dynamics.cv: A function to calculate the approximate CV score

In jie108/dynamics: Semiparametric modelling of nonlinear dynamical systems

Description

This is version 0.2-1 updated in April, 2011. A function to calculate the approximate CV score for a given model (specified by method and knots.u) based on the final estimates of dynamics.fit (x0.final, theta.final, beta.final). Note: two cv scores are returned: one based on the prediction error criterion (cvcur.alt); and another based on the loss function with penalty terms (cvcur.score); cvcur.alt is recommended.

Usage

dynamics.cv(x0.final,theta.final,beta.final,subid=NULL,data.path.u,obstime.u,N.u=1000,method="bspline",knots.u,lambda1.final,lambda2.final,Phi.pen=NULL,ini.fix=FALSE, maxloop=10,thre=0.0001)

Arguments

x0.final	numeric vector:final estimates of the initial conditions by dynamics.fit; vector of length N (total number of curves).
theta.final	numeric vector: final estimates of the subject-specific scale parameters by dynamics.fit; vector of length n (number of cluters);
beta.final	numeric vector: final estimates of the basis coefficients by dynamics.fit; vector of length M (number of basis functions)
subid	vector (numeric of string): cluster id for each curve, vector of length n (number of clusters); default(=NULL): no cluster
data.path.u	list (numeric): list of measurements for each curve, list length=N; each component is a numerical vector corresponding to measurements of one curve
obstime.u	list (numeric): list of measurement times for each curve, list length=N;each component is a numerical vector corresponding to measurement times of one curve
N.u	integer: number of steps for the Runge-Kunta method; default=1000
method	string: method for basis representation; two possible values: "bspline" (default), "natural" (truncated cubic polynomials)
knots.u	numeric vector: sequence of knots; length=M (number of basis funcitons)
lambda1.final	numeric scalar: final value for the penalty parameter of the initial conditions by dynamics.fit
lambda2.final	numeric scalar: final value for the penalty parameter of the scale parameters by dynamics.fit
Phi.pen	numeric matrix: penalty matrix of the basis coefficients. it is a M by M numeric matrix;defaul(=NULL): zero matrix
ini.fix	logic (TRUE or FALSE): indicating whether initial conditions are viewed as known or not; if known, then x0.ini will not be updated;default=FALSE (not known)
maxloop	integer: maximum number of iterations for calculating the drop-one-out initial condition $a^-(i)$; default=10
thre	numeric scalar: threshold to check the convergence of the drop-one-out initial condition estimate; default=0.0001

Details

dynamics.cv uses a second order Taylor expansion to approximate the leave-one-curve-out cv score

Value

A list with five components

cvcur.alt	numeric scalar: the approximate leave-one-curve-out cv score based on prediction error criterion
cvcur.score	numeric scalar: the approximate leave-one-curve-out cv score based on the loss function with penalty terms
x0.drop	numeric vector of length N: the drop-one-curve-out estimates of the initial conditions for each curve
theta.drop	numeric vector of length N: the drop-one-curve-out estimates of the scale parameters for each curve
beta.drop	numeric matrix of dimension M by N: the drop-one-curve-out estimates of the basis coefficients. Note: when method="natural", nrow(beta.NR)=length(knots.u)+3, since the first three terms of beta.NR corresponds to $(x,x^2,x^3)$

Author(s)

J. Peng, D. Paul

References

D. Paul, J. Peng, P. Burman, W. Sacks(2008). Semiparametric modelling of autonomous nonlinear dynamical systems with applications.

jie108/dynamics documentation built on Jan. 28, 2020, 12:03 a.m.