How to put a complicated equation into a R formula?

Question

We have the diameter of trees as the predictor and tree height as the dependent variable. A number of different equations exist for this kind of data and we try to model som

Answer 1

Assuming you are using nls the R formula can use an ordinary R function, H(a, b, c, D), so the formula can be just h ~ H(a, b, c, dbh) and this works:

# use lm to get startingf values
lm1 <- lm(1/(h - 1.3) ~ I(1/dbh) + I(1/dbh^2), df)
start <- rev(setNames(coef(lm1), c("c", "b", "a")))

# run nls
H <- function(a, b, c, D) 1.3 + D^2 / (a + b * D + c * D^2)
nls1 <- nls(h ~ H(a, b, c, dbh), df, start = start)

nls1 # display result

Graphing the output:

plot(h ~ dbh, df)
lines(fitted(nls1) ~ dbh, df)