Aspect as a Covariate

[TGrant]

How have people dealt with this? It involves circular stats that most people aren't super familiar with.

Simply plugging the degrees aspect in as a covariate isn't quite correct. It doesn't account for the fact that psi should return to same point at 0 and 360.

One way is to transform the data as described by Beers et al. 1966. This transforms the data into a sine wave that ranges from 0 to 2. This may be fine, but I'm not entirely comfortable with it. It requires choice of an axis for the sine wave to be mirror image on. An aspect must be chosen that is thought to be the most important. This aspect goes into the transformation and is where the sine wave = 2. Consequently, covariate values are a identical on both sides of the circle around the axis chosen (say 45deg and 225 deg). So the covariate value becomes the same for 15 deg off 45 deg - at 30 and 60 deg. It seems to me this is imposing some trend or structure on the data.

In a book on a circular stats (Fisher 1993), regression using a circular predictor variable is discussed. I wondered if the same principles might apply to using aspect as a covariate in MARK, since the formula structure is similar. If X is the predicted variable, theta is the angle, and B0, B1, and B2 are betas, then the regression model is X = B0+B1cos(theta)+B2sin(theta). It seems to me it would be the same to use the same structure for psi, i.e. logit(psi) = B0+B1cos(theta)+B2sin(theta). I tried this in MARK, but psi doesn't return to the same point at 360deg.

Tyler

[murray.efford]

Tyler
Why do you think aspect might be important? I would be tempted to transform it to 'expected solar radiation' that has a clear biological meaning.
Murray

[TGrant]

That's an interesting idea, because then it wouldn't be circular. Thanks. Not sure how I would do that though. Have you done something like that?

You would lose a little information. For example, if morning sun is important, expected solar radiation doesn't necessarily reflect when the solar radiation occurs. Early morning sun lets a mountain butterfly warm up quicker.

[darryl]

Another option would be to just discretise it, eg four factor levels, one for each main compass direction.