[R] Determining Starting Values for Model Parameters in Nonlinear Regression

[Paul Bernal]

Dear friends,

Hope you are all doing well and having a great weekend.  I have data that
was collected on specific gravity and spectrophotometer analysis for 26
mixtures of NG (nitroglycerine), TA (triacetin), and 2 NDPA (2 -
nitrodiphenylamine).

In the dataset, x1 = %NG,  x2 = %TA, and x3 = %2 NDPA.

The response variable is the specific gravity, and the rest of the
variables are the predictors.

This is the dataset:
dput(mod14data_random)
structure(list(Mixture = c(17, 14, 5, 1, 11, 2, 16, 7, 19, 23,
20, 6, 13, 21, 3, 18, 15, 26, 8, 22), x1 = c(69.98, 72.5, 77.6,
79.98, 74.98, 80.06, 69.98, 77.34, 69.99, 67.49, 67.51, 77.63,
72.5, 67.5, 80.1, 69.99, 72.49, 64.99, 75.02, 67.48), x2 = c(29,
25.48, 21.38, 19.85, 22, 18.91, 29.99, 19.65, 26.99, 29.49, 32.47,
20.35, 26.48, 31.47, 16.87, 27.99, 24.49, 31.99, 24.96, 30.5),
    x3 = c(1, 2, 1, 0, 3, 1, 0, 2.99, 3, 3, 0, 2, 1, 1, 3, 2,
    3, 3, 0, 2), y = c(1.4287, 1.4426, 1.4677, 1.4774, 1.4565,
    1.4807, 1.4279, 1.4684, 1.4301, 1.4188, 1.4157, 1.4686, 1.4414,
    1.4172, 1.4829, 1.4291, 1.4438, 1.4068, 1.4524, 1.4183)), row.names =
c(NA,
-20L), class = "data.frame")

The model is the following:
y = 1/(Beta1x1 + Beta2x2 + Beta3x3)

I need to determine starting (initial) values for the model parameters for
this nonlinear regression model, any ideas on how to accomplish this using
R?

Cheers,
Paul

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