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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:

  1. Since my groups are based on previous research can I use a median-split?
  2. 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)

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  • $\begingroup$ Could you please explain the purpose behind this intended splitting? Only then will it be possible to evaluate whether it is appropriate and to contemplate any alternatives. $\endgroup$
    – whuber ♦
    Commented Feb 11, 2015 at 19:13
  • $\begingroup$ Yes, sorry. I am using a multinomial logistical regression to predict group membership into these groups based on 4 continuous variables. $\endgroup$
    – JJJJJJJJJJ
    Commented Feb 11, 2015 at 19:21
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    $\begingroup$ You appear to use "groups" now in two distinct ways: one is the literature definition and another, based on median splitting, would depend on your particular data. If your purpose is to study relationships between other variables and the groups as defined in the literature, then somehow you must appeal to the literature definition to create those groups. I don't see where your proposal to median-split plays a role. $\endgroup$
    – whuber ♦
    Commented Feb 11, 2015 at 19:45
  • $\begingroup$ Past research has used longitudinal data as opposed to retrospective accounts. My study is to see if retrospective accounts are a viable, cheaper option. Thus, I cannot readily use methods they have in the past. $\endgroup$
    – JJJJJJJJJJ
    Commented Feb 11, 2015 at 20:06
  • $\begingroup$ @JJJJJJJJJJ why not? If you're studying the application of an existing method to a new type of data, you should apply the method as established. Otherwise you can't fairly compare the old and new data types. $\endgroup$
    – shadowtalker
    Commented Feb 12, 2015 at 12:13

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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:

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.

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  • $\begingroup$ I cannot begin to thank you enough! This is exactly the explanation I was looking for. I was contemplating whether to use cluster analysis, but have been attempting to teach myself which type to use. As of now, I think two-step would be appropriate but will have to do some more researching. You're right, the two continuous variables (child and current anxiety) are highly correlated (r = .47), but you lost me regarding how this influences their dimensions. Would you mind elaborating on this point? $\endgroup$
    – JJJJJJJJJJ
    Commented Feb 11, 2015 at 22:39
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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.

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  • $\begingroup$ Correct me if I am wrong, but doesn't PCA assume that variables are uncorrelated and linear? In this case, my two continuous variables (child and current level of anxiety) are correlated and nonlinear. I am still learning so please excuse my ignorance. $\endgroup$
    – JJJJJJJJJJ
    Commented Feb 11, 2015 at 19:27
  • $\begingroup$ PCA assumes nothing about the data. In fact, if it had to assume lack of correlation it wouldn't be able to do anything at all! I wonder what you mean by "nonlinear," given that even multinomial logistic regression posits a linear relationship between log odds of the response and the explanatory variables. $\endgroup$
    – whuber ♦
    Commented Feb 11, 2015 at 19:43
  • $\begingroup$ This is very helpful. Sorry for the confusion. What are the main differences of using PCA as opposed to a multinomial logistic regression? $\endgroup$
    – JJJJJJJJJJ
    Commented Feb 11, 2015 at 20:13
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    $\begingroup$ @JJJJJJJJJJ PCA is pure dimension reduction. Regression expresses one variable (in the multinomial logit case, the variable is a class label) as a function of several others. They're solving completely different problems $\endgroup$
    – shadowtalker
    Commented Feb 12, 2015 at 12:09
  • $\begingroup$ I'm not sure what the specific application of PCA would be here. The groups are the response variable in this case. Are you suggesting that PCA be used to generate some kind of continuous response? $\endgroup$
    – shadowtalker
    Commented Feb 12, 2015 at 12:18

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