How do I calculate the partial correlation with an intraclass correlation? I tried asking earlier, but provided too much detail because it’s not easy to explain what I mean in a short or simple way. I’ll try to ask again in a more simple way but perhaps in a way that’s more interpretable. I want to know how to find/calculate the partial correlation between 2 groups of people using intraclass correlation. The issue that arises here is the following: if we call the value X group 1 and Y group 2 and Z the value we need to adjust for when trying to find the partial intraclass correlation - and we know the correlation between the values in group 1 and 2 is 0.5, (let’s say group 1 is the bmi values in mothers and group 2 the bmi values in their brothers), how do I find out what the correlation between the bmi values in mothers and their brothers is when adjusting for the third variable (let’s call this third variable soft drink consumption? The mother-her brother correlation in terms of bmi is already 0.5, (xy) and if the correlation between mothers bmi and her soft drink consumption is 0.4 (XZ) and the correlation between mothers brother’s soft drink consumption and bmi is 0.45 (YZ), how do I then find the partial correlation after soft drink consumption has been controlled for, when there isn’t anything provided in the partial correlation coefficient that takes into consideration what the correlation between mothers soft drink comsumtpions and her brothers soft drink consumption is? When referring to the adjusted xy,z correlation, and x is mothers bmi and y is her brothers bmi and z is soft drink comsumption, the only things taken into consideration by the partial correlation coefficient is the xy correlation (which is the correlation between mothers bmi and her brothers bmi, xz (which is mothers bmi and her soft drink comsumption and yz (which is mothers brothers bmi and his soft drink comsumption). I feel like the correlation between mothers soft drink consumption and her brothers soft drink comsumption is missing here in order to find out the partial correlation between mother-her brothers bmi after adjusting for soft drink comsumption.
1 Answer
The intraclass correlation (ICC) is an estimate of how consistent a measurement is when it is taken multiple times (e.g., across time). The example you've provided is not a situation where ICC would be appropriate. It sounds like you may be tripped-up by the fact that you are considering associations between family members (i.e., observations are grouped), which in some contexts should be analyzed with a mixed effect model (which can be used to compute the ICC sometimes). However, in your example, the unit of observation would be the family. It would be appropriate the run the analysis as a simple regression. Alternatively, if you really do want the partial correlation, residualize each person's BMI with respect to their own soft drink consumption (i.e., run BMI ~ SoftDrink, then take the residuals, once for mothers-only, then for brothers-only), and then compute the correlation using the residuals.
