nlf {pomp} | R Documentation

## Nonlinear forecasting

### Description

Parameter estimation by maximum simulated quasi-likelihood.

### Usage

    ## S4 method for signature 'data.frame'
    nlf_objfun(data, est = character(0), lags,
      nrbf = 4, ti, tf, seed = NULL, transform.data = identity,
      period = NA, tensor = TRUE, fail.value = NA_real_, params, rinit,
      rprocess, rmeasure, ..., verbose = getOption("verbose"))

    ## S4 method for signature 'pomp'
    nlf_objfun(data, est = character(0), lags, nrbf = 4,
      ti, tf, seed = NULL, transform.data = identity, period = NA,
      tensor = TRUE, fail.value = NA, ...,
      verbose = getOption("verbose"))

    ## S4 method for signature 'nlf_objfun'
    nlf_objfun(data, est, lags, nrbf, ti, tf,
      seed = NULL, period, tensor, transform.data, fail.value, ...,
      verbose = getOption("verbose", FALSE))

### Arguments

`data` | either a data frame holding the time series data, or an object of class ‘pomp’, i.e., the output of another pomp calculation.
`est` | character vector; the names of parameters to be estimated.
`lags` | A vector specifying the lags to use when constructing the nonlinear autoregressive prediction model. The first lag is the prediction interval.
`nrbf` | integer scalar; the number of radial basis functions to be used at each lag.

`ti, tf`

required numeric values. NLF works by generating simulating long time series from the model. The simulated time series will be from `ti` to `tf`, with the same sampling frequency as the data. `ti` should be chosen large enough so that transient dynamics have died away. `tf` should be chosen large enough so that sufficiently many data points are available to estimate the nonlinear forecasting model well. An error will be generated unless the data-to-parameter ratio exceeds 10 and a warning will be given if the ratio is smaller than 30.

`seed` | integer. When fitting, it is often best to fix the seed of the random-number generator (RNG). This is accomplished by setting `seed` to an integer. By default, `seed = NULL`, which does not alter the RNG state.

`transform.data`

optional function. If specified, forecasting is performed using data and model simulations transformed by this function. By default, `transform.data` is the identity function, i.e., no transformation is performed. The main purpose of `transform.data` is to achieve approximately multivariate normal forecasting errors. If the data are univariate, `transform.data` should take a scalar and return a scalar. If the data are multivariate, `transform.data` should assume a vector input and return a vector of the same length.

`period` | numeric; `period=NA` means the model is nonseasonal. `period > 0` is the period of seasonal forcing. `period <= 0` is equivalent to `period = NA`.
`tensor` | logical; if FALSE, the fitted model is a generalized additive model with time mod period as one of the predictors, i.e., a gam with time-varying intercept. If TRUE, the fitted model is a gam with lagged state variables as predictors and time-periodic coefficients, constructed using tensor products of basis functions of state variables with basis functions of time.
`fail.value` | optional numeric scalar; if non-`NA`, this value is substituted for non-finite values of the objective function. It should be a large number (i.e., bigger than any legitimate values the objective function is likely to take).
`params` | optional; named numeric vector of parameters. This will be coerced internally to storage mode `double`.
`rinit` | simulator of the initial-state distribution. This can be furnished either as a C snippet, an R function, or the name of a pre-compiled native routine available in a dynamically loaded library. Setting `rinit=NULL` sets the initial-state simulator to its default. For more information, see ?rinit_spec.
`rprocess` | simulator of the latent state process, specified using one of the rprocess plugins. Setting `rprocess=NULL` removes the latent-state simulator. For more information, see ?rprocess_spec for the documentation on these plugins.
`rmeasure` | simulator of the measurement model, specified either as a C snippet, an R function, or the name of a pre-compiled native routine available in a dynamically loaded library. Setting `rmeasure=NULL` removes the measurement model simulator. For more information, see ?rmeasure_spec.

`...`

additional arguments supply new or modify existing model characteristics or components. See `pomp` for a full list of recognized arguments.

When named arguments not recognized by `pomp` are provided, these are made available to all basic components via the so-called userdata facility. This allows the user to pass information to the basic components outside of the usual routes of covariates (`covar`) and model parameters (`params`). See ?userdata for information on how to use this facility.

`verbose` | logical; if `TRUE`, diagnostic messages will be printed to the console.

### Details

Nonlinear forecasting (NLF) is an ‘indirect inference’ method. The NLF approximation to the log likelihood of the data series is computed by simulating data from a model, fitting a nonlinear autoregressive model to the simulated time series, and quantifying the ability of the resulting fitted model to predict the data time series. The nonlinear autoregressive model is implemented as a generalized additive model (GAM), conditional on lagged values, for each observation variable. The errors are assumed multivariate normal.

The NLF objective function constructed by `nlf_objfun` simulates long time series (`nasymp` is the number of observations in the simulated times series), perhaps after allowing for a transient period (`ntransient` steps). It then fits the GAM for the chosen lags to the simulated time series. Finally, it computes the quasi-likelihood of the data under the fitted GAM.

NLF assumes that the observation frequency (equivalently the time between successive observations) is uniform.

### Value

`nlf_objfun` constructs a stateful objective function for NLF estimation. Specfically, `nlf_objfun` returns an object of class ‘nlf_objfun’, which is a function suitable for use in an `optim`-like optimizer. In particular, this function takes a single numeric-vector argument that is assumed to contain the parameters named in `est`, in that order. When called, it will return the negative log quasilikelihood. It is a stateful function: Each time it is called, it will remember the values of the parameters and its estimate of the log quasilikelihood.

### Periodically-forced systems (seasonality)

Unlike other pomp estimation methods, NLF cannot accommodate general time-dependence in the model via explicit time-dependence or dependence on time-varying covariates. However, NLF can accommodate periodic forcing. It does this by including forcing phase as a predictor in the nonlinear autoregressive model. To accomplish this, one sets `period` to the period of the forcing (a positive numerical value). In this case, if `tensor = FALSE`, the effect is to add a periodic intercept in the autoregressive model. If `tensor = TRUE`, by contrast, the fitted model includes time-periodic coefficients, constructed using tensor products of basis functions of observables with basis functions of time.

### Important Note

Since pomp cannot guarantee that the final call an optimizer makes to the function is a call at the optimum, it cannot guarantee that the parameters stored in the function are the optimal ones. Therefore, it is a good idea to evaluate the function on the parameters returned by the optimization routine, which will ensure that these parameters are stored.

### Author(s)

Stephen P. Ellner, Bruce E. Kendall, Aaron A. King

### References

Ellner, S. P., Bailey, B. A., Bobashev, G. V., Gallant, A. R., Grenfell, B. T. and Nychka D. W. (1998) Noise and nonlinearity in measles epidemics: combining mechanistic and statistical approaches to population modeling. American Naturalist 151, 425–440.

Kendall, B. E., Briggs, C. J., Murdoch, W. W., Turchin, P., Ellner, S. P., McCauley, E., Nisbet, R. M. and Wood S. N. (1999) Why do populations cycle? A synthesis of statistical and mechanistic modeling approaches. Ecology 80, 1789–1805.

Kendall, B. E., Ellner, S. P., McCauley, E., Wood, S. N., Briggs, C. J., Murdoch, W. W. and Turchin, P. (2005) Population cycles in the pine looper moth (Bupalus piniarius): dynamical tests of mechanistic hypotheses. Ecological Monographs 75, 259–276.

### See Also

Other pomp parameter estimation methods: `abc`, `bsmc2`, `kalman`, `mif2`, `pmcmc`, `pomp-package`, `probe.match`, `spect.match`

### Examples

      library(magrittr)

      ricker() %>%
        nlf_objfun(est=c("r","sigma","N_0"),lags=c(4,6),
          partrans=parameter_trans(log=c("r","sigma","N_0")),
          paramnames=c("r","sigma","N_0"),
          ti=100,tf=2000,seed=426094906L) -> m1

      library(subplex)
      subplex(par=log(c(20,0.5,5)),fn=m1,control=list(reltol=1e-4)) -> out

      m1(out$par)
      coef(m1)
      plot(simulate(m1))

[Package pomp version 2.3 Index]