Link Function for Linear-Circular Regression?

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Koen Van de Moortel

It seems like you should just use a periodical function as a model for your data. You can find examples with this software:

www.lerenisplezant.be/fitting.htm

Yasser Al Zaim

Hi,

Almost all the stated three questions have sufficient answers in Downs and Mardia's article "Circular regression".

For example, as I quote from there's, "Rivest’s link function is only one-to-one and onto..."

Now, concerning your findings, I don't know if you've used the 'circular' package in R language. In R language, to fit a regression model for a circular dependent and linear independent variable (s), you can use 'lm.circular.cl ' function.

Regards.

Ahmad Al Khraisat

Advantages and disadvantages of the half-tan link function: The half-tan link function is a popular choice for circular regression models because it has several advantages. One of the main advantages is that it maps a line onto a circle, which is a desirable feature for modeling circular data. It is also easy to implement and has been shown to perform well in simulation studies.

However, the half-tan link function is not without its limitations. One potential disadvantage is that it can only be used for data in the range (0,2pi), which may not be appropriate for all circular data. Additionally, it may not work well if the circular data has a heavy-tailed distribution, in which case other link functions may be more appropriate.

Other link functions for circular regression: There are other link functions that can be used for circular regression, such as the sine-cosine link function, the arctan link function, and the wrapped normal link function. Each of these link functions has its own advantages and disadvantages, and the choice of link function will depend on the specific characteristics of the data being modeled.

When to use them: The choice of link function will depend on the specific characteristics of the circular data being modeled. The half-tan link function is a good choice for circular data in the range (0,2pi) and is easy to implement. Other link functions may be more appropriate for different types of circular data, such as the sine-cosine link function for bimodal data, or the wrapped normal link function for heavy-tailed data. It is important to consider the underlying distribution of the circular data and choose the appropriate link function based on the characteristics of the data.

Norah Almasoud

Thank you very much for your answer. However, I have few concerns.

In you mentioned that one of the disadvantages is that it is good choice for circular data in the range (0,2pi), is not that all circular data have such range (0,2pi)? I am confused here.

Also, regards the characteristics of the data, can you elaborate more.

Thanks in advance!

Yasser Al Zaim, Koen Van de Moortel Thanks for your replies.