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I have a dataset that contains tree height and diameter measurements among the tree stem. I tried to fit my data with GNLS in R, but I'm getting this "step halving factor reduced below minimum in NLS step" error. I think my initial values are not accurate enough. I did some research and found a platform AD Model Builder which estimates initial parameter values for nls however I did not understand how to use that platform. I have this equation called Max&Burkhart (1976) Segmented taper equation that predicts the stem diameter (di) at a given height. The code is like below:

ComputeDi.MaxBurkhart <- function(hi, d, h, b1, b2, b3, b4, a1, a2){
    x <- hi / h
    x1 <- x - 1 
    x2 <- x ^ 2 - 1
    di <- d * sqrt(b1 * x1 + b2 * x2 + b3 * (a1 - x) ^ 2 * ((a1 - x) >= 0.0) + b4 * (a2 - x) ^ 2 * ((a2 - x) >= 0.0))
    return(di)
}

I'm gonna put a link to my whole data set so you may want to download. Mydata

I tried to dput my dataset but it's too long for dputting.

So, how can I estimate starting values for this model. I tried fitting data with NLS and using coef of nls as starting values of gnls however I get the error that I claimed above.

AD Model Builder approach seems pretty good for finding the initial parameters but I really have no idea how to use that platform. There is a user @dave fournier who is really good at Non-Linear regression. I hope he sees my question. Thank you all in advance.

Edit: Typo

Onur Alkan
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    Please see https://stats.stackexchange.com/questions/160552 for some guidance in estimating initial values. In this case, it is attractive to provide meaningful estimates for `a1` and `a2` and compute the other initial values by regressing the *square* of `d1` on the variables. Note, too, that your model is overdetermined: the factor of `d` is superfluous (unless you believe `di` could be negative!). This may be the source of the trouble. – whuber Apr 30 '19 at 16:05
  • Thank you for your commnet @whuber. Before replaying your comment, I made a deep research on the link you gave. In my case, d is the diameter at breast height (1.3 m above ground) of a tree. I asked the same question on stackoverflow in [here](https://stackoverflow.com/questions/55867066/how-can-i-find-non-linear-regression-model-starting-values). I have another data set that contains data of 100 trees (mine is 240) and with that dataset it works like a charm. But when I replace cvs files, trouble begins. You can find my dataset in my post on stackoverflow, if you want. Thank you in advance. – Onur Alkan May 02 '19 at 19:29

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