Colleagues,
I am fitting an Emax model using nls. The code is:
START <- list(EMAX=INITEMAX, EFFECT=INITEFFECT,
C50=INITC50)
CONTROL <- list(maxiter=1000, warnOnly=T)
#FORMULA <- as.formula(YVAR ~ EMAX - EFFECT * XVAR^GAMMA
/ (XVAR^GAMMA + C50^GAMMA)) ## alternate version of formula
FORMULA <- as.formula(YVAR ~ EMAX - EFFECT / (1 +
(C50/XVAR)^GAMMA))
FIT <- nls(FORMULA, start=START,
control=CONTROL, trace=T)
If GAMMA equals 10-80, nls converges successfully and the fit tracks the fit
from a smoother (Supersmoother). However, if I attempt to estimate GAMMA using:
START <- list(EMAX=INITEMAX, EFFECT=INITEFFECT,
C50=INITC50, GAMMA=INITGAMMA)
GAMMA increases rapidly to > 500 and nls terminates with:
Error in chol2inv(object$m$Rmat()) :
element (4, 4) is zero, so the inverse cannot be computed
In addition: Warning message:
In nls(FORMULA, start = START, control = CONTROL, trace = T) :
singular gradient
I also tried fixing GAMMA to > 1000 and I get a similar error message:
Error in chol2inv(object$m$Rmat())
: element (2, 2) is zero, so the inverse cannot be computed
In addition: Warning message:
In nls(FORMULA, start = START, control = CONTROL, trace = T)
: singular gradient
The data do not suggest a very large value for GAMMA so I am surprised that the
estimate is increasing so rapidly. I attempted to use the port algorithm with
an upper bound on GAMMA but the upper bound is reached rapidly, suggesting that
the data support a large value for GAMMA.
A subset of the data (with added noise) is shown below. A GAMMA value of 1280
triggers the error with this subset
XVAR <- c(26, 31.3, 20.9, 24.8, 22.9, 4.79, 19.6, 18, 19.6, 9.69, 21.7,
26.6, 27.8, 9.12, 10.5, 20.1, 16.7, 14.1, 10.2, 19.2, 24.7, 34.6,
26.6, 25.1, 5.98, 13.4, 15.7, 9.59, 7.39, 21.5, 15.7, 12.4, 19.2, 17.8, 19.7,
27.1, 25.6, 36.4, 22.9, 8.68, 27, 25.9, 33.3, 24.2,
21.4, 31, 19.1, 18.7, 23.5, 19.4, 10.3, 12.8, 13.9, 18.5, 21, 15.2, 18.9, 9.12,
16.9, 12.9, 29.5, 15.5, 7.34, 8.97, 8.04, 23.7,
16.3, 37.6, 35.2, 13.7, 28.1, 29.5, 15.1, 26, 6.52)
YVAR <- c(-34.2, -84.2, -71.1, -91.9, -104.1, -23.2, -27.2, -13.4, -143.2,
24.7, -72.1, -38, 25.2, -8, -34.1, -15.1, -112.6, -93.5, -130.9,
-127.8, -118.7, -53.5, -29.8, 98, 0, -37.6, -99.4, 57.9, 0.2, -62.2, -27.3,
8.3, -51.6, -111.6, -25.6, -51.7, -106.4, -85.1,
-63.1, -60.8, -27.7, -20.7, 22.9, -49.4, -85.7, -90.9, -107, -20.6, -36.3,
-40.2, 39.8, -55, -54.5, -103.9, -53.1, -2.3, -72.3,
-65.6, -57.8, -64.4, -129.1, 10.4, -9.9, -29.6, -40.8, 52, -94, 8.8, -98.8, 28,
-16.3, -99.2, -48.5, -111.9, -15.4)
I suspect that I am making a conceptual error in the use of nls. Any help
would be appreciated. If a different function to fit nonlinear regression
would work better, please direct me.
Dennis
Dennis Fisher MD
P < (The "P Less Than" Company)
Phone: 1-866-PLessThan (1-866-753-7784)
Fax: 1-866-PLessThan (1-866-753-7784)
www.PLessThan.com
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