Structure for incorporating covariates into a `fit_seromodel_covariates` function

[ben18785]

Proposed interface:

fit <- fit_seromodel_covariates(
  serosurvey = serodata,
  formula = ~...,
  covariates=...,
   ...
)

Note that by allowing covariates to be a data frame separate from the serosurvey, this allows more flexible types of covariates to be included. For example, time- or age-varying covariates.

Formula can indicate the model type. For example:

Constant model:

formula ~ 1

Time-varying model:

formula ~ time

Age-varying model:

formula ~ age

Formula can also be used to specify, for example, covariate effects:

formula = ~ sex

or it can be used to allow a difference in the base rate by a multiplicative factor across regions;

formula = ~ sex + (1 | region)

In the above, if the model is a time-varying model this would mean a decomposition of the form:

$$ \log \lambda(t,region) = \eta(t) + \theta(region) + beta * sex $$

Alternatively, we could also allow each region to have its own time-varying base:

formula = ~ sex + (time | region)

$$ \log \lambda(t,region) = \eta(t, region) + beta * sex $$

We could also output a regression summary type thing here.

We could also do:

formula = ~ (age | sex)

Note: existing users could use fit_seromodel with model_type which would internally call fit_seromodel_covariates.

Ideas:

• We may want to make a shiny app to facilitate users in choosing an appropriate prior for the FOI
• Facilitate prior-predictive checks
• Workflow for setting priors; e.g. try fitting model with males/females separately