log_lklh {REffectivePred}

The likelihood function

Description

The negative log likelihood function of the model.

Usage

log_lklh(
  param,
  params_limits,
  restrictions = NULL,
  restriction.starts = NULL,
  ranges = NULL,
  rt_func = 1,
  silence.errors = FALSE,
  fit.t.pred,
  lt,
  cases,
  scenario = NULL,
  H.E,
  H.W,
  adj.period,
  population,
  rho,
  serial_mean,
  serial_var,
  window_size
)

Arguments

param

Includes the following sets of parameters in a vector, in this order:

• a1,a2,a3,a4 - Parameters for curve c() specified by rt_func.

• nu - Loss of Immunity rate.

• v2,v3,v4,v5 - Transmissibility of variants in waves 2+, as relative multiplication factors compared to transmissibility in wave 1.

• psi1,psi2,psi3,psi4 - Psi parameters for severity levels 1,2,3 and 4.

• u,v - Variance parameters. Only u is currently in use.

• beta0,beta.R,beta.E,beta.W - When restrictions = NULL. Currently unsupported.

params_limits

Boundaries/limits of the ini_params.

restrictions

A numeric integer vector giving the severity of restrictions. Zero means no restriction, and higher numbers means greater severity/disruption. The ordered unique values should be consecutive integers starting from zero. Each number (other than 0) adds a new parameter to the fit. restrictions = NULL causes the function to use mobility data instead of the psi values (currently unsupported).

restriction.starts

A vector of same length as restrictions, of times when restrictions came into effect. Note: the first index time should be 1.

ranges

An vector of time ranges for the different waves. The wave ranges should be contiguous, with at least one unit of time between consecutive waves.

rt_func

The parametric form of function c(). Options are listed under function c_helper.

silence.errors

Ignores (skips) NA or NaN values when summing up likelihood contributions over time.

fit.t.pred

Time of prediction.

lt

Length of cases.

cases

A vector containing cases for each time-point.

scenario

A character string describing options to deal with restrictions. Currently unsupported.

H.E

Mobility metrics for category Retail & Entertainment. Currently unsupported.

H.W

Mobility metrics for category Workplaces. Currently unsupported.

adj.period

Delays in society adjusting.

population

total population size.

rho

Under-reporting fraction.

serial_mean

Mean of the serial interval on the log scale.

serial_var

Variance of the serial interval on the log scale.

window_size

The maximum value for the serial interval.

Details

The predicted curve is computed based on parameters supplied, by first calling the prediction function pred.curve. The probability model used to compute the likelihood assumes that observed infection at time t are \sim N(mean = I_t, sd = \sqrt{u*I_t}), where I_t are predicted infections, and sums the log-likelihood contributions for each time t during waves, and up to fit.t.pred.

Value

The negative log likelihood value of the data.