Modeling polar coordinates

Hello,

unless I'm misunderstanding, isn't this one of those cases were you need to 
use circular regression methods? e.g. for an example:

S. Rao Jammalamadaka and Ulric J. Lund (2006) "The effect of wind direction 
on ozone levels - a case study".
Environmental and Ecological Statistics 13(3): 287-298

so to analyse a variable like day of the year you need to multiply it by 
2*pi/365, then you can model it as a combination of sin and cos terms of the 
circualr variable in mixed effects models (please check the details for the 
polar coordinates - I think you can look up the examples where wind 
direction is modeled?).


HTH


Cheers,

Luca



----- Original Message ----- 
From: "Titus von der Malsburg" <malsburg at gmail.com>
To: "Luciano Selzer" <luciano.selzer at gmail.com>
Cc: <r-sig-mixed-models at r-project.org>
Sent: Wednesday, August 18, 2010 12:00 PM
Subject: Re: [R-sig-ME] Modeling polar coordinates

On Wed, Aug 18, 2010 at 12:37:23PM -0300, Luciano Selzer wrote:

I don't know if there's anything to deal with that builtin in lme4. But
perhaps you could transform your polar coordinates to cartesian
coordinates??

Hi Luciano.  Thanks for the suggestion but using cartesian coordinates
is unfortunately not possible.  I have one map for each experimental
item.  Each subject contributes one point to each map.  The maps where
derived using multi-dimensional scaling (MDS) and the solutions of MDS
are invariant to rotation.  This means that x- and y-axis do not mean
the same on those maps.  One goal of modeling the polar coordinates is
to find out how I have to rotate the maps in order to align them.  The
amount I have to rotate the maps would be given by the random
intercept for items.

 Titus

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