I would like to fit a nonlinear model with "nlme."
The model is a nonlinear growth model with five time points: y = X*b +
e, where design matrix X is defined as
X= | 1 0 |
| 1 1 |
| 1 k |
| 1 2k |
| 1 3k |
and parameter vector b = (b0, b1). And where "k" is a parameter to be
estimated. Of course I also want to estimate the intercept (b0), slope
(b1). Error variances (e) with 5 free parameters and random effects
covariance matrix (2x2: for b0 and b1).
I am not certain how to get the design matrix in the code so that the
"nlme" procedure will be able to
estimate parameter "k" as well as the intercept and slope.
I have tried the following:
meanfunc <- function(x,b0,b1,k){
meangrad <-
array(0,c(length(x),2),list(NULL,c("b0","b1")))
for(i in 1:length(x)){
if(x[i]==0){
err[i] <- b0 + b1*x[i]
meangrad[i,"b0"] <- 1
meangrad[i,"b1"] <- x[i]}
if(x[i]==1){
err[i] <- b0 + b1*x[i]
meangrad[i,"b0"] <- 1
meangrad[i,"b1"] <- x[i]}
if(x[i]==2){
err[i] <- b0 + b1*(x[i]-1)*k
meangrad[i,"b0"] <- 1
meangrad[i,"b1"] <- (x[i]-1)*k}
if(x[i]==3){
err[i] <- b0 + b1*2*(x[i]-1)*k
meangrad[i,"b0"] <- 1
meangrad[i,"b1"] <- (x[i]-1)*k}
if(x[i]==4){
err[i] <- b0 + b1*3*(x[i]-1)*k
meangrad[i,"b0"] <- 1
meangrad[i,"b1"] <- (x[i]-1)*k}
}
# compute analytical dervivatives
attr(err,"gradient") <- meangrad
err
}
data.mlfit <- nlme(y ~ meanfunc(x,b0,b1,k),
fixed=list(b0 ~ 1, b1 ~ 1, k ~ 1),
random=list(b0 ~ 1, b1 ~ 1),
groups = ~subj,
data=nd,
start=list(fixed=c(300,50,1)),
method="ML",verbose=T)
I get the following error message:
Error in meangrad[i, "b1"] <- (x[i] - 1) * k :
number of items to replace is not a multiple of replacement length
In addition: Warning messages:
1: In err[i] <- b0 + b1 * x[i] :
number of items to replace is not a multiple of replacement length
2: In err[i] <- b0 + b1 * x[i] :
number of items to replace is not a multiple of replacement length
3: In err[i] <- b0 + b1 * (x[i] - 1) * k :
number of items to replace is not a multiple of replacement length
Any suggestions or insights would be greatly appreciated.
Thank you,
Jeff
--
**********************************************************
Jeffrey R. Harring, Assistant Professor
Department of Measurement, Statistics & Evaluation (EDMS)
1230 Benjamin Building
University of Maryland
College Park, MD 20742-1115
Phone: 301.405.3630
Fax: 301.314.9245
Email: harring at umd.edu
Web: http://www.education.umd.edu/EDMS/fac/Harring/webpage.html