Correlation between non-independent variables

#1
Hi,

I want to conduct correlation between two variables, that have common term (difference scores).

Originally there are three variables X, Y, Z. I want to conduct correlation between two variables that are computed as:

First variable: X - Y
Second variable: Y - Z

I know, that the correlation will be spurious and I wonder whether it is possible to correct it in some way. From theoretical reasons, I need correlation (or some other measure of relation) between variables that have this common term.

I will add also, that what I am interested is not the value of correlation coefficient, but I want to compare relative strength of correlation between these variables in different conditions. That is why I thought that maybe I can transform r values to Z values using Fisher's transformation, because I assumed that even if values of correlation coefficents will be inflated, it still would be possible to compare they relative strength.

I will be greatefull for help.
 

spunky

Smelly poop man with doo doo pants.
#4
From theoretical reasons, I need correlation (or some other measure of relation) between variables that have this common term.
would you mind expanding on these "theoretical reasons"? at first i thought something like partial correlations could be useful, but we'd really need to know what X, Y and Z are and what you're trying to do.

as it stands, my hunch would be there isn't much you can do about it. your X-Y and Y-Z variables are linear combinations of their respective components and, as such, they will be highly correlated with the variables that make them up.
 
#5
It is a research in psychology.

X is an index (averaged from few items) of how participants evaluate themselves, Y - how they evaluate their ingroup (e.g. other people from their country), Z - is the evaluation of outgroup (e.g. people from other country).

I am interested in relation between so called self-enhancement and ingroup bias. Self-enhancement is defined as the extent to which someone evaluate her/himself as superior to other members of the ingroup, and is calculated as difference between X and Y. Ingroup bias is defined as the extent to which someone evaluate the ingroup as superior to outgroup, and is calculated as difference between Y and Z.

In one paper in exact same scenario as mine, there was used a correction described in this paper (http://onlinelibrary.wiley.com/doi/10.1002/j.2333-8504.1965.tb00900.x/abstract), but in my opinion it does not solve the problem.
 

spunky

Smelly poop man with doo doo pants.
#6
but in my opinion it does not solve the problem.
why would you say it doesn't solve it? i haven't had a look a the paper (i'm on my cellphone) but it just by skimming through it, it seems like its some variant of residualized difference scores which are a common (and statistically correct) approach to modeling change-scores.

now that you've clarified that these are difference/change scores (which is how these models are usually known in psychometrics) perhaps you could use a much more appropriate technique like latent change scores, instead of using a composite score for X? difference scores tend to have issues with their reliability (i.e. it tends to be lower) unless certain conditions are met.
 
#7
Thank you for your response. I am not sure, if formulas described in this paper solve the problem, because as far as I understand them, they purpose is to compute true difference score between administration of one test in two time points. And I think the source of my problem is that two variables have common term. I did not find in this and any other paper aby formula, that refers to such problem.