Question

Is there any package that automatically fits a curve using many simple models?
By simple models I mean:

• ax+b
• ax^2+bx+c
• a*log(x) + b
• a*x^n+b
• ax/(1+bx)
• ax^n/(1+bx^n)
• …

The best would be to have a function that takes two vector parameters X and Y and returns a list of fitted simple models with their SSE.

Answer 1

Try this. rhs is a character vector of right sides and x and y are the data. It constructs the formula fo for each and then extracts the parameters and sets each to 1 for the starting value. Finally it runs nls and returns the SSEs sorted so that the result is a vector of SSE’s named via the right hand sides. If verbose=TRUE (which it is by default) then it also displays the output from each fit.

sse <- function(rhs, x, y) sort(sapply(rhs, function(rhs, x, y, verbose = TRUE) {
    fo <- as.formula(paste("y", rhs, sep = "~"))
    nms <- setdiff(all.vars(fo), c("x", "y"))
    start <- as.list(setNames(rep(1, length(nms)), nms))
    fm <- nls(fo, data.frame(x, y), start = start)
    if (verbose) { print(fm); cat("---\n") }
    deviance(fm)
}, x = x, y = y))

## test

set.seed(123)
x <- 1:10
y <- rnorm(10, x)

# modify to suit
rhs <- c("a*x+b", "a*x*x+b*x+c")

sse(rhs, x, y)