On Sun, 12 Jun 2011, peter dalgaard wrote:
On Jun 12, 2011, at 18:57 , Diviya Smith wrote:
Hello there,
I am trying to fit an exponential fit using Least squares to some data.
#data
x <- c(1 ,10, 20, 30, 40, 50, 60, 70, 80, 90, 100)
y <- c(0.033823, 0.014779, 0.004698, 0.001584, -0.002017, -0.003436,
-0.000006, -0.004626, -0.004626, -0.004626, -0.004626)
sub <- data.frame(x,y)
#If model is y = a*exp(-x) + b then
fit <- nls(y ~ a*exp(-x) + b, data = sub, start = list(a = 0, b = 0), trace
= TRUE)
This works well. However, if I want to fit the model : y = a*exp(-mx)+c then
I try -
fit <- nls(y ~ a*exp(-m*x) + b, data = sub, start = list(a = 0, b = 0, m=
0), trace = TRUE)
It fails and I get the following error -
Error in nlsModel(formula, mf, start, wts) :
singular gradient matrix at initial parameter estimates
If a==0, then a*exp(-m*x) does not depend on m. So don't use a=0 as initial
value.
Any suggestions how I can fix this? Also next I want to try to fit a sum of
2 exponentials to this data. So the new model would be y = a*exp[(-m1+
m2)*x]+c .
That's not a sum of exponentials. Did you mean a*(exp(-m1*x) +
exp(-m2*x)) + c?
OK, that makes more sense. Also, scaling of the variables may help.
Something like this could work:
## scaled data
d <- data.frame(x = c(1, 1:10 * 10), y = 100 * c(
0.033823, 0.014779, 0.004698, 0.001584, -0.002017, -0.003436, -0.000006,
-0.004626, -0.004626, -0.004626, -0.004626))
## model fits
n1 <- nls(y ~ a*exp(-m * x) + b, data = d,
start = list(a = 1, b = 0, m = 0.1))
n2 <- nls(y ~ a * (exp(-m1 * x) + exp(-m2 * x)) + b, data = d,
start = list(a = 1, b = 0, m1 = 0.1, m2 = 0.5))
## visualization
plot(y ~ x, data = d)
lines(d$x, fitted(n1), col = 2)
lines(d$x, fitted(n2), col = 4)
## ANOVA
anova(n1, n2)
## LR test
library("lmtest")
lrtest(n1, n2)
which both seem to indicate that n1 is sufficient.
hth,
Z
Anyways, same procedure with more parameters. Just
beware the fundamental exchangeability of m1 and m2, so don't initialize
them to the same value.
Any suggestion how I can do this... Any help would be most
appreciated. Thanks in advance.
--
Peter Dalgaard
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd....@cbs.dk Priv: pda...@gmail.com
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