NLS: Error with the summary function

["Ilouga, Pierre" <Pierre.Ilouga@evotec.com>]

Dear all,

I’m wondering what is going on in this simple example. Sorry for the length of the e-mail. There was no other way to describe the problem.

Let  the 4x2 data frame X <- data.frame(Log.conc= c(-4.04920,  -3.61423,  -3.17926,  -2.74429), inh= c(9.930, 20.345, 23.915, 50.495) ).

The objective is to perform a simple nonlinear regression with “Log.conc” being the design and “inh” the dependent variable.

For this purpose the two models (resulting in sigmoidal shaped curves)  mdl.1 and mdl.2 were tried.

The start points for both runs are p1.start = 20.34500;   p3.start = -3.61423;   p4.start = 1.00000

RUN_1:

mdl.1 <-   inh ~ (p1 + (50.495 - p1)/(1 + 10^((p3 - Log.conc) * p4)))

M1 <- nls(mdl.1  , data="" start=list(p1=p1.start, p3=p3.start, p4=p4.start) )    yields

> M1

Residual sum of squares : 53.89067

parameters:

       p1        p3       p4

 15.05986 -3.087366 5.115297

> names(summary(M1))

[1] "parameters"   "sigma"        "df"           "cov.unscaled" "correlation"

[6] "formula"    

as  expected.

RUN_2: (replacing  “p1” by the “expected value”  p1 = 20.345   in  mdl.1)

mdl.2 <-  inh ~ (20.345 + (50.495 - 20.345)/(1 + 10^((p3 - Log.conc) * p4)))

M2 <- nls(mdl.2  , data="" start=list(p3=p3.start, p4=p4.start) )    results in 

Residual sum of squares : 108.4723

parameters:

        p3       p4

 -3.141419 23.02177

But

> summary(M2)

Problem in backsolve(R, rinv): Zero diagonal in column 2

Use traceback() to see the call stack

The question is: what is the reason for this error message?

S-PLUS : Copyright (c) 1988, 2002 Insightful Corp.

S : Copyright Lucent Technologies, Inc.

Version 6.1.2 Release 2 for Linux 2.2.12 : 2002

Working data will be in .Data

Dr. Pierre Ilouga

Screening Operations/Discovery Informatics

EVOTEC AG

Schnackenburgallee 114

22525 Hamburg

Germany

pierre.ilouga@evotec.com

www.evotec.com

Evotec AG Hamburg. Amtsgericht Hamburg HRB 68223
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