Specify Covariates

Add covariates to a model.

Usage

set_covariates(mod, formula)

Arguments

mod: An object of class "bage_mod", created with mod_pois(), mod_binom(), or mod_norm().
formula: A one-sided R formula, specifying the covariates.

Value

A modified version of mod

Covariate data

All variables contained in the formula argument to set_covariates() should be in the dataset supplied in the original call to mod_pois(), mod_binom(), or mod_norm().

set_covariates() processes the covariate data before adding it to the model:

numerical variables are standardized, using x <- scale(x).
categorical variables are converted to sets of indicator variables, using 'treatment' contrasts (stats::contr.treatment()). For instance, variable x with categories "high", "medium", and "low", is converted into two indicator variables, one called xmedium and one called xlow.

Mathematical details

When a model includes covariates, the quantity

$$\pmb{Z} \pmb{\zeta}$$

is added to the linear predictor, where $\pmb{Z}$ is a matrix of standardized covariates, and $\pmb{\zeta}$ is a vector of coefficients. The elements of $\pmb{\zeta}$ have prior

$$\zeta_p \sim \text{N}(0, 1)$$.

Examples

## create a COVID covariate
library(dplyr, warn.conflicts = FALSE)
births <- kor_births |>
  mutate(is_covid = time %in% 2020:2022)
mod <- mod_pois(births ~ age * region + time,
                data = births,
                exposure = popn) |>
  set_covariates(~ is_covid)
mod
#> 
#>     ------ Unfitted Poisson model ------
#> 
#>    births ~ age * region + time
#> 
#>   exposure = popn
#> 
#>         term  prior along n_par n_par_free
#>  (Intercept) NFix()     -     1          1
#>          age   RW()   age     9          9
#>       region    N()     -    16         16
#>         time   RW()  time    13         13
#>   age:region   RW()   age   144        144
#> 
#>  covariates: ~is_covid
#> 
#>  disp: mean = 1
#> 
#>  n_draw var_time var_age
#>    1000     time     age
#>