The MI Procedure

Example 63.6 FCS Method for Continuous Variables

This example uses FCS regression methods to impute values for all continuous variables in a data set with an arbitrary missing pattern.

The following statements invoke the MI procedure and impute missing values for the `Fitness1` data set:

```proc mi data=Fitness1 seed=1213 nimpute=4 mu0=50 10 180 out=outex6;
fcs nbiter=20 reg(/details);
var Oxygen RunTime RunPulse;
run;
```

The NIMPUTE=4 option specifies the total number of imputations. The FCS statement requests multivariate imputations by FCS methods, and the NBITER=20 option (which is the default) specifies the number of burn-in iterations before each imputation.

The "Model Information"  table in Output 63.6.1 describes the method and options used in the multiple imputation process.

Output 63.6.1: Model Information

The MI Procedure

Model Information
Data Set WORK.FITNESS1
Method FCS
Number of Imputations 4
Number of Burn-in Iterations 20
Seed for random number generator 1213

The "FCS Model Specification"  table in Output 63.6.2 describes methods and imputed variables in the imputation model. With the REG option in the FCS statement, the procedure uses the regression method to impute variables `RunTime`, `RunPulse`, and `Oxygen` in the model.

Output 63.6.2: FCS Model Specification

FCS Model Specification
Method Imputed Variables
Regression Oxygen RunTime RunPulse

The "Missing Data Patterns" table in Output 63.6.3 lists distinct missing data patterns with corresponding frequencies and percentages.

Output 63.6.3: Missing Data Patterns

Missing Data Patterns
Group Oxygen RunTime RunPulse Freq Percent Group Means
Oxygen RunTime RunPulse
1 X X X 21 67.74 46.353810 10.809524 171.666667
2 X X . 4 12.90 47.109500 10.137500 .
3 X . . 3 9.68 52.461667 . .
4 . X X 1 3.23 . 11.950000 176.000000
5 . X . 2 6.45 . 9.885000 .

When you use the DETAILS option, the parameters used in each imputation are displayed in Output 63.6.4, Output 63.6.5, and Output 63.6.6.

Output 63.6.4: FCS Regression Model for `Oxygen`

Regression Models for FCS Method
Imputed
Variable
Effect Imputation
1 2 3 4
Oxygen Intercept -0.132359 0.093555 0.078587 0.063256
Oxygen RunTime -0.908663 -0.753423 -1.125549 -0.634844
Oxygen RunPulse -0.134745 0.052640 -0.135864 -0.158692

Output 63.6.5: FCS Regression Model for `RunTime`

The MI Procedure

Regression Models for FCS Method
Imputed
Variable
Effect Imputation
1 2 3 4
RunTime Intercept -0.127880 -0.125666 -0.074802 0.058724
RunTime Oxygen -0.592047 -1.067554 -1.020216 -0.827592
RunTime RunPulse 0.110865 -0.311273 -0.158049 0.060715

Output 63.6.6: FCS Regression Model for `RunPulse`

The MI Procedure

Regression Models for FCS Method
Imputed
Variable
Effect Imputation
1 2 3 4
RunPulse Intercept -0.072862 -0.089964 0.049778 0.082088
RunPulse Oxygen 0.226951 -0.439850 -0.440705 -0.353438
RunPulse RunTime 0.545914 0.067482 0.234528 -0.273761

The following statements list the first 10 observations of the data set `Outex6` in Output 63.6.7. Note that all missing values of all variables are imputed.

```proc print data=outex6(obs=10);
title 'First 10 Observations of the Imputed Data Set';
run;
```

Output 63.6.7: Imputed Data Set

 First 10 Observations of the Imputed Data Set

Obs _Imputation_ Oxygen RunTime RunPulse
1 1 44.6090 11.3700 178.000
2 1 45.3130 10.0700 185.000
3 1 54.2970 8.6500 156.000
4 1 59.5710 10.1985 185.842
5 1 49.8740 9.2200 173.379
6 1 44.8110 11.6300 176.000
7 1 44.6299 11.9500 176.000
8 1 47.4258 10.8500 183.926
9 1 39.4420 13.0800 174.000
10 1 60.0550 8.6300 170.000

After the completion of the specified four imputations, the "Variance Information" table in Output 63.6.8 displays the between-imputation variance, within-imputation variance, and total variance for combining complete-data inferences. The relative increase in variance due to missingness, the fraction of missing information, and the relative efficiency for each variable are also displayed. These statistics are described in the section Combining Inferences from Multiply Imputed Data Sets.

Output 63.6.8: Variance Information

Variance Information
Variable Variance DF Relative
Increase
in Variance
Fraction
Missing
Information
Relative
Efficiency
Between Within Total
Oxygen 0.044012 0.936794 0.991809 25.911 0.058727 0.057401 0.985853
RunTime 0.002518 0.063583 0.066730 26.328 0.049500 0.048575 0.988002
RunPulse 3.552893 3.488832 7.929948 5.3995 1.272952 0.630073 0.863917

The "Parameter Estimates" table in Output 63.6.9 displays a 95% mean confidence interval and a t statistic with its associated p-value for each of the hypotheses requested with the MU0= option.

Output 63.6.9: Parameter Estimates

Parameter Estimates
Variable Mean Std Error 95% Confidence Limits DF Minimum Maximum Mu0 t for H0:
Mean=Mu0
Pr > |t|
Oxygen 47.200681 0.995896 45.1532 49.2481 25.911 47.075129 47.512585 50.000000 -2.81 0.0093
RunTime 10.578418 0.258322 10.0478 11.1091 26.328 10.526891 10.627704 10.000000 2.24 0.0338
RunPulse 171.368390 2.816016 164.2877 178.4490 5.3995 168.633931 172.932612 180.000000 -3.07 0.0253