I am measuring two continuous variables over time in four groups. Firstly, I want to determine if the two variables correlate in each group. I then want to determine if there is significant differences in these correlations between groups.
For context, one variable is weight, and one is a behaviour score. The groups are receiving various treatment and I want to test if weight change influences the behaviour score differently in each group.
I have found the r package rmcorr (Bakdash & Marusich, 2017) to calculate correlation coefficients for each group, but am struggling to determine how to correctly compare correlations between more than two groups. The package diffcorr allows comparing between two groups only.
I came across this article describing a different method in SPSS:
https://www.ibm.com/support/pages/testing-group-difference-correlation-glm-approach
However, I don't have access to SPSS so am wondering if anyone has any suggestions on how to do this analysis in r (or even Graphpad Prism).
Or I could the diffcorr package to calculate differences for each combination of groups, but then would I need to apply a multiple comparison correction?
Alternatively, Mohr & Marcon 2005 describe a different method using spearman correlation that seems like it might be more relevant, however I wonder why their method doesn’t seem to have been used by other researches? It also looks difficult to implement so I’m unsure if it’s the right choice.
Any advice would be much appreciated!
It sounds like you have directional hypotheses about the relationship between weight change (independent variable) and behavior (dependent variable) as well as about the moderating role of treatment (interaction effect). I wonder whether you could use moderated regression analysis and/or path analysis with treatment group as a moderator. This would allow you to examine the strength of the relationship between weight change and behavior in each group as well as testing whether the size of the relationship varies across treatment groups.
You wrote: "For context, one variable is weight, and one is a behaviour score. The groups are receiving various treatment and I want to test if weight change influences the behaviour score differently in each group."
I'm not sure this is best tested with a correlation coefficient. This sounds like an interaction hypothesis (or moderation if you prefer). What you need I think is the interaction of weight change by group. This is usually tested by the regression coefficient for the interaction. You can standardize this to scale it similarly to a correlation coefficient (though that's actually best done outside the model for interactions).
You can compare correlations but that isn't necessarily sensible because you risk confounding the effects of interest with changes in SD of the variables across groups (and there seems no rationale for needing that).
A further complication is including weight change without baseline weight as a covariate might be a poor choice. Even if groups are randomized including baseline weight may increase precision of the estimates of the. other effects.
Hello Jake Harris. Pearson r is a symmetrical measure of association that does not distinguish between explanatory and outcome variables. But as Christian Geiser noted, it sounds like you are thinking of weight--or more precisely, weight change--as the explanatory and (change in) behaviour as the outcome variable. You also mentioned that you are measuring these variables over time. I assume that means repeatedly over time. Putting all of those pieces together, I would be thinking about using a multilevel model for change. One of the classic textbooks for this is Applied Longitudinal Data Analysis by Singer & Willett (2003?). I bet your library has it. Another more recent book is the one by Lesa Hoffman. Here is the website that accompanies her book:
https://www.pilesofvariance.com/
I hope this helps. Good luck with your research.
In addition to the good points raised above, you say "I want to test if weight change influences the behaviour score differently in each group" so your research question is causal. This adds further considerations about the design/analyses compared with if you were just interested in whether the association between weight change and behaviour differed among the three groups. Am I correct in this interpretation of your question?
Thank you all for your helpful comments.
it seems correlation was not the correct analysis, thank you Christian Geiser , Thom Baguley and Bruce Weaver for your alternative suggestions, I've got some reading to do!
Daniel Wright , yes I think you are correct, my question is causal. To clarify, I initially was interested in the causal relationship between treatment and behaviour which is what the experiment was designed for. I anecdotally observed that weight loss appeared to influence behaviour and am trying to see if i can analyse the data to determine if this is a true relationship, and then if the treatment isn't just affecting weight which then results in the behaviour differences.
I jumped the gun and went straight into correlation analysis between weight and score when this may not have been the right method.
I did consider analysing actual weight rather than weight change as Thom suggested, however the baseline weights were taken a while before behaviour scores started being taken, and I was unsure of how to process a timepint that had values for weight and not behaviour.
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