[R] Effect of each term in the accuracy of Nonlinear multivariate regression fitting equation

[David Winsemius]

On Nov 27, 2012, at 7:44 AM, Keith Jewell wrote:

> In this context, "linear model" means linear in the _coefficients_  
> not (necessarily) linear in the predictors, so your model:
>   JIM ~ z1*A + z2*B + z3*A*B^2 + z4*C*D^3 + z5*A^2*B^2 ...
> is a linear model (in z1, z2, ...).
>
> So you don't need to use nls, lm is probably favourite. You can use  
> all the techniques around for evaluating linear models; anova.lm  
> might give you a start.

The additional R coding tip would be the I() function,

lm(JIM ~  B + A*I(B^2) + I(C*D^3) + I(A^2*B^2) + ...

Note that A and I(B^2) would also get estimates because of the way "*"  
is interpreted in formulas. If the "*" is inside the I() function that  
interpretation is not expanded.

In the linear models context it might be wiser to forego this approach  
and instead use regression splines.

-- 
David.


>
> KJ
>
> On 27/11/2012 11:40, dsfakianakis wrote:
>> Dear all,
>>
>> I have a set of data with 4 inputs (independent variables) and one  
>> output
>> (dependent variable). I want to perform a regression analysis in  
>> order to
>> fit these data to a regression model, however due to the non- 
>> linearity of
>> the model I do not have a clue which equation to use. I am thinking  
>> of
>> starting with a very general equation including ^3 terms and  
>> interactions
>> between the variables however this will lead to a very long  
>> equation. Is
>> there a way to assess the effect of each term to the accuracy of the
>> regression model in order to discard the terms with the least  
>> importance?
>> Something like a sensitivity analysis of the effect of each term to  
>> the
>> accuracy regression model. I know one possible solution to my  
>> problem is
>> simply 'trial and error' however before going down that road I want  
>> to check
>> if there is an easier way.
>>
>> e.g. Let's say I have four input variables A B C and D, one output  
>> 'JIM' and
>> let z1, z2, ...  be the coefficients of the terms of the equation.   
>> The
>> regression will be something like that:
>>
>> Result = nls(JIM ~ z1*A + z2*B + z3*A*B^2 + z4*C*D^3 +  
>> z5*A^2*B^2 ... )
>>
>> Is there a way to assess the contribution of each term (z1*A,  
>> z3*A*B^3 etc)
>> to the accuracy of the regression model?
>>
>> Thanks a lot
>>
>>
>>
>> --
>> View this message in context: http://r.789695.n4.nabble.com/Effect-of-each-term-in-the-accuracy-of-Nonlinear-multivariate-regression-fitting-equation-tp4650949.html
>> Sent from the R help mailing list archive at Nabble.com.
>>
>
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David Winsemius, MD
Alameda, CA, USA