Example 9.3: Regression Method

The MI Procedure

Example 9.3: Regression Method

This example uses the regression method to impute missing values in a data set with a monotone missing pattern. The following statements invoke the MI procedure and request the regression method. The resulting data set is named outreg.

   proc mi data=FitMono round=.001 .01 1  mu0= 50 10 150
           seed=55417 out=outreg;
      monotone method=reg;   
      var Oxygen RunTime RunPulse; 
   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 Oxygen, RunTime, and RunPulse in the order listed with 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 Oxygen=50, RunTime=10, and RunPulse=150.

The "Missing Data Patterns" table lists distinct missing data patterns with corresponding frequencies and percents. It is identical to the table in the previous example.

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

Output 9.3.1: Variance Information

The MI Procedure

Multiple Imputation Variance Information
Variable	Variance			DF	Relative Increase in Variance	Fraction Missing Information
Variable	Between	Within	Total	DF	Relative Increase in Variance	Fraction Missing Information
RunTime	0.004443	0.068684	0.074016	25.294	0.077629	0.074435
RunPulse	1.790531	4.045134	6.193770	11.846	0.531166	0.382947

The "Multiple Imputation Parameter Estimates" table 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 9.3.2: Parameter Estimates

The MI Procedure

Multiple Imputation Parameter Estimates
Variable	Mean	Std Error	95% Confidence Limits		DF	Minimum	Maximum	Mu0	t for H0: Mean=Mu0	Pr > \|t\|
RunTime	10.575871	0.272059	10.0159	11.1359	25.294	10.506452	10.680968	10.000000	2.12	0.0443
RunPulse	170.425806	2.488729	164.9955	175.8561	11.846	169.290323	171.935484	150.000000	8.21	<.0001

The following statements list the first ten observations of the data set outreg. Note that the imputed values rounded to the same precision as the observed values.

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

Output 9.3.3: Imputed Data Set

First 10 Observations of the Imputed Data Set

Obs	_Imputation_	Oxygen	RunTime	RunPulse
1	1	44.609	11.37	178
2	1	45.313	10.07	185
3	1	54.297	8.65	156
4	1	59.571	7.18	156
5	1	49.874	9.22	192
6	1	44.811	11.63	176
7	1	45.681	11.95	176
8	1	49.091	10.85	174
9	1	39.442	13.08	174
10	1	60.055	8.63	170

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