Im working with a negative binomial regression where the dependent variable is number of trips by any given mode (i.e. car trips, train trips etc).
I would like to create a variable to segment the data based on theoretical grounds. The variables that I would like to transform to do so are a set of six questions regarding individual preference and measured on a five point likert scale. I would like to segment the data into two mutually exclusive groups according to two different types of residential preference (lets say Group A and Group B). In this case, and again, based on the fields literature, three of the questions relate to Preference A and three questions relate to Preference B.
Now, since I do not have enough factors to conduct factor analysis, I was thinking of coming up with a rule to decide whether an individual fits in one of the two classes. My thinking is as follows:
1.Take the median of the first group of three questions (related to Preference A) for the ith individual.
2.Take the median of the second group of three questions (related to Preference B) for the ith individual.
*Since the mean cannot be used as a centrality measure for ordinal data because of the unknown distance between each point, im assuming that even if the distances might be different for two different individuals, for any given individual i the distance from 1 to 2 and from 3 to 4 are the same for ALL six questions.
3.In that sense, if the median of the Preference A questions is higher than the median for the Preference B questions, I am assigning that indiviudal to preference group A and viceversa. In the case the median is the same for both sides I am assuming that the individual has no particular preference for either group.
Of course I undesrtand it is a very strong assumption given the we do not know the distance between each point but given the constraints of a secondary dataset, I am wondering to what extent this reasoning is adequate to address the problem.
Thanks in advance.
