### Example 61.7 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(Width/details);
var Species Length 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 61.7.1 describes the method and options used in the multiple imputation process.

Output 61.7.1: 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 61.7.2 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 61.7.2: FCS Model Specification

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

The Missing Data Patterns table in Output 61.7.3 lists distinct missing data patterns with corresponding frequencies and percentages.

Output 61.7.3: Missing Data Patterns

Missing Data Patterns
Group Species Length Width Freq Percent Group Means
Length Width
1 X X X 67 77.01 27.910448 4.361860
2 X X . 5 5.75 24.620000 .
3 X . X 6 6.90 . 4.167667
4 . X X 6 6.90 26.683333 4.136233
5 . X . 2 2.30 31.500000 .
6 . . X 1 1.15 . 3.663600

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 61.7.4 and in the Regression Models for FCS Method table in Output 61.7.5.

Output 61.7.4: FCS Discrim Model for `Species`

Group Means for FCS Discriminant Method
Species Variable Imputation
1 2 3 4 5
Parkki Length -0.268298 -0.611484 -0.430752 -0.508489 -1.096890
Parkki Width -0.374514 -0.920031 -0.695627 -0.444730 -1.183297
Perch Length 0.073272 0.281238 0.135766 0.105996 0.280959
Perch Width 0.104187 0.345404 0.211220 0.109806 0.365960
Roach Length -0.293847 -0.296757 -0.485885 0.094638 -0.028394
Roach Width -0.507327 -0.352964 -0.626142 -0.033285 -0.243456

Output 61.7.5: FCS Regression Model for `Height`

Regression Models for FCS Method
Imputed
Variable
Effect Species Imputation
1 2 3 4 5
Width Intercept   -0.080952 -0.008262 -0.040466 -0.083230 -0.047121
Width Species Parkki -0.100521 -0.096675 -0.022778 -0.160418 -0.092341
Width Species Perch 0.150457 0.119791 0.108795 0.132785 0.152929
Width Length   0.928032 0.939600 1.039315 0.975903 0.961029

The following statements list the first 10 observations of the data set `Outex7` in Output 61.7.6:

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

Output 61.7.6: Imputed Data Set

 First 10 Observations of the Imputed Data Set

Obs _Imputation_ Species Length Width
1 1 Roach 16.2000 2.26800
2 1 Roach 20.3000 2.82170
3 1 Roach 21.2000 2.40895
4 1 Roach 18.6497 3.17460
5 1 Roach 22.2000 3.57420
6 1 Roach 22.8000 3.35160
7 1 Roach 23.1000 3.39570
8 1 Perch 23.7000 3.88340
9 1 Roach 24.7000 3.75440
10 1 Roach 24.3000 3.54780

After the completion of five imputations by default, the Variance Information table in Output 61.7.7 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 61.7.7: Variance Information

Variance Information
Variable Variance DF Relative
Increase
in Variance
Fraction
Missing
Information
Relative
Efficiency
Between Within Total
Length 0.003204 0.813872 0.817717 83.633 0.004724 0.004713 0.999058
Width 0.000326 0.029149 0.029540 82.653 0.013427 0.013336 0.997340

The Parameter Estimates table in Output 61.7.8 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 61.7.8: Parameter Estimates

Parameter Estimates
Variable Mean Std Error 95% Confidence Limits DF Minimum Maximum Mu0 t for H0:
Mean=Mu0
Pr > |t|
Length 27.533359 0.904277 25.73499 29.33173 83.633 27.447764 27.581915 0 30.45 <.0001
Width 4.299028 0.171873 3.95716 4.64090 82.653 4.275600 4.320615 0 25.01 <.0001