The MI Procedure

Example 76.3 Monotone Regression Method

(View the complete code for this example.)

This example uses the regression method to impute missing values for all variables in a data set with a monotone missing pattern. The following statements invoke the MI procedure and request the regression method for the variable Length2 and the predictive mean matching method for variable Length3. The resulting data set is named Outex3.

proc mi data=Fish1 round=.1  mu0= 0 35 45
        seed=13951639 nimpute=8 out=outex3;
   monotone reg(Length2/ details)
            regpmm(Length3= Length1 Length2 Length1*Length2/ details);
   var Length1 Length2 Length3;
run;

The ROUND= option is used to round the imputed values to the same precision as observed values. The values specified with the ROUND= option are matched with the variables Length1, Length2, and Length3 in the order listed in the VAR statement. The MU0= option requests t tests for the hypotheses that the population means corresponding to the variables in the VAR statement are Length2=35 and Length3=45.

The "Missing Data Patterns" table lists distinct missing data patterns with corresponding frequencies and percentages. It is identical to the table in Output 76.2.3 in Example 76.2.

The "Monotone Model Specification" table in Output 76.3.1 displays the model specification.

Output 76.3.1: Monotone Model Specification

The MI Procedure

Monotone Model Specification
MethodImputed Variables
RegressionLength2
Regression-PMM( K= 5)Length3


When you use the DETAILS option, the parameters estimated from the observed data and the parameters used in each imputation are displayed in Output 76.3.2 and Output 76.3.3.

Output 76.3.2: Regression Model

Regression Models for Monotone Method
Imputed
Variable
EffectObs-DataImputation
12345678
Length2Intercept-0.04249-0.049184-0.055470-0.051346-0.064193-0.030719-0.030694-0.050964-0.017976
Length2Length10.985871.0019340.9952750.9922940.9831220.9958830.9891930.9684800.977476


Output 76.3.3: Regression Predicted Mean Matching Model

Regression Models for Monotone Predicted Mean Matching Method
Imputed
Variable
EffectObs DataImputation
12345678
Length3Intercept-0.013040.004134-0.011417-0.034177-0.0105320.004685-0.0139170.012658-0.020144
Length3Length1-0.013320.025320-0.0374940.3087650.156606-0.1471180.097745-0.2540540.086950
Length3Length20.989180.9555101.0257410.6733740.8283841.1464400.8605641.2260150.879854
Length3Length1*Length2-0.02521-0.034964-0.022017-0.017919-0.029335-0.034671-0.023384-0.023829-0.026785


After the completion of eight imputations (NIMPUTE=8), the "Variance Information" table in Output 76.3.4 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 76.3.4: Variance Information

Variance Information (8 Imputations)
VariableVarianceDFRelative
Increase
in Variance
Fraction
Missing
Information
Relative
Efficiency
BetweenWithinTotal
Length20.0000896500.4392080.43930932.1550.0002300.0002300.999971
Length30.0004330.4873560.48784232.130.0009980.0009980.999875


The "Parameter Estimates" table in Output 76.3.5 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 76.3.5: Parameter Estimates

Parameter Estimates (8 Imputations)
VariableMeanStd Error95% Confidence LimitsDFMinimumMaximumMu0t for H0:
Mean=Mu0
Pr > |t|
Length233.1060710.66280431.7562434.4559032.15533.08857133.11714335.000000-2.860.0074
Length338.4167860.69845736.9943039.8392732.1338.38285738.44571445.000000-9.43<.0001


The following statements list the first 10 observations of the data set Outex3 in Output 76.3.6. Note that the imputed values of Length2 are rounded to the same precision as the observed values.

proc print data=outex3(obs=10);
   title 'First 10 Observations of the Imputed Data Set';
run;

Output 76.3.6: Imputed Data Set

First 10 Observations of the Imputed Data Set

Obs_Imputation_Length1Length2Length3
1123.225.430.0
2124.026.331.2
3123.926.531.1
4126.329.033.5
5126.529.034.7
6126.829.734.7
7126.828.834.7
8127.630.035.0
9127.630.035.1
10128.530.736.2