Hi all,
I am interested in whether the strength of correlation estimates between personality & depression scores is equally strong on two measurement occasions - when adolescents are 13yrs old vs. 15yrs old. This means I am comparing the coefficients in the same sample and the same set of variables, just measured at a different time point.
So far I was only able to figure out how to compare coefficients with independent observations (e.g. using Fisher’s r to z transformation).
Can I simply perform regression analysis and use "time" (categorical) as a moderator or this is only ok with independent observations?
Thanks a lot for your help!
Kind regards
Michaela
Hi. I believe I would try to model this as an ANCOVA in regression form with the 15 yo score as the Dependent variable and the 13 yo score as a covariate. This allows you to study other possible predictors much more easily. You can Google examples easily.including how to do this in your fav stat package. Best wishes David Booth
In case you are familiar with programs for structural equation modeling (SEM) such as Mplus, a convenient way to approach this problem is by setting up a simple correlation "model" with equality constraints on the correlations in question. A model test statistic (chi-square) then allows you to test whether the null hypothesis of equal correlations can be rejected at the chosen level of alpha. In Mplus, this can very easily be done with the MODEL CONSTRAINT option. For 6 or fewer variables, you can use the free demo version of the program. Other SEM programs such as lavaan (package in the free R software) have similar options for setting up and testing parameter equality constraints.
The following is an excerpt from my 2013 article with Karl Wuensch:
--- start of excerpt ---
Two nonindependent correlations with no variables in common
Pearson and Filon (1898) devised a method for comparing two nonindependent correlations with no variables in common, but a revised version of it by Steiger (1980) yields a “theoretically better test statistic” (Raghunathan et al., 1996, p. 179).
--- end of excerpt ---
SPSS and SAS code for this test can be found in file #7 on the following web pages:
- https://core.ecu.edu/wuenschk/W&W/W&W-SAS.htm
- https://sites.google.com/a/lakeheadu.ca/bweaver/Home/statistics/spss/my-spss-page/weaver_wuensch
And here is an online resource that uses R:
- http://comparingcorrelations.org/
HTH.
Thank you all so much for your recommendations! I will check how I can proceed from here on and keep you posted. Bruce, thanks so much for all the detailed info, but unfortunately my non-independent correlations are with the same set of variables, or do I misunderstand that what you suggest requires a different set of variables?
Hi Michaela Kaneva. You have the same variables, but at two different times. You want to compare r(X13, Y13) to r(X15, Y15). In a wide dataset with one row per person, those are 4 different variables (or 4 different columns). So the method I recommended is appropriate. HTH.
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