Caution: External email.
Colleagues,
At the risk of starting a forest fire, or perhaps a brush fire, while it is
good to see that nlxb can find a solution from arbitrary starting values, I
think Paul’s question has merit despite Professor Nash’s excellent and helpful
observation.
Although non-linear algorithms can converge, they can converge to a false
solution if starting values are sub-optimally specified. When possible, I try
to specify thought-out starting values. Would it make sense to plot y as a
function of (x1, x2) at different values of x3 to get a sense of possible
starting values? Or, perhaps using median values of x1, x2, and x3 as starting
values. Comparing results from different starting values can give some
confidence that the solution obtained using arbitrary starting values are
likely “correct”.
I freely admit that my experience (and thus expertise) using non-linear
solutions is limited. Please do not flame me, I am simply urging caution.
John
John David Sorkin M.D., Ph.D.
Professor of Medicine
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology and Geriatric
Medicine
Baltimore VA Medical Center
10 North Greene Street<x-apple-data-detectors://12>
GRECC<x-apple-data-detectors://12> (BT/18/GR)
Baltimore, MD 21201-1524<x-apple-data-detectors://13/0>
(Phone) 410-605-711<tel:410-605-7119>9
(Fax) 410-605-7913<tel:410-605-7913> (Please call phone number above prior to
faxing)
On Aug 19, 2023, at 4:35 PM, J C Nash
<profjcn...@gmail.com<mailto:profjcn...@gmail.com>> wrote:
Why bother. nlsr can find a solution from very crude start.
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)
mydata<-data.frame(Mixture, x1, x2, x3, y)
mydata
mymod <- y ~ 1/(Beta1*x1 + Beta2*x2 + Beta3*x3)
library(nlsr)
strt<-c(Beta1=1, Beta2=2, Beta3=3)
trysol<-nlxb(formula=mymod, data=mydata, start=strt, trace=TRUE)
trysol
# or pshort(trysol)
Output is
residual sumsquares = 1.5412e-05 on 20 observations
after 29 Jacobian and 43 function evaluations
name coeff SE tstat pval gradient
JSingval
Beta1 0.00629212 5.997e-06 1049 2.425e-42 4.049e-08
721.8
Beta2 0.00867741 1.608e-05 539.7 1.963e-37 -2.715e-08
56.05
Beta3 0.00801948 8.809e-05 91.03 2.664e-24 1.497e-08
10.81
J Nash
On 2023-08-19 16:19, Paul Bernal wrote:
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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