uvector {resde}

ML estimation vector for reducible SDEs

Description

These functions are not normally called directly by the user. Function uvector() is used by sdefit(). Function uvector_noh() is a more limited version, maintained for documentation purposes. Function logdet_and_v() is used by uvector() and uvector_noh().

Usage

uvector(x, t, unit = NULL, beta0, beta1, eta, eta0, x0, t0, lambda,
  mum = 1, mu0 = 1, mup = 1, sorted = FALSE, final = FALSE)

uvector_noh(x, t, beta0, beta1, eta, eta0, x0, t0, lambda, final = FALSE)

logdet.and.v(cdiag, csub = NULL, z)

Arguments

x, t

Data vectors

unit

Unit id vector, if any.

beta0, beta1, eta, eta0, x0, t0

SDE parameters or re-parameterizations.

lambda

Named list of parameters(s) for phi(), possibly local vectors.

mum, mu0, mup

Optional \sigma multipliers.

sorted

Data already ordered by increasing t?

final

Mode, see below.

cdiag

Vector with the diagonal elements c_{ii} of C.

csub

Vector with sub-diagonal c_{i, i-1} for i > 1.

z

A numeric vector

Details

uvector() and uvector_noh() calculate a vector of residuals for sum of squares minimization by nls() or nlme(). The first one works both for single-unit and for bilevel hierarchical models. It is backward-compatible with uvector_noh(), which is only for single-unit models but simpler and easier to understand. They require a transformation function phi(x, theta), and a function phiprime(x, theta) for the derivative dy/dx, where theta is a list containing the transformation parameters.

logdet_and_v() calculates \log[\det(L)] and v = L^{-1} z, where C = LL', with L lower-triangular.

The three functions are essentially unchanged from García (2019) <doi:10.1007/s00180-018-0837-4>, except for a somewhat safer computation for very small beta1, and adding in logdet_and_v() a shortcut for when L is diagonal (e.g., when \sigma_m = 0). The transformation functions phi and phiprime can be passed as globals, as in the original, or in an environment named trfuns.

Value

uvector() and uvector_noh(): If final = FALSE (default), return a vector whose sum of squares should be minimized over the parameters to obtain maximum-likelihood estimates. If final = TRUE, passing the ML parameter estimates returns a list with the sigma estimates, the maximized log-likelihood, and AIC and BIC criteria..

logdet_and_v(): List with elements logdet and v.

Functions

• uvector(): Estimation vector, general

• uvector_noh(): Estimation vector, non-hierarchical

• logdet.and.v(): Logarithm of determinant, and v vector