R help - May 2018 - error in chol.default((value + t(value))/2) : , the leading minor of order 1 is not positive definite

Dear friends - I'm having troubles with nlme fitting a simplified model 
as shown below eliciting the error

Error in chol.default((value + t(value))/2) :
 ? the leading minor of order 1 is not positive definite -

I have seen the threads on this error but it didn't help me solve the 
problem.

The model runs well in brms and identifies the used parameters even with 
fixed effects for TRT? - but here in nlme TRT is ignored and I guess 
this is not the reason for the said error

Below is the quite clumsy simulated data set and specification of call 
to nlme - the start values are taken from fitted values in brms

library(ggplot2)
windows(record=TRUE)
#generate 3*10? rats - add fixed effects to the four parameters 
according to the three groups - add random effects pr each rat - add 
residual random effect
#Parameter values taken from Sapirstein AJP 181:330-6, 1955


set.seed(1234)
Time <- seq(1,60,by=1)
A <- 275; B <-? 140;? g1 <- 0.1105; g2 <- .0161

N <- 30

AA <- rep(A,30)+rnorm(30,0,30);BB <- rep(B,30)+rnorm(30,0,15) ;
gg1 <- rep(g1,30)+rnorm(30,0,0.01); gg2 <- rep(g2,30)+rnorm(30,0,0.001)

TRT <- gl(3,10*60)
levels(TRT) <- c("CTRL","DIAB","HYPER")
AA1 <- AA + c(rep(0,10),rep(10,10),rep(-10,10))
BB1 <- BB + c(rep(0,10),rep(5,10),rep(-5,10))
Gg1 <- gg1 + c(rep(0,10),rep(0.01,10),rep(-0.01,10))
Gg2 <- gg2 + c(rep(0,10),rep(0.005,10),rep(-0.005,10))

getY <- function(A,B,g1,g2) {
Y? <- A*exp(-g1*Time) + B*exp(-g2*Time)
Y <- Y + rnorm(60,0,20)
}
YY <-? c()
for (i in 1:N) YY <- c(YY,getY(AA1[i],BB1[i],Gg1[i],Gg2[i]))
TT <- rep(Time,N)
RAT <- gl(N,length(Time))
dats? <- data.frame(RAT,TRT,TT,YY)
Dats <- dats
names(Dats)[c(3,4)] <- c("Time","Y")
dput(Dats,"dats0505.dat")

with(Dats,plot(Time,Y,pch=19,cex=.1,col=TRT))
ggplot(data=Dats,aes(x=Time,y=Y,group=RAT,col=TRT)) + geom_line()

library(nlme)

gfr.nlme <- nlme(Y ~ A*exp(-Time*g1)+B*exp(-Time*g2),
data = Dats,
fixed = A+g1+B+g2 ~1,
random = A+g1+B+g2 ~1,groups = ~ RAT,
start = c(255,115,130*1e-3,17*1e-3),
na.action = na.omit,verbose=TRUE,control = list(msVerbose = TRUE))
summary(gfr.nlme)

> On May 5, 2018, at 1:19 AM, Troels Ring <tring at gvdnet.dk> wrote:
> 
> Dear friends - I'm having troubles with nlme fitting a simplified model
as shown below eliciting the error
> 
> Error in chol.default((value + t(value))/2) :
>   the leading minor of order 1 is not positive definite -
> 
> I have seen the threads on this error but it didn't help me solve the
problem.
> 
> The model runs well in brms and identifies the used parameters even with
fixed effects for TRT  - but here in nlme TRT is ignored and I guess this is not
the reason for the said error
> 
> Below is the quite clumsy simulated data set and specification of call to
nlme - the start values are taken from fitted values in brms
> 
> library(ggplot2)
> windows(record=TRUE)
> #generate 3*10  rats - add fixed effects to the four parameters according
to the three groups - add random effects pr each rat - add residual random
effect
> #Parameter values taken from Sapirstein AJP 181:330-6, 1955
> 
> 
> set.seed(1234)
> Time <- seq(1,60,by=1)
> A <- 275; B <-  140;  g1 <- 0.1105; g2 <- .0161
> 
> N <- 30
> 
> AA <- rep(A,30)+rnorm(30,0,30);BB <- rep(B,30)+rnorm(30,0,15) ;
> gg1 <- rep(g1,30)+rnorm(30,0,0.01); gg2 <-
rep(g2,30)+rnorm(30,0,0.001)
> 
> TRT <- gl(3,10*60)
> levels(TRT) <- c("CTRL","DIAB","HYPER")
> AA1 <- AA + c(rep(0,10),rep(10,10),rep(-10,10))
> BB1 <- BB + c(rep(0,10),rep(5,10),rep(-5,10))
> Gg1 <- gg1 + c(rep(0,10),rep(0.01,10),rep(-0.01,10))
> Gg2 <- gg2 + c(rep(0,10),rep(0.005,10),rep(-0.005,10))
> 
> getY <- function(A,B,g1,g2) {
> Y  <- A*exp(-g1*Time) + B*exp(-g2*Time)
> Y <- Y + rnorm(60,0,20)
> }
> YY <-  c()
> for (i in 1:N) YY <- c(YY,getY(AA1[i],BB1[i],Gg1[i],Gg2[i]))
> TT <- rep(Time,N)
> RAT <- gl(N,length(Time))
> dats  <- data.frame(RAT,TRT,TT,YY)
> Dats <- dats
> names(Dats)[c(3,4)] <- c("Time","Y")
> dput(Dats,"dats0505.dat")
> 
> with(Dats,plot(Time,Y,pch=19,cex=.1,col=TRT))
> ggplot(data=Dats,aes(x=Time,y=Y,group=RAT,col=TRT)) + geom_line()
> 
> library(nlme)
> 
> gfr.nlme <- nlme(Y ~ A*exp(-Time*g1)+B*exp(-Time*g2),
> data = Dats,
> fixed = A+g1+B+g2 ~1,
> random = A+g1+B+g2 ~1,groups = ~ RAT,
Your fixed and random formulae look the same. That would seem to create
problems, at leas the way I understand mixed models analysis. At any rate this
is much more likely to get expert eyes (which mine definitely are not) on the
problem if it were posted to the mixed models list.
> start = c(255,115,130*1e-3,17*1e-3),
> na.action = na.omit,verbose=TRUE,control = list(msVerbose = TRUE))
> summary(gfr.nlme)
> 
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David Winsemius
Alameda, CA, USA

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