Extract Values for Hyper-Parameters

Extract values for hyper-parameters from a model object. Hyper-parameters include main effects and interactions, dispersion and variance terms, and SVD or spline coefficients.

Usage

# S3 method for class 'bage_mod'
components(
  object,
  standardize = c("terms", "anova", "none"),
  quiet = FALSE,
  ...
)

Arguments

object: Object of class "bage_mod", typically created with mod_pois(), mod_binom(), or mod_norm().
standardize: Standardization method: one of "terms", "anova", or "none". The default is "terms". See below for details.
quiet: Whether to suppress messages. Default is FALSE.
...: Unused. Included for generic consistency only.

Value

A tibble with four columns columns:

The return value contains the following columns:

term Model term that the hyper-parameter belongs to.
component Component within term.
level Element within component .
.fitted An rvec containing draws from the posterior distribution.

Fitted vs unfitted models

components() is typically called on a fitted model. In this case, the modelled values are draws from the joint posterior distribution for the hyper-parameters in the model.

components() can, however, be called on an unfitted model. In this case, the modelled values are draws from the joint prior distribution. In other words, the modelled values are informed by model priors, and by any exposure, size, or weights argument in the model, but not by the observed outcomes.

Standardizing estimates

Often the sum of the intercept, main effect, and interaction terms is well-identified by the data, but the values for individual terms is not. This indeterminancy does not affect the ultimate estimation of rates, probabilities, and means, but does complicate the interpretation of the higher-level terms.

One way of dealing with poorly- identified terms is to post-process the estimates, imposing some sort of standardization. There are three options, specified through the standardize argument:

"terms" Each main effect or interaction, and any component terms such as trend or seasonal effects, are independently scaled so that they sum to 0.
"anova" An ANOVA-style decomposition is carried out so that all variation associated with age is attributed to the age term, all variation associated with the interaction between age and sex is attributed to the age-sex term, and so on. Components terms such as trend and seasonal effects are left untouched.
"none" No standardization is done.

"terms" standardization is helpful for understanding model dynamics. "anova" standardization is helpful for understanding the contribution of each variable to overall patterns.

For a description of the standardization algorithms used by bage, see vignette("vig2_math").

Examples

## specify model
mod <- mod_pois(injuries ~ age + sex + year,
                data = injuries,
                exposure = popn)

## extract prior distribution
## of hyper-parameters
mod |>
  components()
#> ℹ Model not fitted, so values drawn straight from prior distribution.
#> # A tibble: 37 × 4
#>    term        component level                   .fitted
#>    <chr>       <chr>     <chr>              <rdbl<1000>>
#>  1 (Intercept) effect    (Intercept)    -0.015 (-2, 1.8)
#>  2 age         effect    0-4          -0.013 (-4.2, 4.4)
#>  3 age         effect    5-9          -0.00086 (-3.6, 4)
#>  4 age         effect    10-14         0.00028 (-3, 3.2)
#>  5 age         effect    15-19       0.00058 (-2.2, 2.7)
#>  6 age         effect    20-24        -0.00074 (-2, 2.7)
#>  7 age         effect    25-29        0.0053 (-2.1, 2.2)
#>  8 age         effect    30-34       0.00041 (-2.1, 2.2)
#>  9 age         effect    35-39         0.016 (-2.2, 2.5)
#> 10 age         effect    40-44         0.012 (-2.4, 2.7)
#> # ℹ 27 more rows

## fit model
mod <- mod |>
  fit()

## extract posterior distribution
## of hyper-parameters
mod |>
  components()
#> # A tibble: 37 × 4
#>    term        component level                    .fitted
#>    <chr>       <chr>     <chr>               <rdbl<1000>>
#>  1 (Intercept) effect    (Intercept)   -2.5 (-4.3, -0.86)
#>  2 age         effect    0-4         -0.43 (-0.51, -0.36)
#>  3 age         effect    5-9            -1.7 (-1.9, -1.6)
#>  4 age         effect    10-14          -1.3 (-1.4, -1.2)
#>  5 age         effect    15-19           0.44 (0.38, 0.5)
#>  6 age         effect    20-24          0.59 (0.52, 0.64)
#>  7 age         effect    25-29          0.43 (0.37, 0.49)
#>  8 age         effect    30-34           0.34 (0.28, 0.4)
#>  9 age         effect    35-39           0.34 (0.28, 0.4)
#> 10 age         effect    40-44          0.33 (0.28, 0.39)
#> # ℹ 27 more rows