Performs and bootstraps a non-linear least-squares fit to data with y and x errors.
bootstrap.nlsfit(fn, par.guess, y, x, bsamples, priors = list(param = c(), p
= c(), psamples = c()), ..., lower = rep(x = -Inf, times =
length(par.guess)), upper = rep(x = +Inf, times = length(par.guess)), dy,
dx, CovMatrix, gr, dfn, mask, use.minpack.lm = TRUE, parallel = FALSE,
error = sd, cov_fn = cov, maxiter = 500, success.infos = 1:3,
relative.weights = FALSE, na.rm = FALSE)fn(par, x, ...). The (non-linear) function to be fitted to the
data. Its first argument must be the fit parameters named par. The
second must be x, the explaining variable. Additional parameters
might be passed to the function. Currently we pass boot.r which is 0
for the original data and the ID (1, ...) of the bootstrap sample otherwise.
As more parameters might be added in the future it is recommended that the
fit function accepts ... as the last parameter to be forward compatible.
initial guess values for the fit parameters.
the data as a one-dimensional numerical vector to be described by the fit function.
values of the explaining variable in form of a one-dimensional numerical vector.
bootstrap samples of y (and x, if applicable).
Must be provided as array of dimensions c(boot.R, n) with n
equals to length(y) in case of 'yerrors' and For 'xyerrors' to
length(y) + length(x).
List possessing the elements param, p and psamples.
The vector param includes the indices of all fit parameters that are
to be constrained and the vector p the corresponding paramater values
(e.g. known from a previous fit). The list element psamples is a matrix of
dimensions (boot.R, length(param)) and contains the corresponding
bootstrap samples. If this list is not specified priors are omitted
within the fit.
Additional parameters passed to fn, gr and dfn.
Numeric vector of length length(par.guess)
of lower bounds on the fit parameters. If missing, -Inf
will be set for all.
Numeric vector of length length(par.guess)
of upper bounds on the fit parameters. If missing, +Inf
will be set for all.
Numeric vector. Errors of the dependent and independent variable, respectively. These do not need to be specified as they can be computed from the bootstrap samples. In the case of parametric bootstrap it might would lead to a loss of information if they were computed from the pseudo-bootstrap samples. They must not be specified if a covariance matrix is given.
complete variance-covariance matrix of dimensions
c(length(y), length(y)) or c(length(y)+length(x),
length(y)+length(x)) depending on the errormodel. Pass NULL if the matrix
has to be calculated from the bsamples. In that case, if the number of
boostrap samples is small compared to the number of variables, singular value
decomposition with small eigenvalue replacement will be used (see invertCovMatrix)
to attempt a clean inversion.
In case a variance-covariance matrix is passed, the inversion will simply be attempted
using solve on the Cholesky decomposition.
Finally, if CovMatrix is missing, an uncorrelated fit will be performed.
gr(par, x, ...). gr=d(fn) / d(par) is a function to
return the gradient of fn. It must return an array with
length(x) rows and length(par) columns.
dfn(par, x, ...). dfn=d(fn) / dx is the canonical
derivative of fn by x and only relevant if x-errors are
provided.
logical or integer index vector. The mask is applied to select the observations from the data that are to be used in the fit. It is applied to x, y, dx, dy, bsamples and CovMatrix as applicable.
use the minpack.lm library if available. This
is usually faster than the default optim but somtimes also less
stable.
parallelise over bootstrap samples. The package
parallel is required.
Function that takes a sample vector and returns the error estimate. This is a parameter in order to support different resampling methods like jackknife.
function. Function to compute the covariance (matrix). Default is cov.
integer. Maximum number of iterations that can be used in the optimization process.
integer vector. When using minpack.lm there is the
info in the return value. Values of 1, 2 or 3 are certain success. A value
of 4 could either be a success or a saddle point. If you want to interpret
this as a success as well just pass 1:4 instead of the default 1:3.
are the errors on y (and x) to be interpreted as relative weights instead of absolute ones? If TRUE, the covariance martix of the fit parameter results is multiplied by chi^2/dof. This is the default in many fit programs, e.g. gnuplot.
logical. If set to true, NAs in y and dy will be ignored.
If x-errors are taken into account, NAs in x and dx will be ignored, too.
returns a list of class 'bootstrapfit'. It returns all input parameters and adds in addition the following:
the one dimensional numerical vector of length
npar+1. npar is the number of fit parameters. In case
of 'yerrors' this equals length(par.guess). For 'xyerrors'
this equals length(par.guess) + length(x). t0 contains
the best fit parameters
obtained on the original data. The last element in t0 is the
chisquare value.
an array of dimensions (npar+1, boot.R) with
npar as in t0. The rows contain the individual
bootstrap observations.
the bootstrap samples used as an array of dimensions
(length(y), boot.R) or (length(y)+length(x), boot.R)
depending on the error model with npar as in t0.
the p-value of the fit on the original data
the residual chisqr value.
the residual degrees of freedom of the fit.
the number of x-values.
the original ... list of parameters to be passed on to the
fit function
original mask value
Other NLS fit functions:
parametric.bootstrap.cov(),
parametric.bootstrap(),
parametric.nlsfit.cov(),
parametric.nlsfit(),
plot.bootstrapfit(),
predict.bootstrapfit(),
print.bootstrapfit(),
simple.nlsfit(),
summary.bootstrapfit()
# NOT RUN {
## Declare some data.
value <- c(0.1, 0.2, 0.31)
dvalue <- c(0.01, 0.01, 0.015)
x <- c(1, 2, 3)
dx <- c(0.1, 0.1, 0.1)
boot.R <- 1500
fn <- function (par, x, boot.r, ...) par[1] + par[2] * x
## Before we can use the fit with this data, we need to create bootstrap
## samples. We do not want to use the correlation matrix here. Note that you
## can simply use the parametric.nlsfit function as a convenient wrapper of
## the two steps.
bsamples <- parametric.bootstrap(boot.R, c(value, x), c(dvalue, dx))
head(bsamples)
fit.result <- bootstrap.nlsfit(fn, c(1, 1), value, x, bsamples)
summary(fit.result)
plot(fit.result, main = 'Ribbon on top')
plot(fit.result, ribbon.on.top = FALSE, main = 'Ribbon below')
residual_plot(fit.result, main = 'Residual Plot')
# }
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