Nonlinear term with unknown in R

Question

I have a logistic regression using glm and I would like to add a term of the form

c₁(k+ac₂)/(t+c₂)

where k and t are columns in a data frame, a is a constant. I would like R to find best-fit values for c₁ and c₂. Is this possible?

If I only wanted a fixed value, say c₂ = 2,

c₁(k+2a)/(t+2)

I could just write

glm( model$y ~ I((model$k + 2*a)/(model$t + 2)) + model$otherterms,
  family = binomial(logit) )

which is similar to what I am doing now. But I don't think that 2 is optimal and iterating 'manually' is very time-consuming.

@mnel: How can I tell it that two of the parameters are equal? — Charles, Dec 22 '12 at 21:23

Wojciech Sobala · Accepted Answer · 2013-01-06T20:51:40.053

4

You can use function gnm from package gnm.

gnm(y~Mult(1, # c1
           offset(k)+1,# c3=a*c2 
           Inv(offset(t)+1)) # c2
           +other terms, 
    family=binomial, 
    data=models)

EDIT (solution for constrained coefficients)

term_fun <- function(predLabels, varLabels){
                     paste0(predLabels[1],"*(",varLabels[1],
                            "+",predLabels[2],"*3)/(", # a=3 for example
                            varLabels[2],"+", predLabels[3],")")}

  Ratio <- function(t,x){
   list(predictors = list(C1 = 1, C2 = 1),
        variables = list(substitute(t), substitute(x)),
        term = term_fun)
  }
  class(Ratio) <- "nonlin"

  fit <- gnm(Y~Ratio(k,t), data=models, family=binomial)

edited Jan 06 '13 at 20:51

answered Dec 19 '12 at 07:38

Wojciech Sobala

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How can I constrain c3 = a*c2 for a given value of a? For example, suppose a = 0.4. – Charles Dec 21 '12 at 23:39
In other words, the second and third constants aren't independent and need to be fixed multiples of each other; how can I achieve this? – Charles Dec 21 '12 at 23:41
I have added solution for constrained c3=a*c2. – Wojciech Sobala Jan 06 '13 at 20:54
That is awesome and complicated. Thank you, I don't think I ever would have come up with that. – Charles Jan 06 '13 at 21:14

Nonlinear term with unknown in R

1 Answers1