I would like to explore the extent to which the intercorrelations between scores on a battery of cognitive tests is influenced by IQ. While I understand this can be explored at a group level using partial correlations, I would like to adjust intercorrelations between tests according to a specific IQ (e.g. 80 vs. 110). Is there a way of adjusting intercorrelations at an individual level?
Hello Andrew,
Assuming a sufficiently large sample from which to work, there's no reason you couldn't subdivide that sample on the basis of some control/extraneous/nuisance variable and evaluate the observed relationships among the variables of interest (with the selected cases having control variable score held at some specific value or falling within some target range of values).
In effect, that's what partial correlation is intended to offer, albeit over the full range of observed scores. Its utility (and interpretability) presumes linear relationships, of course.
Good luck with your work.
I am not sure that I understand. A correlation for an individual, say between their x and y scores w, would suggests that person has multiple x and multiple y scores. Is this what what you have?
If you just mean can you take a subsample and do a correlation then yea, but if the subsample is based on x or y (or related to those) there are some issues.
Can you clarify what you mean?
If you follow @David Morse's pragmatic solution you would need to put credible intervals around the estimated correlation to acknowledge sample uncertainty in each 'segment' of the IQ variable .
Daniel Wright I should probably provide some context for this question- a correlation matrix can be used to calculate the expected number of abnormally low scores on a battery of cognitive tests, however empirical studies have shown IQ influences the expected number of low scores (lower IQ --> more expected low scores).
I'm interested in whether there is a way to adjust test inter-correlations which have derived from the total sample (e.g. between letter and category fluency) according to a specified IQ score. Although subdividing the sample would be helpful, the angle I would like to explore focusses on using a specific value of a covariate (I appreciate this is probably a poor comparison but in a similar manner to a regression equation). I hope that clarifies things.
So you want to estimate the correlation matrix for a specified value of a related variable? But your original question talks about doing this for an individual from the sample. I am still confused, but since other commentators seem to get what you want, I assume it is me and I will leave this to them!
Daniel Wright I think my original question could have been clearer! thank you for your response
David Morse Thank you for your response- are you aware of any ways of achieving this without subdividing the sample e g using a specific value?
Daniel Wright is not the only one who is struggling to understand what is being asked for here. To simplify things, suppose X and Y are the variables of primary interest, and you want to compute r(X,Y) at several values of Z, a third variable. If Z is correlated with X, you'll restrict the range of X quite severely when you filter on a particular value of Z, will you not? What's the bigger picture? What are you trying to do that cannot be achieved by looking at a regression model with both X and Z as predictors of Y? Apologies if it is completely obvious to everyone else (apart from Daniel & me). ;-)
Hello again Andrew.
To your follow-up question: No.
If you want to know how scores on variables relate among a restricted sample (based on some other attribute), you'll need to look at that restricted sample, especially if you already have evidence that relationships are inconsistent across levels of some other attribute.
Good luck with your work.
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