R: Fit a hydromad model using general optimisation algorithms.

fitByOptim {hydromad}

R Documentation

Fit a hydromad model using general optimisation algorithms.

Description

Fits a hydromad model using R's optim or nlminb functions. Has multi-start and pre-sampling options.

Usage

fitByOptim(MODEL, objective = hydromad.getOption("objective"),
           method = hydromad.getOption("optim.method"), control = list(),
           samples = hydromad.getOption("fit.samples"),
           sampletype = c("latin.hypercube", "random", "all.combinations"),
           initpars = NULL, multistart = FALSE,
           vcov = FALSE, hessian = vcov)

fitByOptim1(MODEL, objective = hydromad.getOption("objective"),
            tol = .Machine$double.eps^0.25)

Arguments

`MODEL`	a model specification created by `hydromad`. It should not be fully specified, i.e one or more parameters should be defined by ranges of values rather than exact values.
`objective`	objective function to maximise, given as a `function(Q, X, ...)`. See `objFunVal`.
`method, control`	optimisation algorithm and settings. See `optim`. The default is `"Nelder-Mead"` (a simplex algorithm). An additional method `"PORT"` can be given, which calls `nlminb`.
`samples`	number of parameter sets to test.
`sampletype`	sampling scheme – see `parameterSets`.
`initpars`	initial parameter set.
`multistart`	if this is `TRUE`, then each of the initial parameter samples (based on `samples` and `sampletype`) are used as a starting value for a separate optimisation run, and the best result is kept.
`vcov, hessian`	if `vcov = TRUE`, the parameter variance-covariance matrix will be estimated as the inverse of the hessian matrix returned by `optim()`. This may be a very poor estimate! It can be extract using `vcov`. Does not work with `method = "PORT"`.
`tol`	convergence tolerance, see `optimize`.

Details

See optim for a brief description of the available algorithms, including references to literature.

fitByOptim1 handles a single free parameter using optimize; it is called by fitByOptim, with a warning, in that case.

Value

the best model from those sampled, according to the given objective function. Also, these extra elements are inserted:

`fit.result`	the result from `optim`.
`objective`	the `objective` function used.
`funevals`	total number of evaluations of the model simulation function.
`timing`	timing vector as returned by `system.time`.

Author(s)

Felix Andrews felix@nfrac.org

Examples

data(Cotter)
x <- Cotter[1:1000]

## IHACRES CWI model with power law unit hydrograph
modx <- hydromad(x, sma = "cwi", routing = "powuh")
modx

set.seed(0)
foo <- fitByOptim(modx, samples = 100)

summary(foo)

## return value from optim (with 'objseq' added):
str(foo$fit.result)

## plot objective function value convergence over time
xyplot(optimtrace(foo), type = "b",
  xlab = "function evaluations", ylab = "objective fn. value")

## repeat optimisation with single random starting points
fooreps <-
  replicate(4,
      fitByOptim(modx, samples = 1, sampletype = "random",
                 objective = hmadstat("r.squared"),
                 method = "Nelder-Mead"),
      simplify = FALSE)
names(fooreps) <- paste("rep.", seq_along(fooreps))
## extract and plot the optimisation traces
traces <- lapply(fooreps, optimtrace)
tracesraw <- lapply(fooreps, optimtrace, raw = TRUE)
xyplot(do.call("merge", traces), superpose = TRUE,
    sub = 'method = "Nelder-Mead"',
    xlab = "Fn. evaluations", ylab = "Objective value",
    auto.key = list(corner = c(1,0))) +
xyplot(do.call("merge", tracesraw), superpose = TRUE,
    type = "p", cex = 0.5)

## if you try it again with method = "PORT" you will find that all
## replicates converge to the optimum regardless of starting point.

[Package hydromad version 0.9-18 Index]