Estimate Rt via piecewise constant changepoint model

This option models the effective reproduction number Rt over time as a piecewise constant function. The changepoints of the constant pieces are estimated from the data using an approximate changepoint model. This option is suitable when Rt follows a step-like trajectory with occasional large jumps, e.g. due to strong interventions. It is less suitable for modeling gradual changes in Rt over time.

Usage

R_estimate_piecewise(
  R_start_prior_mu = 1,
  R_start_prior_sigma = 0.8,
  changepoint_max_distance = 14,
  changepoint_min_distance = 7,
  change_prior_shape = 0.5,
  change_prior_scale = 1e-04,
  change_tolerance = 0.05,
  link = "inv_softplus",
  R_max = 6,
  strictness_alpha = 1,
  modeldata = modeldata_init()
)

Arguments

R_start_prior_mu

Prior (mean) on the initial reproduction number (intercept).

R_start_prior_sigma

Prior (standard deviation) on the initial reproduction number (intercept).

changepoint_max_distance

Maximum distance between changepoints in days. This setting guarantees that two consecutive changes in Rt can be captured if they are changepoint_max_distance days or more apart. Faster changes are not guaranteed to be captured.

changepoint_min_distance

Minimum distance between changepoints in days. This setting guarantees that two consecutive changes in Rt are at least changepoint_min_distance days apart. This avoids Rt trajectories that are unrealistically volatile. For example, a minimum distance of 7 implies that you don't expect Rt to make more than one large jump within a week.

change_prior_shape

Exponential-Gamma (EG) prior (shape) for the strength of changes between the pieces. At each estimated changepoint, the change in Rt is sampled from a normal distribution with standard deviation given by the EG prior. This prior has a strong peak towards zero and a long tail. In other words, while most changes are expected to be small, the prior allows for occasional large jumps in Rt. Smaller shape parameters will lead to more sparseness, i.e. a longer tail. Note that when adjusting the shape, you will likely also have to adjust the scale. See details for more advice on choosing a suitable prior.

change_prior_scale

Exponential-Gamma (EG) prior (scale) for the strength of changes between the pieces. See change_prior_shape above for an explanation. Larger scales will lead to more variability: a doubling of the scale roughly corresponds to a doubling of all quantiles of the prior.

change_tolerance

Tolerance for "negligible" changes in Rt. Changes smaller than change_tolerance are ignored by changepoint_min_distance, i.e. they can also occur closer to each other. This tolerance gives the model more flexibility in placing changepoints with large jumps.

link

Link function. Currently supported are inv_softplus (default) and scaled_logit. Both of these links are configured to behave approximately like the identity function around R=1, but become increasingly non-linear below (and in the case of scaled_logit also above) R=1.

R_max

If link=scaled_logit is used, a maximum reproduction number must be assumed. This should be higher than any realistic R value for the modeled pathogen. Default is 6.

strictness_alpha

The concentration parameter of the Dirichlet prior for the changepoint positions. Choosing smaller values of strictness_alpha will lead to more discrete changepoints. Note that choosing small values of strictness_alpha can impede MCMC sampling.

modeldata

A modeldata object to which the above model specifications should be added. Default is an empty model given by modeldata_init(). Can also be an already partly specified model returned by other EpiSewer modeling functions.

Value

A modeldata object containing data and specifications of the model to be fitted. Can be passed on to other EpiSewer modeling functions to add further data and model specifications.

The modeldata object also includes information about parameter initialization (.init), meta data (.metainfo), and checks to be performed before model fitting (.checks).

Details

The Exponential-Gamma (EG) prior on the strength of changes is parameterized via the arguments change_prior_shape and change_prior_scale. It has a long tail to support large changes while keeping the variation low most of the time. The default configuration should work well in most contexts except for really extreme changes in Rt over a short time window. To check the quantiles of your prior, you can use the function qexpgamma() with corresponding shape and scale parameters.

If you need to adjust the overall variation, you can adjust the change_prior_scale parameter. A doubling of the scale roughly corresponds to a doubling of the quantiles. For example, when the 95% quantile is 0.2 for a given scale and you double that scale, the 95% quantile will be at 0.4.

If you need to support more extreme changes, you can decrease the change_prior_shape parameter, which will emphasize the long-tail behavior of the prior. Note however that this will substantially increase all quantiles of the prior, so you will also have to decrease the scale parameter to achieve a similar level of day-to-day variation.

See also

Other Rt models: R_estimate_approx(), R_estimate_changepoint_splines(), R_estimate_ets(), R_estimate_gp(), R_estimate_rw(), R_estimate_smooth_derivative(), R_estimate_splines()