Creating groups using two continuous variables without using median-splitting? I have two continuous variables, one of individuals' retrospective childhood anxiety and another regarding their current level of anxiety. Research has demonstrated that during a snapshot of development individuals' trajectory of anxious emotion fall into four groups: increasers (e.g., becomers), decreasers (e.g., escapers), stable-high, and stable-low.
I have a small sample (n = 123) of sub clinical undergraduates, and would like to split them into these groups, but have been warned about using a median split (see: On the practice of dichotomization of quantitative variables, pdf). My questions are: 


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*Since my groups are based on previous research can I use a median-split?

*If not, what are my alternatives?


EDIT: The study plans to use a multinomial logistic regression to predict group membership into these groups based on 4 other continuous variables (e.g., measures of behavior, cognitive, and social constructs)
 A: It seems to me there are several questions lying in the background here.  First, there is the question of whether there really are four distinct, latent groups.  The fact that someone took two continuous variables, dichotomized both of them, and came up with four categorizations proves nothing.  You may want to investigate the possibility of these groups actually existing by using cluster analyses.  In particular, you may want to explore Gaussian mixture models.  If you are unfamiliar with these, I have demonstrated them in a couple of answers:  


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*Mclust function of mclust package overfitting Gaussians

*What is the relationship between Y and X in this plot?

*Test for bimodal distribution
Second, while there is undoubted theoretical interest in whether these groups actually exist, often part of the interest is driven by the belief that the groups are causally related to, or predictive of, something else downstream.  Note that, even if the groups exist, this does not necessarily follow.  It may well be that a person's actual position on the continuous variables is what is important, and the latent grouping is extraneous.  You could investigate this by using both the grouping indicator and the continuous variable values in a multiple regression model predicting the downstream effects.  Does the grouping add anything, or is the model equally predictive without it?  
Regarding your explicit questions, I would not use median splits.  If there did seem to be meaningful latent groupings, I would use the grouping indicators that came from the mixture model as your response.  If there did not seem to be meaningful groupings, you could fit separate multiple regression models for both variables, or for the principle components instead.  
For what it's worth, your variables sound to me (i.e., someone who knows nothing about this) as though they would be highly correlated.  In fact, there may only really be one dimension of information there, plus some measurement error.  You may want to do a factor analysis to assess if there are two dimensions of information, or if only one latent factor can be supported by the data.  
Edit: As two (or more) variables become increasingly correlated, they become increasingly interchangeable.  (Actually, this isn't necessarily quite true, but is probably good enough for now.)  That is, they contain similar information, so you could use either.  The question is, do the two variables contain the same information or two highly related, but different, pieces of information?  The factor analysis will answer that question.  
A: Any creation of "groups" will be ill-advised.  This will be arbitrary and highly information-losing.  Consider principal components analyses and other continuous variable approaches.  Research that claims to show that groups exist is undoubtedly flawed.
