The MI Procedure

Missing Data Patterns

The MI procedure sorts the data into groups based on whether the analysis variables are observed or missing. Note that the input data set does not need to be sorted in any order.

For example, with variables $Y_{1}$, $Y_{2}$, and $Y_{3}$ (in that order) in a data set, up to eight groups of observations can be formed from the data set. Figure 63.6 displays the eight groups of observations and an unique missing pattern for each group.

Figure 63.6: Missing Data Patterns

Missing Data Patterns

Group Y1 Y2 Y3
1 X X X
2 X X .
3 X . X
4 X . .
5 . X X
6 . X .
7 . . X
8 . . . 




            

            


            
An "X" in Figure 63.6 means that the variable is observed in the corresponding group and a "." means that the variable is missing. The MI procedure
               denotes variables that have missing values by "." or "O". The value "." means that the variable is missing and will be imputed,
               and the value "O" means that the variable is missing and will not be imputed. 
            

            
The variable order is used to derive the order of the groups from the data set, and thus determines the order of missing values
               in the data to be imputed. If you specify a different order of variables in the VAR statement, then the results are different
               even if the other specifications remain the same. 
            

            
A data set with variables $Y_{1}$, $Y_{2}$, …, $Y_{p}$ (in that order) is said to have a monotone missing pattern when the event that a variable $Y_{j}$ is missing for a particular individual implies that all subsequent variables $Y_{k}$, $k > j$, are missing for that individual. Alternatively, when a variable $Y_{j}$ is observed for a particular individual, it is assumed that all previous variables $Y_{k}$, $k < j$, are also observed for that individual. 
            

            
For example, Figure 63.7 displays a data set of three variables with a monotone missing pattern. 
            

            
  

            


Figure 63.7: Monotone Missing Patterns

               

                  

                     
                     

                        
                        
                        

Monotone Missing Data Patterns
                              
                           



                           
                           

                              
                              









Group
                                       
                                       Y1
                                       
                                       Y2
                                       
                                       Y3
                                       
                                    




1
                                       
                                       X
                                       
                                       X
                                       
                                       X
                                       
                                    



2
                                       
                                       X
                                       
                                       X
                                       
                                       .
                                       
                                    



3
                                       
                                       X
                                       
                                       .
                                       
                                       .
                                       
                                    






                           
                        

                        



                     
                     
                  





            

            


            
Figure 63.8 displays a data set of three variables with a non-monotone missing pattern. 
            

            
  

            


Figure 63.8: Non-monotone Missing Patterns

               

                  

                     
                     

                        
                        
                        

Non-monotone Missing Data Patterns
                              
                           



                           
                           

                              
                              









Group
                                       
                                       Y1
                                       
                                       Y2
                                       
                                       Y3
                                       
                                    




1
                                       
                                       X
                                       
                                       X
                                       
                                       X
                                       
                                    



2
                                       
                                       X
                                       
                                       .
                                       
                                       X
                                       
                                    



3
                                       
                                       .
                                       
                                       X
                                       
                                       .
                                       
                                    



4
                                       
                                       .
                                       
                                       .
                                       
                                       X
                                       
                                    






                           
                        

                        



                     
                     
                  





            

            


            
A data set with an arbitrary missing pattern is a data set with either a monotone missing pattern or a non-monotone missing pattern.