spect: Power spectrum computation and spectrum-matching for...
In pomp: Statistical Inference for Partially Observed Markov Processes

Description Usage Arguments Details Value Author(s) References See Also Examples

spect estimates the power spectrum of time series data and model simulations and compares the results. It can be used to diagnose goodness of fit and/or as the basis for frequency-domain parameter estimation (spect.match).

spect.match tries to match the power spectrum of the model to that of the data. It calls an optimizer to adjust model parameters to minimize the discrepancy between simulated and actual data.

## S4 method for signature 'pomp'
spect(object, params, vars, kernel.width, nsim, seed = NULL,
     transform = identity,
     detrend = c("none","mean","linear","quadratic"),
     ...)
## S4 method for signature 'spect.pomp'
spect(object, params, vars, kernel.width, nsim, seed = NULL, transform,
     detrend, ...)
spect.match(object, start, est = character(0),
            vars, nsim, seed = NULL,
            kernel.width, transform = identity, 
            detrend = c("none","mean","linear","quadratic"),
            weights, method = c("subplex","Nelder-Mead","SANN"),
            verbose = getOption("verbose"),
            eval.only = FALSE, fail.value = NA, ...)

`object`	An object of class `pomp`.
`params`	optional named numeric vector of model parameters. By default, `params=coef(object)`.
`vars`	optional; names of observed variables for which the power spectrum will be computed. This must be a subset of `rownames(obs(object))`. By default, the spectrum will be computed for all observables.
`kernel.width`	width parameter for the smoothing kernel used for calculating the estimate of the spectrum.
`nsim`	number of model simulations to be computed.
`seed`	optional; if non-`NULL`, the random number generator will be initialized with this seed for simulations. See `simulate`.
`transform`	function; this transformation will be applied to the observables prior to estimation of the spectrum, and prior to any detrending.
`detrend`	de-trending operation to perform. Options include no detrending, and subtraction of constant, linear, and quadratic trends from the data. Detrending is applied to each data series and to each model simulation independently.
`weights`	optional. The mismatch between model and data is measured by a weighted average of mismatch at each frequency. By default, all frequencies are weighted equally. `weights` can be specified either as a vector (which must have length equal to the number of frequencies) or as a function of frequency. If the latter, `weights(freq)` must return a nonnegative weight for each frequency.
`start`	named numeric vector; the initial guess of parameters.
`est`	character vector; the names of parameters to be estimated.
`method`	Optimization method. Choices are `subplex` and any of the methods used by `optim`.
`verbose`	logical; print diagnostic messages?
`eval.only`	logical; if `TRUE`, no optimization is attempted. Instead, the probe-mismatch value is simply evaluated at the `start` parameters.
`fail.value`	optional scalar; if non-`NA`, this value is substituted for non-finite values of the objective function.
`...`	Additional arguments. In the case of `spect`, these are currently ignored. In the case of `spect.match`, these are passed to `optim` or `subplex` in the `control` list.

A call to spect results in the estimation of the power spectrum for the (transformed, detrended) data and nsim model simulations. The results of these computations are stored in an object of class spect.pomp.

A call to spect.match results in an attempt to optimize the agreement between model and data spectrum over the parameters named in est. The results, including coefficients of the fitted model and power spectra of fitted model and data, are stored in an object of class spect.matched.pomp.

spect returns an object of class spect.pomp, which is derived from class pomp and therefore has all the slots of that class. In addition, spect.pomp objects have the following slots:

kernel.width: width parameter of the smoothing kernel used.
transform: transformation function used.
freq: numeric vector of the frequencies at which the power spectrum is estimated.
datspec, simspec: estimated power spectra for data and simulations, respectively.
pvals: one-sided p-values: fraction of the simulated spectra that differ more from the mean simulated spectrum than does the data. The metric used is L2 distance.
detrend: detrending option used.

spect.match returns an object of class spect.matched.pomp, which is derived from class spect.pomp and therefore has all the slots of that class. In addition, spect.matched.pomp objects have the following slots:

est, weights, fail.value: values of the corresponding arguments in the call to spect.match.
evals: number of function and gradient evaluations by the optimizer. See optim.
value: Value of the objective function.
convergence, msg: Convergence code and message from the optimizer. See optim.

Daniel C. Reuman, Cai GoGwilt, Aaron A. King

D.C. Reuman, R.A. Desharnais, R.F. Costantino, O. Ahmad, J.E. Cohen (2006) Power spectra reveal the influence of stochasticity on nonlinear population dynamics. Proceedings of the National Academy of Sciences 103, 18860-18865.

D.C. Reuman, R.F. Costantino, R.A. Desharnais, J.E. Cohen (2008) Color of environmental noise affects the nonlinear dynamics of cycling, stage-structured populations. Ecology Letters, 11, 820-830.

pomp, probe

pompExample(ou2)
good <- spect(
              ou2,
              vars=c("y1","y2"),
              kernel.width=3,
              detrend="mean",
              nsim=500
              )
summary(good)
plot(good)

ou2.bad <- ou2
coef(ou2.bad,c("x1.0","x2.0","alpha.1","alpha.4")) <- c(0,0,0.1,0.2)
bad <- spect(
             ou2.bad,
             vars=c("y1","y2"),
             kernel.width=3,
             detrend="mean",
             nsim=500
             )
summary(bad)
plot(bad)