I am puzzled with how I should analyze the following data:
The dependent variable is respiratory sinus arrhythmia, a measure of parasympathetic activity (RSA). I have a $5\times5$ full factorial design: There are 5 levels of imposed breathing and 5 different moments in time. There are two groups (males and females) and a sample size of $n=20$. Additionally data from respiratory frequency (Fresp) in all conditions.
Respiratory frequency has a direct effect on RSA, so I want to include this as a covariate. I.e. each data point of RSA contains information on Fresp.
SPSS does not allow that since the covariate is implied to be something that is related to the group differences.
The possible approaches I have considered:
- Standardize the RSA and the Fresp and subtract the standardized score from each other (so that I obtain variability in RSA 'free' of the variability of Fresp) and the perform a mixed anova on these data.
- Perform a regression of Fresp on RSA within each individual and subject the residuals to a mixed anova.
- Perform a multilevel regression with dummy variables and Fresp as independent variable.
Are any of the approaches recommended or is there are different approach that someone would propose?