### Example 57.7 FCS Method for CLASS Variables

This example uses FCS methods to impute missing values in both continuous and CLASS variables in a data set with an arbitrary missing pattern. The following statements invoke the MI procedure and impute missing values for the `Fish3` data set:

```proc mi data=Fish3 seed=1305417 out=outex7;
class Species;
fcs nbiter=10 discrim(Species/details) reg(Height/details);
var Species Length Height Width;
run;
```

The DISCRIM option uses the discriminant function method to impute the classification variable `Species`, and the REG option uses the regression method to impute the continuous variable `Height`. By default, the regression method is also used to impute other continuous variables, `Length` and `Width`.

The Model Information  table in Output 57.7.1 describes the method and options used in the multiple imputation process.

Output 57.7.1: Model Information

The MI Procedure

Model Information
Data Set WORK.FISH3
Method FCS
Number of Imputations 5
Number of Burn-in Iterations 10
Seed for random number generator 1305417

The FCS Model Specification  table in Output 57.7.2 describes methods and imputed variables in the imputation model. The procedure uses the discriminant function method to impute the variable `Species`, and the regression method to impute other variables.

Output 57.7.2: FCS Model Specification

FCS Model Specification
Method Imputed Variables
Regression Length Height Width
Discriminant Function Species

The Missing Data Patterns table in Output 57.7.3 lists distinct missing data patterns with corresponding frequencies and percentages.

Output 57.7.3: Missing Data Patterns

Missing Data Patterns
Group Species Length Height Width Freq Percent Group Means
Length Height Width
1 X X X X 38 73.08 41.515789 12.531526 5.266474
2 X . X X 2 3.85 . 14.448000 6.886000
3 X . X . 1 1.92 . 18.037000 .
4 . X X X 3 5.77 38.433333 11.797667 4.587667
5 . X X . 3 5.77 45.033333 13.647667 .
6 . X . X 2 3.85 36.100000 . 5.135000
7 . X . . 2 3.85 40.150000 . .
8 . . X . 1 1.92 . 12.444000 .

With the specified DETAILS option for variables `Species` and `Height`, parameters used in each imputation for these two variables are displayed in the Group Means for FCS Discriminant Method table in Output 57.7.4 and in the Regression Models for FCS Method table in Output 57.7.5.

Output 57.7.4: FCS Discrim Model for `Species`

Group Means for FCS Discriminant Method
Species Variable Imputation
1 2 3 4 5
Bream Length -0.635560 -0.539102 -0.183231 -0.312298 -0.501390
Bream Height 0.505922 0.540880 0.761373 0.736716 0.582379
Bream Width -0.203055 0.030787 0.403116 0.422214 0.080807
Pike Length 1.074270 0.904169 0.409041 1.234640 0.479436
Pike Height -1.293411 -1.359962 -1.418251 -1.177828 -1.428490
Pike Width 0.060791 -0.463132 -0.702662 0.004479 -0.659505

Output 57.7.5: FCS Regression Model for `Height`

Regression Models for FCS Method
Imputed
Variable
Effect Species Imputation
1 2 3 4 5
Height Intercept   -0.366066 -0.359325 -0.272079 -0.353772 -0.357781
Height Species Bream 0.973036 0.980092 0.818649 1.035374 0.963826
Height Length   0.170407 0.099879 -0.018424 0.187469 0.090964
Height Width   0.242966 0.382906 0.430107 0.299173 0.325195

The following statements list the first 10 observations of the data set `outex7` in Output 57.7.6:

```proc print data=outex7(obs=10);
title 'First 10 Observations of the Imputed Data Set';
run;
```

Output 57.7.6: Imputed Data Set

 First 10 Observations of the Imputed Data Set

Obs _Imputation_ Species Length Height Width
1 1 Bream 30.0000 11.5200 4.02000
2 1 Bream 31.2000 12.4800 4.30600
3 1 Bream 31.1000 12.3780 4.69600
4 1 Bream 33.5000 12.7300 4.45600
5 1 Pike 68.6009 12.4440 7.65040
6 1 Bream 34.7000 13.6020 4.92700
7 1 Bream 34.5000 14.1800 5.27900
8 1 Pike 35.0000 5.7684 4.69000
9 1 Bream 35.1000 14.0050 4.84400
10 1 Bream 36.2000 14.2270 4.95900

After the completion of five imputations by default, the Variance Information table in Output 57.7.7 displays the between-imputation variance, within-imputation variance, and total variance for combining complete-data inferences for continuous variables. 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 57.7.7: Variance Information

Variance Information
Variable Variance DF Relative
Increase
in Variance
Fraction
Missing
Information
Relative
Efficiency
Between Within Total
Length 0.076551 1.351968 1.443828 43.942 0.067946 0.065513 0.987067
Height 0.024597 0.311347 0.340863 41.379 0.094801 0.089997 0.982319
Width 0.000307 0.015361 0.015730 47.645 0.024018 0.023723 0.995278

The Parameter Estimates table in Output 57.7.8 displays a 95% mean confidence interval and a t statistic with its associated p-value for each of the hypotheses requested with the default MU0=0 option.

Output 57.7.8: Parameter Estimates

Parameter Estimates
Variable Mean Std Error 95% Confidence Limits DF Minimum Maximum Mu0 t for H0:
Mean=Mu0
Pr > |t|
Length 41.952213 1.201594 39.53047 44.37396 43.942 41.702410 42.286360 0 34.91 <.0001
Height 12.785938 0.583835 11.60719 13.96469 41.379 12.555560 12.988405 0 21.90 <.0001
Width 5.345132 0.125420 5.09291 5.59735 47.645 5.324639 5.366759 0 42.62 <.0001