Maximum likelihood for a compartmental model under the Gaussian approximation

Maximises ga_loglik() over the parameters in start, on an unconstrained scale (logarithms of positive parameters, logits of those in unit), by a Nelder-Mead search (relative tolerance 1e-8) from each starting point followed by BFGS refinement of the best optimum. Parameters in fixed are held at their values.

Usage

ga_fit(
  model,
  data,
  obs,
  N,
  init,
  start,
  fixed = list(),
  unit = NULL,
  blocks = NULL,
  Delta = 1,
  nsub = 10L,
  hessian = TRUE,
  maxit = 1500
)

Arguments

model: A ga_model().
data: Matrix or data frame of counts, one column per element of obs (in the same order), one row per interval. NA marks a missing count.
obs: List of ga_incidence() / ga_prevalence() streams.
N: Population size.
init: A function of the parameter list returning the named vector of initial fractions, e.g. function(p) c(S = 1 - p$i0, I = p$i0, R = 0, D = 0).
start: Named list of starting values of the free parameters, or a list of such lists (several starts). A parameter listed in blocks takes a vector with one value per block (a scalar is recycled).
fixed: Named list of parameters held fixed.
unit: Names of free parameters constrained to (0, 1). By default, the reporting probabilities named in obs and any free parameter whose name ends in 0 (initial fractions such as i0).
blocks: Optional named list giving, for a time-varying rate parameter, an integer vector with the block (1, ..., B) of each observation interval; the parameter then takes one value per block.
Delta: Length of the observation interval.
nsub: Runge-Kutta steps per interval.
hessian: Logical; compute the numerical Hessian at the optimum.
maxit: Iteration limit of each Nelder-Mead run.

Value

An object of class ga_fit with elements coef (estimates on the natural scale, block-specific values named name[b]), loglik, convergence (the optim code of the final run), par and hessian (unconstrained scale), vcov (on that scale), starts (log-likelihood reached from each start) and the inputs needed by ga_profile(), confint.ga_fit() and predict.ga_fit().