[R] Non-Linear Regression on a Matrix

[Douglas Bates]

apjaworski at mmm.com wrote:
> 
> 
> 
> 
> If your "non-linear function (A, B)" is parametric nls should do it for
> you.  If you have R version 2 (perhaps even 1.9) do ?nls to see the help
> page.  Older versions of R require library(nls) first.
> 
> Hope this helps,
> 
> Andy
> 
> __________________________________
> Andy Jaworski
> 518-1-01
> Process Laboratory
> 3M Corporate Research Laboratory
> -----
> E-mail: apjaworski at mmm.com
> Tel:  (651) 733-6092
> Fax:  (651) 736-3122
> 
> 
>                                                                            
>              Diana Abdueva                                                 
>              <diana.abdueva at gm                                             
>              ail.com>                                                   To 
>              Sent by:                  r-help at stat.math.ethz.ch            
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>              at.math.ethz.ch                                               
>                                                                    Subject 
>                                        [R] Non-Linear Regression on a      
>              11/16/2004 08:33          Matrix                              
>              PM                                                            
>                                                                            
>                                                                            
>              Please respond to                                             
>                Diana Abdueva                                               
>              <diana.abdueva at gm                                             
>                  ail.com>                                                  
>                                                                            
>                                                                            
> 
> 
> 
> 
> Hi, I'm terribly sorry for submitting my primitive question, I'm a
> beginner in R and was hoping to get some help re: non-linear fit.
> 
> I have a 2D data with the following structure:
> 
> A     B        C
> 1      1      111
> 1      2      121
> 1      3      131
> 2      1      141
> 2      2      151
> 2      3      161
> 3      1      171
> 3      2      181
> 3      3      191
> 
> I'm trying to fit C = non-linear function (A,B). I was wondering if
> there's a package that would save my time of doing direct least square
> estimation.
> 
> Thank you,
> Diana

By "non-linear" do you mean something like a response surface model that 
has quadratic terms in A and B and an interaction term?

If so, you can fit the model using the lm function, as in

 > rs <- read.table("/tmp/rs.dat", header = TRUE)
 > rs
   A B   C
1 1 1 111
2 1 2 121
3 1 3 131
4 2 1 141
5 2 2 151
6 2 3 161
7 3 1 171
8 3 2 181
9 3 3 191
 > fm <- lm(C ~ A * B + I(A^2) + I(B^2), rs)
 > fm

Call:
lm(formula = C ~ A * B + I(A^2) + I(B^2), data = rs)

Coefficients:
(Intercept)            A            B       I(A^2)       I(B^2) 
  A:B
   7.100e+01    3.000e+01    1.000e+01   -1.174e-15    7.217e-16 
-4.008e-15