Profile.LS.TV.DDE: Profile Estimation Functions for DDE with Time Varying...
In gpDDE: General Profiling Method for Delay Differential Equation

Description Usage Arguments Value Author(s)

This function runs generalized profiling for DDE models with time varying coefficients. This function carry out the profiled optimization method for DDe models using a sum of squared errors criteria for both fit to data and the fit of the derivatives to a delay differential equation with time varying coefficients.

Profile.LS.TV.DDE(fn, data, times, pars, beta, kappa, coefs = NULL,
  basisvals = NULL, lambda, fd.obj = NULL, more = NULL, weights = NULL,
  quadrature = NULL, in.meth = "nlminb", out.meth = "nls",
  control.in = list(), control.out = list(), eps = 1e-06, active = NULL,
  posproc = FALSE, discrete = FALSE, poslik = FALSE, names = NULL,
  sparse = FALSE, basisvals0 = NULL, coefs0 = NULL, nbeta, ndelay, tau)

`fn`	fn A named list of functions giving the righthand side of a delay differential equation. The functions should have arguments times he times at which the righthand side is being evaluated. x The state values at those times. p Parameters to be entered in the system. more A list object containing additional inputs to `fn`, The distributed delay state are passed into derivative calculation as `more$y`. The list of functions should contain the elements: fn Function to calculate the right hand sid. dfdx Function to calculate the derivative of each right-hand function with respect to the states. dfdp calculates the derivative of therighthand side function with respect to parameters. d2fdx2 Function to calculate the second derivatives with respect to states. d2fdxdp Function to calculate the cross derivatives of each right-hand function with respect to state and parameters. dfdx.d Function to calculate the the derivative of each righthand function with respect to the delayed states. d2fdx.ddp Function to calculate the cross derivatives of each righthand function with respect to the delayed states and parameters. d2fdxdx.d Function to calculate the cross derivatives of each right-hand function with respect to the state and the delayed states. d2fdx.d2 Function to calculate the second derivatives of the right-hand function with respect to the delayed states.
`data`	Matrix of observed data values.
`times`	Vector observation times for the data.
`pars`	Initial values of parameters to be estimated processes.
`beta`	Initial values of the contribution of lags for the delay.
`kappa`	Initial values of parameters for a time varying function.
`coefs`	Vector giving the current estimate of the coefficients in the spline.
`basisvals`	Values of the collocation basis to be used. This should be a basis object from the fda package.
`lambda`	Penalty value trading off fidelity to data with fidelity to dif- ferential equations.
`fd.obj`	A functional data object; if this is non-null, coefs and basisvals is extracted from here.
`more`	An object specifying additional arguments to fn.
`weights`	Weights for weighted estimation.
`quadrature`	Quadrature points, should contain two elements (if not `NULL`) qpts sQuadrature points; defaults to midpoints between knots qwts Quadrature weights; defaults to normalizing by the length of qpts.
`in.meth`	Inner optimization function currently one of `'nlminb'`, `'optim'`, or `'trustOptim'`.
`out.meth`	Outer optimization function to be used, depending on the type of method. nls Nonlinear least square nnls.eq Nonlinear least square with equality or/and inequality constraints of the parameters.
`control.in`	Control object for inner optimization function.
`control.out`	Control object for outer optimization function.
`eps`	Finite differencing step size, if needed.
`active`	Incides indicating which parameters of pars should be estimated; defaults to all of them.
`posproc`	Should the state vector be constrained to be positive? If this is the case, the state is represented by an exponentiated basis expansion in the proc object.
`discrete`	Is it a discrete process.
`poslik`	Should the state be exponentiated before being compared to the data? When the state is represented on the log scale (posproc=TRUE), this is an alternative to taking the log of the data.
`names`	The names of the state variables if not given by the column names of coefs.
`sparse`	Should sparse matrices be used for basis values? This option can save memory when using 'trust' optimization method.
`basisvals0`	Values of the collocation basis to be used for the history part of the data. This should be a basis object from the fda package.
`coefs0`	Vector giving the estimate of the coefficients in the spline for the history part of the data.
`nbeta`	The number of lags for the delay.
`ndelay`	A vector inidicating which state process has a delay term.
`tau`	A list of delay lags.

A list with elements

data: The matrix for the observed data.
res: The inner optimization result.
ncoefs: The estimated coefficients.
lik: The lik object generated.
proc: The proc object generated.
pars: The estimated parameters.
beta: The estimated contribution of lags for the delay.
kappa: The estimated parameters for the time varying function.
times: The times at which the data are observed.
fdobj.d: The functional data object for the estimated state process.
fdobj0: The functional data object for the estimated state process of the history part.
tau: The lags of delays.