在指数衰减中设置截距

Question

I am trying to fit my data to an exponential model

y=exp(a-b*x)

The value of y in x=0 must be exactly 13.75, so I want to set the intercept before I fit the data.

a=log(13.75)

I am using the function gnm . I have read that I am supposed to use constrain or constrainTo to set the coefficients; however, I can't understand how to do it.

x=seq(0,3120,120)

y= c(13.75, 13.74, 13.73, 13.71, 13.70, 13.69, 13.68,
     13.66, 13.65,13.64, 13.64, 13.63, 13.63, 13.62,
     13.62, 13.61, 13.61, 13.60,13.60, 13.60, 13.60,
     13.59, 13.59, 13.59, 13.59, 13.59, 13.59)

xl<-gnm(y ~ Exp(1 - x), verbose = FALSE,constrain=????)

#

Hi, everybody. Thank you very much. I've been working following your advice and I finally got a quite good fitting. Now I'll work on the weights to polish it. I did this:

 xl<-gnm(y ~ Exp(1 + x) -1, verbose = FALSE, constrain="Exp(.+x).Intercept",constrainTo=a,start=c(a,-0.05), prior.weights=W,weights=W) 

There was a big problem too. I needed to substract a number from y, in order to place the horizontal asymptote of my data at zero.

Answer 1

Using -1 in the Exp tells the mode not to set an intercept term in the exponential. Try using this model: Exp(1 + x) -1 , to remove the actual y intercept.

To set the intercept in the exponential, you can try:

xl<-gnm(y ~ Exp(1 + x) -1, verbose = FALSE,constrain="Exp(.+x).Intercept",constrainTo=a,start=c(a,-0.05))
xl

Had to input start parameters for the model to be estimated To choose the constrained parameter interactively, you can also do:

xl<-gnm(y ~ Exp(1 + x) -1, verbose = FALSE,constrain="[?]",constrainTo=a,start=c(a,-0.05))