[R-sig-ME] LME and nonlinearity?

[Kevin E. Thorpe]

John Maindonald wrote:
> Additional to the comments below: Think/check also whether 
> transformation of one or more of the variables (log transformation?) 
> makes the relationship more nearly linear.
> 
> On 10/04/2009, at 7:13 AM, Balázs Lestár wrote:
> 
>> 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)
> 
> In general, this makes poor use of the information in the data.  You 
> lose power.
> 
>> 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).
> 
> Yes.

I also used ns from the splines package recently to handle 
non-linearity.  It seemed to work like a charm.

> 
>> I'm a bit confused, 'cause the LME supposes linear relation between 
>> variables. Isn't it right?
> 
> Linear models are linear in the parameters.  They can model highly 
> nonlinear effects.
> 
>> 3.)        Do I need a non-linear model?
> 
> Only if you need a model that is non-linear in the parameters.  Without 
> checking out your data and model, one cannot say.
> 
> 
> 
> 
>> Which solution is the best?
>>
>>
>> Regards,
>> Balazs


-- 
Kevin E. Thorpe
Biostatistician/Trialist, Knowledge Translation Program
Assistant Professor, Dalla Lana School of Public Health
University of Toronto
email: kevin.thorpe at utoronto.ca  Tel: 416.864.5776  Fax: 416.864.6057