nlsr (version 2023.8.31)

nlxb: nlxb: nonlinear least squares modeling by formula

Description

A simplified and hopefully robust alternative to finding the nonlinear least squares minimizer that causes 'formula' to give a minimal residual sum of squares.

Usage

nlxb(
  formula,
  data = parent.frame(),
  start,
  trace = FALSE,
  lower = NULL,
  upper = NULL,
  weights = NULL,
  control = list(),
  ...
)

Value

list of solution elements

resid

weighted residuals at the proposed solution

jacobian

Jacobian matrix at the proposed solution

feval

residual function evaluations used to reach solution from starting parameters

jeval

Jacobian function (or approximation) evaluations used

coefficients

a named vector of proposed solution parameters

ssquares

weighted sum of squared residuals (often the deviance)

lower

lower bounds on parameters

upper

upper bounds on parameters

maskidx

vector if indices of fixed (masked) parameters

weights0

weights specified in function call

weights

weights at the final solution

formula

the modeling formula

resfn

the residual function (unweighted) based on the formula

Arguments

formula

The modeling formula. Looks like 'y~b1/(1+b2*exp(-b3*T))'

data

a data frame containing data for variables used in the formula that are NOT the parameters. This data may also be defined in the parent frame i.e., 'global' to this function

start

MUST be a named vector with all elements present e.g., start=c(b1=200, b2=50, b3=0.3)

trace

TRUE for console output during execution

lower

a vector of lower bounds on the parameters. If a single number, this will be applied to all parameters Default NULL.

upper

a vector of upper bounds on the parameters. If a single number, this will be applied to all parameters. Default NULL.

weights

A vector of fixed weights or a function or formula producing one. See the Details below.

control

a list of control parameters. See nlsr.control().

...

additional data needed to evaluate the modeling functions

Author

J C Nash 2014-7-16 nashjc _at_ uottawa.ca

Details

nlxb is particularly intended to allow for the resolution of very ill-conditioned or else near zero-residual problems for which the regular nls() function is ill-suited.

This variant uses a qr solution without forming the sum of squares and cross products t(J)

Neither this function nor nlfb have provision for parameter scaling (as in the parscale control of optim and package optimx). This would be more tedious than difficult to introduce, but does not seem to be a priority feature to add.

There are many controls, and some of them are important for nlxb. In particular, if the derivatives needed for developing the Jacobian are NOT in the derivatives table, then we must supply code elsewhere as specified by the control japprox. This was originally just for numerical approximations, with the character strings "jafwd", "jaback", "jacentral" and "jand" leading to the use of a forward, backward, central or package numDeriv approximation. However, it is also possible to use code embedded in the residual function created using the formula. This is particularly useful for selfStart models, and we use the character string "SSJac" to point to such Jacobian code. Note how the starting parameter vector is found using the getInitial function from the stats package as in an example below.

The weights argument can be a vector of fixed weights, in which case the objective function that will be minimized is the sum of squares where each residual is multiplied by the square root of the corresponding weight. Default NULL implies unit weights.

weights may alternatively be a function with header function(parms, resids) to compute such a vector, or a formula whose right hand side gives an expression for the weights. Variables in the expression may include the following:

A variable named resid

The current residuals.

A variable named fitted

The right hand side of the model formula.

Parameters

The parameters of the model.

Data

Values from data.

Vars

Variables in the environment of the formula.

Examples

library(nlsr)
weed <- c(5.308, 7.24, 9.638, 12.866, 17.069, 23.192, 31.443,
        38.558, 50.156, 62.948, 75.995, 91.972)
tt <- 1:12
weeddf <- data.frame(tt, weed)
frm <- 
wmodu <- weed ~ b1/(1+b2*exp(-b3*tt)) # Unscaled
## nls from unit start FAILS
start1<-c(b1=1, b2=1, b3=1)
hunls1 <- try(nls(wmodu, data=weeddf, start=start1, trace=FALSE))
if (! inherits(hunls1, "try-error")) print(hunls1) ## else cat("Failure -- try-error\n")
## nlxb from unit start
hunlx1 <- try(nlxb(wmodu, data=weeddf, start=c(b1=1, b2=1, b3=1), trace=FALSE))
if (! inherits(hunlx1, "try-error")) print(hunlx1)

st2h<-c(b1=185, b2=10, b3=.3)
#' hunls2 <- try(nls(wmodu, data=weeddf, start=st2h, trace=FALSE))
if (! inherits(hunls1, "try-error")) print(hunls1) ## else cat("Failure -- try-error\n")
## nlxb from unit start
hunlx1 <- try(nlxb(wmodu, data=weeddf, start=st2h, trace=FALSE))
if (! inherits(hunlx1, "try-error")) print(hunlx1)

# Functional models need to use a Jacobian approximation or external calculation.
# For example, the SSlogis() selfStart model from \code{stats} package.

# nls() needs NO starting value
hSSnls<-try(nls(weed~SSlogis(tt, Asym, xmid, scal), data=weeddf))
summary(hSSnls)
# We need to get the start for nlxb explicitly
stSS <- getInitial(weed ~ SSlogis(tt, Asym, xmid, scal), data=weeddf)
hSSnlx<-try(nlxb(weed~SSlogis(tt, Asym, xmid, scal), data=weeddf, start=stSS))
hSSnlx

# nls() can only bound parameters with algorithm="port"
#   and minpack.lm is unreliable in imposing bounds, but nlsr copes fine.
lo<-c(0, 0, 0)
up<-c(190, 10, 2) # Note: start must be admissible.
bnls0<-try(nls(wmodu, data=weeddf, start=st2h,
         lower=lo, upper=up)) # should complain and fail
 
bnls<-try(nls(wmodu, data=weeddf, start=st2h,
         lower=lo, upper=up, algorith="port"))
summary(bnls)
bnlx<-try(nlxb(wmodu, data=weeddf, start=st2h, lower=lo, upper=up))
bnlx

# nlxb() can also MASK (fix) parameters. The mechanism of maskidx from nls
# is NO LONGER USED. Instead we set upper and lower parameters equal for
# the masked parameters. The start value MUST be equal to this fixed value.
lo<-c(190, 0, 0) # mask first parameter
up<-c(190, 10, 2)
strt <- c(b1=190, b2=1, b3=1)
mnlx<-try(nlxb(wmodu, start=strt, data=weeddf, 
         lower=lo, upper=up))
mnlx
mnls<-try(nls(wmodu, data=weeddf, start=strt,
         lower=lo, upper=up, algorith="port"))
summary(mnls)

# Try first parameter masked and see if we get SEs 
lo<-c(200, 0, 0) # mask first parameter
up<-c(100, 10, 5)
strt <- c(b1=200, b2=1, b3=1)
mnlx<-try(nlxb(wmodu, start=strt, data=weeddf, 
         lower=lo, upper=up))
mnlx
mnls<-try(nls(wmodu, data=weeddf, start=strt,
         lower=lo, upper=up, algorith="port"))
summary(mnls) 

# Try with weights on the observations
mnlx<-try(nlxb(wmodu, start=strt, data=weeddf, 
               weights = ~ 1/weed))
mnlx