The MI Procedure
Example 76.4 Monotone Logistic Regression Method for CLASS Variables
(View the complete code for this example.)
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 76.4.1 describes the method and options used in the multiple imputation process.
Output 76.4.1: Model Information
The "Monotone Model Specification" table in Output 76.4.2 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 76.4.2: Monotone Model Specification
The "Missing Data Patterns" table in Output 76.4.3 lists distinct missing data patterns with corresponding frequencies and percentages. The table confirms a monotone missing pattern for these variables.
Output 76.4.3: Missing Data Patterns
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 76.4.4.
Output 76.4.4: 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 76.4.5: 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 76.4.6:
proc print data=outex4(obs=10); title 'First 10 Observations of the Imputed Data Set'; run;
Output 76.4.6: Imputed Data Set
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.
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