Example 9.5: Producing Monotone Missingness with MCMC

The MI Procedure

Example 9.5: Producing Monotone Missingness with MCMC

This example uses the MCMC method to impute just enough missing values for a data set with an arbitrary missing pattern so that each imputed data set has a monotone missing pattern based on the order of variables in the VAR statement.

The following statements invoke the MI procedure and specify the the IMPUTE=MONOTONE option to create the imputed data set with a monotone missing pattern. You must specify a VAR list to provide the order of variables for the imputed data to achieve a monotone missing pattern.

   proc mi data=FitMiss seed=55417 out=outmono;
      mcmc impute=monotone;   
      var Oxygen RunTime RunPulse; 
   run;

Output 9.5.1: Model Information

The MI Procedure

Model Information
Data Set	WORK.FITMISS
Method	Monotone-data MCMC
Multiple Imputation Chain	Single Chain
Initial Estimates for MCMC	EM Posterior Mode
Start	Starting Value
Prior	Jeffreys
Number of Imputations	5
Number of Burn-in Iterations	200
Number of Iterations	100
Seed for random number generator	55417

The following "Missing Data Patterns" table lists distinct missing data patterns with corresponding statistics. Here, an "X" means that the variable is observed in the corresponding group, a "." means that the variable is missing and will be imputed to achieve the monotone missingness for the imputed data set, and an "O" means that the variable is missing and will not be imputed. The table also displays group-specific variable means.

Output 9.5.2: Missing Data Pattern

The MI Procedure

Missing Data Patterns
Group	Oxygen	RunTime	RunPulse	Freq	Percent	Group Means
Group	Oxygen	RunTime	RunPulse	Freq	Percent	Oxygen	RunTime	RunPulse
1	X	X	X	21	67.74	46.353810	10.809524	171.666667
2	X	X	O	4	12.90	47.109500	10.137500	.
3	X	O	O	3	9.68	52.461667	.	.
4	.	X	X	1	3.23	.	11.950000	176.000000
5	.	X	O	2	6.45	.	9.885000	.

As shown in the table, the MI procedure only needs to impute three missing values from Group 4 and Group 5 to achieve a monotone missing pattern for the imputed data set.

When using the MCMC method to produce an imputed data set with a monotone missing pattern, tables of variance information and parameter estimates are not created.

The following statements are used just to show the monotone missingness of the output data set outmono.

   proc mi data=outmono ( where= (_Imputation_=1) )
      nimpute=0;
      var Oxygen RunTime RunPulse; 
   run;

Output 9.5.3: Monotone Missing Data Pattern

The MI Procedure

Missing Data Patterns
Group	Oxygen	RunTime	RunPulse	Freq	Percent	Group Means
Group	Oxygen	RunTime	RunPulse	Freq	Percent	Oxygen	RunTime	RunPulse
1	X	X	X	22	70.97	46.307744	10.861364	171.863636
2	X	X	.	6	19.35	46.372151	10.053333	.
3	X	.	.	3	9.68	52.461667	.	.

The following statements impute one value for each missing value in the monotone missingness data set outmono. The variable _Imputation_ is renamed to Impute so that it will not be overwritten by the the new variable _Imputation_ being created in the MI procedure.

   proc mi data=outmono( rename=(_Imputation_=Impute))
           nimpute=1 seed=43672
           out=outds( rename=(Impute=_Imputation_) drop=_Imputation_);
      monotone method=reg;   
      var Oxygen RunTime RunPulse; 
      by Impute;
   run;

The variable Impute is renamed to _Imputation_ in the output data outds. This makes the output data set have the same structure as output data sets generated from other imputation methods. You can then analyze these data sets by using other SAS procedures and combine these results by using the procedure MIANALYZE. Note that the VAR statement is required with a MONOTONE statement to provide the variable order for the monotone missing pattern.

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