How to correlate count variables that are nested / non-independent?

Above is a snapshot of a subset of a larger dataset, N=61.

• Group is the group number,
• Iterations is indicating the iteration number for every group,
• TradeoffTalk is the frequency count of a certain 'level of discussion' by the group for every iteration ('level of discussion' is an ordinal variable but not used directly here),
• IDRef is the frequency count of a certain 'action' by the group for every iteration ('action' is a nominal variable but not used directly here),
• ProcPrompt is the frequency count of certain 'instruction' ('instruction' is a nominal variable but not used directly here) given to the group during the iteration

Can I treat TradeoffTalk, IDRef and ProcPrompt as continuous variables and run Pearson's correlation and partial correlation between them? I am trying to find if these are related and describe the relationship (positive / negative) between them. For example, one claim I'd like to make is, there is a strong positive relationship between TradeoffTalk and IDRef (enough to indicate significant relationship, causal claim is not needed).

• You have many rows with the same Group ID; are the rows independent? – gung - Reinstate Monica Feb 15 '15 at 2:39
• @gung- Every iteration is unique even if it belongs to the same group. (sorry, I'm fairly new to stats so let me know if this doesn't answer your question) – CDG Feb 15 '15 at 3:40
• The iterations may be unique, but you have multiple observations from the each group w/ many different groups, right? That would make the observation non-independent. – gung - Reinstate Monica Feb 15 '15 at 3:45
• yes, I do have multiple observations from each group with many different groups. What would be the right way to analyze this then? – CDG Feb 15 '15 at 3:52

I don't have a problem with your correlating count variables. (Whether this will adequately correspond to your substantive question is another matter, and one that I cannot evaluate.) The test of your correlation can be invalidated if you mostly have $0$ counts and a few high values, so you should bear that in mind. The issue with the nesting is that correlating two variables while ignoring the groups will conflate two different aspects of the data: how variable x is associated with y within groups, and the variations between groups. This is almost certainly not what you want. I strongly suspect your question has to do with how x is related to y within groups. A quick and dirty way to deal with this might be to mean center each variable within each group, then you could get a correlation.