The MI Procedure

Example 75.7 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 nimpute=15 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 75.7.1 describes the method and options used in the multiple imputation process.

Output 75.7.1: Model Information

The MI Procedure

Model Information
Data Set WORK.FISH3
Method FCS
Number of Imputations 15
Number of Burn-in Iterations 10
Seed for random number generator 1305417



The "FCS Model Specification"  table in Output 75.7.2 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 75.7.2: FCS Model Specification

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



The "Missing Data Patterns" table in Output 75.7.3 lists distinct missing data patterns with corresponding frequencies and percentages.

Output 75.7.3: 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 75.7.4 and in the "Regression Models for FCS Method" table in Output 75.7.5.

Output 75.7.4: FCS Discrim Model for Species

Group Means for FCS Discriminant Method
Species Variable Imputation
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Parkki Length -0.268298 -0.611484 -0.430752 -0.508489 -1.096890 -0.691899 -1.097177 -0.605319 -0.349771 -0.717117 -0.636064 -0.501049 -0.384597 -0.640036 -1.019628
Parkki Width -0.374514 -0.920031 -0.695627 -0.444730 -1.183297 -0.684968 -1.230322 -0.630649 -0.599680 -0.735174 -0.834453 -0.520368 -0.569160 -0.741567 -1.064032
Perch Length 0.073272 0.281238 0.135766 0.105996 0.280959 -0.003145 0.356800 0.347392 0.055848 0.448266 0.371622 0.231022 0.150028 0.237300 0.341506
Perch Width 0.104187 0.345404 0.211220 0.109806 0.365960 0.116315 0.397011 0.404836 0.125563 0.524498 0.482840 0.286552 0.260146 0.287303 0.341318
Roach Length -0.293847 -0.296757 -0.485885 0.094638 -0.028394 -0.258734 -0.391279 -0.426078 -0.616262 -0.305244 -0.451065 -0.205316 -0.125811 -0.320887 -0.420115
Roach Width -0.507327 -0.352964 -0.626142 -0.033285 -0.243456 -0.459994 -0.429801 -0.433738 -0.668304 -0.419368 -0.466063 -0.317969 -0.238243 -0.467192 -0.520025



Output 75.7.5: FCS Regression Model for Height

Regression Models for FCS Method
Imputed
Variable
Effect Species Imputation
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Width Intercept   -0.080952 -0.008262 -0.040466 -0.083230 -0.047121 -0.028571 -0.055278 -0.051276 -0.095069 -0.075439 -0.029298 -0.033294 -0.059441 -0.117950 -0.090120
Width Species Parkki -0.100521 -0.096675 -0.022778 -0.160418 -0.092341 0.006502 -0.022182 -0.111298 -0.101806 -0.025496 0.015175 -0.035755 -0.082546 -0.214051 -0.076865
Width Species Perch 0.150457 0.119791 0.108795 0.132785 0.152929 0.056631 0.114786 0.159393 0.118097 0.114437 0.091675 0.068180 0.120584 0.238069 0.125656
Width Length   0.928032 0.939600 1.039315 0.975903 0.961029 0.976143 0.977985 0.973528 0.973916 1.013839 0.943677 0.956911 0.995960 0.924327 0.919800



The following statements list the first 10 observations of the data set Outex7 in Output 75.7.6:

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

Output 75.7.6: 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 75.7.7 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 75.7.7: Variance Information

Variance Information (15 Imputations)
Variable Variance DF Relative
Increase
in Variance
Fraction
Missing
Information
Relative
Efficiency
Between Within Total
Length 0.004567 0.812129 0.817001 83.548 0.005999 0.005968 0.999602
Width 0.000162 0.029149 0.029321 83.555 0.005920 0.005890 0.999607



The "Parameter Estimates" table in Output 75.7.8 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 75.7.8: Parameter Estimates

Parameter Estimates (15 Imputations)
Variable Mean Std Error 95% Confidence Limits DF Minimum Maximum Mu0 t for H0:
Mean=Mu0
Pr > |t|
Length 27.584713 0.903881 25.78710 29.38232 83.548 27.447764 27.716689 0 30.52 <.0001
Width 4.298698 0.171235 3.95815 4.63924 83.555 4.275600 4.320615 0 25.10 <.0001