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Maximum (approximate) likelihood estimation for the SIRD-GA model

Source: R/sird_ga_fit.R
sird_ga_fit.Rd

Estimates theta = (lambda, gamma, alpha, i0, p, tau2) (and optionally r0) by Nelder-Mead maximisation of the Kalman-filter approximate log-likelihood (sird_ga_loglik()), following the estimation strategy described in the SIRD-GA manuscript. Positivity and unit-interval constraints are enforced through a log/logit reparametrisation, so the optimiser itself runs unconstrained.

Usage

sird_ga_fit(
  y,
  N,
  Delta = 1,
  start,
  r0_fixed = 0,
  estimate_r0 = FALSE,
  p_max = 0.999,
  n_sub = 10L,
  Q0_diag = 1e-08,
  control = list(maxit = 3000, reltol = 1e-10),
  hessian = TRUE
)

Arguments

y

Numeric vector of observed infectious counts, y_0, ..., y_n.

N

Population size.

Delta

Time step between observations.

start

Named numeric vector/list with starting values for lambda, gamma, alpha, i0, p, tau2 (and r0 if estimate_r0 = TRUE).

r0_fixed

Value at which r0 is held fixed when estimate_r0 = FALSE (default 0, appropriate for data starting at or near the onset of the epidemic).

estimate_r0

Logical; estimate r0 jointly instead of fixing it.

p_max

Upper bound enforced on the reporting probability p (default 0.999). Real daily case series are rarely reported with near-100% completeness; without an upper cap strictly below 1, the optimiser can drive p -> 1 and tau2 to a degenerate extreme (perfect reporting, all residual variance absorbed by the measurement-noise term), a boundary artefact rather than a genuine optimum. Setting p_max around 0.95-0.98 is recommended for real data; simulation studies where the reporting rate is itself the target of recovery can use p_max = 0.999.

n_sub, Q0_diag

Passed to sird_ga_loglik().

control

List of control parameters passed to stats::optim().

hessian

Logical; compute the numerical Hessian in the unconstrained parametrisation (used only for a quick asymptotic diagnostic — see sird_ga_bootstrap() for the inferential confidence intervals reported in the manuscript).

Value

A list with elements theta (named vector of MLEs in natural scale), loglik, convergence, optim_fit (raw stats::optim() output in the unconstrained parametrisation), and free_se (delta-free standard errors on the unconstrained scale, or NULL).