Multiple Responses/Dichotomies - Paired Crosstabulation of Multiple Response Variables

A unique option for tabulating multiple response variables is to treat the variables in two or more multiple response variables as matched pairs. Again, this method is best illustrated with a simple example. Suppose we conducted a survey of past and present home ownership. We asked the respondents to describe their last three (including the present) homes that they purchased. Naturally, for some respondents the present home is the first and only home; others have owned more than one home in the past. For each home we asked our respondents to write down the number of rooms in the respective house, and the number of occupants. Here is how the data for one respondent (say case number 112) may be entered into a data file:

Case no.

Rooms

 1 

 2 

 3 

No. Occ.

 1 

 2 

 3 

 112

 

 3 

 3 

 4 

 

 2 

 3 

 5 

This respondent owned three homes; the first had 3 rooms, the second also had 3 rooms, and the third had 4 rooms. The family apparently also grew; there were 2 occupants in the first home, 3 in the second, and 5 in the third.

Now suppose we wanted to crosstabulate the number of rooms by the number of occupants for all respondents. One way to do so is to prepare three different two-way tables; one for each home. We can also treat the two factors in this study (Rooms, No. Occ.) as multiple response variables. However, it would obviously not make any sense to count the example respondent 112 shown above in cell 3 Rooms - 5 Occupants of the crosstabulation table (which we would, if we simply treated the two factors as ordinary multiple response variables). In other words, we want to ignore the combination of occupants in the third home with the number of rooms in the first home. Rather, we would like to count these variables in pairs; we would like to consider the number of rooms in the first home together with the number of occupants in the first home, the number of rooms in the second home with the number of occupants in the second home, and so on. This is exactly what will be accomplished if we asked for a paired crosstabulation of these multiple response variables.