Modeling polar coordinates
On Tue, 24 Aug 2010, Titus von der Malsburg wrote:
Your [Luca's] suggestion about using sin and cos combinations sounds interesting, but your description is a bit too terse for me. mer.cos <- lmer(cos(x) ~ 1 + factor + (1|subject), my.data.frame) mer.sin <- lmer(sin(x) ~ 1 + factor + (1|subject), my.data.frame) This is of course modulo some transformation that makes the residuals being normally distributed. (Which would that be?)
I can't see it being that simple. AFAICT (Song, Correlated Data Analysis), the Fisher and Lee model uses a tan(z/2) link function for the mean, *and* 1/2 sec^2(z/2) for the dispersion. You might be able to directly maximize the wrapped normal likelihood (from the circular package) for your model. Just 2c, David Duffy.
| David Duffy (MBBS PhD) ,-_|\ | email: davidD at qimr.edu.au ph: INT+61+7+3362-0217 fax: -0101 / * | Epidemiology Unit, Queensland Institute of Medical Research \_,-._/ | 300 Herston Rd, Brisbane, Queensland 4029, Australia GPG 4D0B994A v