Converting a circular outcome variable to a linear one I have a problem where I want to measure deviations from zero degrees. This outcome variable is a circular measure, since a deviation of -180 degrees is equivalent to 180 degrees.
However, I don't want to complicate my model (using a linear mixed effects model) by using circular statistics, so I was wondering if I can use the absolute deviation expressed as a percentage of 180?
So for instance, -180 and 180 degrees would both give 100% deviation, while 90 and -90 would both give 50% deviation. Is this a legitimate fix? Namely, would their be any caveats I need to be aware of by 'linear-izing' my circular outcome measure?
**Edit: To give more context into my problem. I am looking to predict peaks in a real-time signal. I make a prediction and see how far off I was to the closest peak (0 degrees corresponds to peaks, while 180 degrees corresponds to antipeaks). I'm interested in computing how 'accurate' my different prediction strategies are, so I was considering just looking at deviations from zero degrees. I'm not sure whether this is a completely circular problem in the first place, since an outcome measure of is bounded between 180 and -180 degrees.

Since you are interested in deviation from 0 (and not the direction), it would be appropriate to use $|\theta|$ as your variable.
You've defined the problem in a way such that $-90$ and $+90$ (and similarly, $-2$ and $+2$) are the same outcome so one can take the absolute value and replace the circular problem with a linear scale going from $0$ to $180$.
Your solution is equivalent to what I describe but rescaling (dividing by $1.8$) to go from $0$ to $100$ instead.
Circular statistics are vital when we care about position on a circle and need to account for the ends of the line wrapping around. In your problem instead of connecting the ends of the line together we are folding the line in half (not just matching $-180$ to $180$, but matching every $-\theta$ to $\theta$).
