Dennis Fisher wrote on 10/11/2011 07:20:35 PM:
> 
> 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


It's great that you provided code, data, and error messages for clarity. 
But, without knowing what the starting values are (INITEMAX, INITEFFECT, 
INITC50, and INITGAMMA), I can't reproduce what you're doing.

I'm also a bit confused about GAMMA.  In your first fit you don't provide 
a starting value for GAMMA, so it is being treated as an independent 
variable.  But in your second fit, you do provide starting values for 
GAMMA, so it is being treated as a parameter to be estimated.  Which is 
correct?

Finally, I was able to look at the plot of XVAR vs. YVAR, and there is so 
much noise that it's not surprising you're having difficulty fitting a 
four-parameter non-linear model.

Jean
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