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 75.4.2: Monotone Model Specification

Monotone Model Specification
Method Imputed Variables
Regression Width
Logistic Regression Species



The "Missing Data Patterns" table in Output 75.4.3 lists distinct missing data patterns with corresponding frequencies and percentages. The table confirms a monotone missing pattern for these variables.

Output 75.4.3: 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 75.4.4.

Output 75.4.4: Regression Model

Regression Models for Monotone Method
Imputed
Variable
Effect Obs-Data Imputation
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Width Intercept 0.00284 -0.029987 0.049363 -0.015273 -0.064915 0.059375 0.018049 -0.028171 -0.016050 -0.012890 -0.056099 -0.013302 0.031642 0.051256 -0.032029 0.030396
Width Length 0.96212 0.981287 0.906104 0.962814 0.978103 0.952034 0.920482 0.908541 0.962650 0.949542 0.962843 0.921873 0.947360 1.003013 0.950239 0.955749



Output 75.4.5: Logistic Regression Model

Logistic Models for Monotone Method
Imputed
Variable
Effect Obs-Data Imputation
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Species Intercept -3.93577 -5.016163 -3.422209 -4.706398 -2.049090 -4.568278 -4.336259 -4.250352 -2.843154 -1.055153 -3.501466 -2.140199 -3.629155 -4.020008 -2.615227 -4.964532
Species Length 10.41940 16.262215 6.082966 9.832246 4.992717 11.886805 5.789312 7.662947 5.757570 0.572346 10.900700 10.743223 10.504352 12.346335 5.432583 11.926760
Species Width -14.56630 -21.856472 -8.653119 -15.534802 -7.401465 -15.621272 -12.855797 -14.816308 -8.792538 -1.775130 -15.547003 -12.353169 -14.555215 -16.481415 -11.694606 -18.401905
Species Length*Width -0.48936 -0.208880 0.795883 -0.011135 -0.461227 0.080406 -2.586760 -2.604478 -0.317211 0.027353 -0.809353 -0.060720 -0.544245 -0.507705 -2.484002 -2.094407



The following statements list the first 10 observations of the data set Outex4 in Output 75.4.6:

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

Output 75.4.6: 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.