uvector function

ML estimation vector for reducible SDEs

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().

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 $c[i, i]$ of $C$.
• csub: Vector with sub-diagonal $c[i, i-1]$ for c("$i >\n$", "$1$").
• z: A numeric vector

Returns

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.

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) <tools:::Rd_expr_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.

Functions

• uvector(): Estimation vector, general
• uvector_noh(): Estimation vector, non-hierarchical
• logdet.and.v(): Logarithm of determinant, and $v$ vector