Parameter and initial conditions fitting ODE models with nls.lm - r

Question

I am currently trying to fit ODE functional responses using the Levenberg-Marquardt routine (nls.lm) in pkg-minpack.lm following the tutorial here (http://www.r-bloggers.com/learning-r-parameter-fitting-for-models-involving-differential-equations/).
In the example, he fits the data by first setting up a function rxnrate which I modified shown below:
library(ggplot2) #library for plotting
library(reshape2) # library for reshaping data (tall-narrow <-> short-wide)
library(deSolve) # library for solving differential equations
library(minpack.lm) # library for least squares fit using levenberg-marquart algorithm
# prediction of concentration
# rate function
rxnrate=function(t,c,parms){
# rate constant passed through a list called parms
k1=parms$k1
k2=parms$k2
k3=parms$k3
# c is the concentration of species
# derivatives dc/dt are computed below
r=rep(0,length(c))
r[1]=-k1*c["A"] #dcA/dt
r[2]=k1*c["A"]-k2*c["B"]+k3*c["C"] #dcB/dt
r[3]=k2*c["B"]-k3*c["C"] #dcC/dt
# the computed derivatives are returned as a list
# order of derivatives needs to be the same as the order of species in c
return(list(r))
}
My problem is that the initial condition of each states can be also considered as the estimated parameters. However, it does not work properly at the moment.
Below is my code:
# function that calculates residual sum of squares
ssq=function(myparms){
# inital concentration
cinit=c(A=myparms[4],B=0,C=0)
# time points for which conc is reported
# include the points where data is available
t=c(seq(0,5,0.1),df$time)
t=sort(unique(t))
# parms from the parameter estimation routine
k1=myparms[1]
k2=myparms[2]
k3=myparms[3]
# solve ODE for a given set of parameters
out=ode(y=cinit,times=t,func=rxnrate,parms=list(k1=k1,k2=k2,k3=k3))
# Filter data that contains time points where data is available
outdf=data.frame(out)
outdf=outdf[outdf$time %in% df$time,]
# Evaluate predicted vs experimental residual
preddf=melt(outdf,id.var="time",variable.name="species",value.name="conc")
expdf=melt(df,id.var="time",variable.name="species",value.name="conc")
ssqres=preddf$conc-expdf$conc
# return predicted vs experimental residual
return(ssqres)
}
# parameter fitting using levenberg marquart algorithm
# initial guess for parameters
myparms=c(k1=0.5,k2=0.5,k3=0.5,A=1)
# fitting
fitval=nls.lm(par=myparms,fn=ssq)
Once I run this, an error comes out like this
Error in chol.default(object$hessian) :
the leading minor of order 1 is not positive definite

Answer 1

The problem of your code is the following one:
In the code-line cinit=c(A=myparms[4],B=0,C=0) you gave A the value of myparms[4] AND the name of myparms[4]. Let's see:
myparms=c(k1=0.5,k2=0.5,k3=0.5,A=1)
cinit=c(A=myparms[4],B=0,C=0)
print(cinit)
A.A B C
1 0 0
to solve this problem, you can do this:
myparms=c(k1=0.5,k2=0.5,k3=0.5,A=1)
cinit=c(A=unname(myparms[4]),B=0,C=0)
print(cinit)
A B C
1 0 0
or this:
myparms=c(k1=0.5,k2=0.5,k3=0.5,1)
cinit=c(A=unname(myparms[4]),B=0,C=0)
print(cinit)
A B C
1 0 0
Then your code will work!
Best regards,
J_F