[R-sig-ME] Modeling polar coordinates

[Luca Borger]

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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