PROC MI: Regression Method :: SAS/STAT(R) 9.2 User's Guide, Second Edition

The MI Procedure

Example 54.3 Regression Method

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 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 percents. It is identical to the table in Output 54.2.3 in Example 54.2.

The "Monotone Model Specification" table in Output 54.3.1 displays the model specification.

Output 54.3.1 Monotone Model Specification

The MI Procedure

Monotone Model Specification
Method	Imputed Variables
Regression	Length2
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 54.3.2 and Output 54.3.3.

Output 54.3.2 Regression Model

Regression Models for Monotone Method
Imputed Variable	Effect	Obs-Data	Imputation
Imputed Variable	Effect	Obs-Data	1	2	3	4	5
Length2	Intercept	-0.04249	-0.049184	-0.055470	-0.051346	-0.064193	-0.030719
Length2	Length1	0.98587	1.001934	0.995275	0.992294	0.983122	0.995883

Output 54.3.3 Regression Predicted Mean Matching Model

Regression Models for Monotone Predicted Mean Matching Method
Imputed Variable	Effect	Obs Data	Imputation
Imputed Variable	Effect	Obs Data	1	2	3	4	5
Length3	Intercept	-0.01304	0.004134	-0.011417	-0.034177	-0.010532	0.004685
Length3	Length1	-0.01332	0.025320	-0.037494	0.308765	0.156606	-0.147118
Length3	Length2	0.98918	0.955510	1.025741	0.673374	0.828384	1.146440
Length3	Length1*Length2	-0.02521	-0.034964	-0.022017	-0.017919	-0.029335	-0.034671

After the completion of five imputations by default, the "Variance Information" table in Output 54.3.4 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 54.3.4 Variance Information

Variance Information
Variable	Variance			DF	Relative Increase in Variance	Fraction Missing Information	Relative Efficiency
Variable	Between	Within	Total	DF	Relative Increase in Variance	Fraction Missing Information	Relative Efficiency
Length2	0.000133	0.439512	0.439672	32.15	0.000363	0.000363	0.999927
Length3	0.000386	0.486913	0.487376	32.131	0.000952	0.000951	0.999810

The "Parameter Estimates" table in Output 54.3.5 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 54.3.5 Parameter Estimates

Parameter Estimates
Variable	Mean	Std Error	95% Confidence Limits		DF	Minimum	Maximum	Mu0	t for H0: Mean=Mu0	Pr > \|t\|
Length2	33.104571	0.663078	31.75417	34.45497	32.15	33.088571	33.117143	35.000000	-2.86	0.0074
Length3	38.424571	0.698123	37.00277	39.84637	32.131	38.397143	38.445714	45.000000	-9.42	<.0001

The following statements list the first 10 observations of the data set outex3 in Output 54.3.6. 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 54.3.6 Imputed Data Set

First 10 Observations of the Imputed Data Set

Obs	_Imputation_	Length1	Length2	Length3
1	1	23.2	25.4	30.0
2	1	24.0	26.3	31.2
3	1	23.9	26.5	31.1
4	1	26.3	29.0	33.5
5	1	26.5	29.0	34.7
6	1	26.8	29.7	34.7
7	1	26.8	28.8	34.7
8	1	27.6	30.0	35.0
9	1	27.6	30.0	35.1
10	1	28.5	30.7	36.2

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