[R-sig-ME] LME and nonlinearity?

[Rob Robinson]

>  3.)        Do I need a non-linear model?
> 

Probably not. As others have pointed out, models need only be linear in
their (transformed) parameters, they can model highly non-linear
relationships. Non-linear models are not linear in their parameters and
cannot be transormed so (the wikipedia page on nonlinear regression might
help in understanding the difference). Before progressing further it sounds
like you need to think carefully about the mechanism behind the relationship
you are trying to model. How is the non-linearity generated? this might help
in thinking the best model to fit. For exploratory purposes gams or splines
might help characterise the pattern (try gamm in mgcv). I'm not sure fitting
higher-order polynomials is really helpful as it's hard to think of what
would generate a quartic, quintic, ... (or even cubic) relationship. If
there's some sort of threshold in the response, then converting to a
factorial variable might help.
Hope that helps
Cheers
rob

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> -----Original Message-----
> From: r-sig-mixed-models-bounces at r-project.org 
> [mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf 
> Of Balázs Lestár
> Sent: 09 April 2009 22:14
> To: r-sig-mixed-models at r-project.org
> Subject: [R-sig-ME] LME and nonlinearity?
> 
> Dear All,
> 
> I have a mixed model (LME), but one of my explanatory 
> variables is not linearly related to the dependent variable.
> 
>  1.)     Somebody told me, to make a 2 or 3 level factor from 
> the continuous variable. (I wouldn't prefer this)
> 
>   2.)     I saw in some statistical books that in these 
> cases, I have to use in the model the quadratic term of the 
> variable. (but the AIC is much greater than with the  
> factorized variable)
> 
> OR
> 
>  Is that possible, to use a poly() function in the lme? (this 
> model seems to be the best, based on AIC).
>  
> 
> I'm a bit confused, 'cause the LME supposes linear relation 
> between variables. Isn't it right?
> 
>  3.)        Do I need a non-linear model?
> 
> Which solution is the best?
> 
> 
> Regards,
> Balazs
> 
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