Regression with circular data as dependent variable

[Lisa Pfeiffer]

I have found and read all of Nick's circular statistics write-ups (Analysing circular data in Stata, Circular statistics in Stata revisited, and To the vector belong the spoils [including the presentation and accompanying Stata example folder), looked at the help file for circstat and circular, and even checked out Fisher's "Statistical analysis of circular data". However, they all seem to end at discussions of circular data as a dependent variable in a regression (often referred to as circular-linear regression), without actually telling me how to do it.

I'd like to regress time of day that z happened (as a circular variable) on independent variable such as wind speed, precipitation, and individual fixed effects.

I fully admit I may be missing something, but, am I missing something? Is this easy? Or, is this hard and that's why it hasn't been extensively discussed?

I'd love any help, example code, or additional explanation. Thank you.

[Nick Cox]

I think this is discussed in Fisher's book. You're right if you gather that it's never been a scientific problem for me and so isn't represented in my programs by any modelling command. In what I do, direction is a response I want to describe or a predictor but not a response I want to predict.

Is for you an outcome at any time of day or night possible in principle?

[Lisa Pfeiffer]

Yes, an outcome at any time of the day or night is possible. I've seen some examples including time of hospital admissions (Fisher's book), time of birth, and time of criminal activity, but only displayed as summary statistics or the difference between several comparison groups, not in a regression framework where marginal effects and predictions are desired.

[Nick Cox]

I don't have access to Fisher's book right now to check what he did. A wild guess is trying a multivariate regression with sine and cosine of time of day as responses.