Describe a model family's distribution parameters

Inspect the meaning and order of distribution parameters independently of the numerical representation used by the fitting package.

Usage

family_parameters(object, ...)

Arguments

object

A fitted mgcv model, an existing GAM wrapper, or an mgcv family object. Other fitting packages require their own specification.

...

Arguments reserved for methods.

Value

A tibble with parameter, symbol, definition, native, predictor, source, link, component, returned, and uncertainty. Predictor indices follow the fitting package's equation order. Global parameters have no predictor and are omitted from fitted parameter output; they remain fixed during coefficient sampling. Derived rows identify constraints such as a multinomial reference category. The package and family attributes identify the parameterisation provider. The parameterisation attribute describes the mathematical distribution. expectation_condition records conditions for a finite expected response.

Details

fitted_values() and fitted_samples() default to the parameters marked returned. On the response scale these are natural distribution parameters, which can differ from the fitting package's native response predictions. For example, Gaussian LSS output contains standard deviation, whereas mgcv predicts reciprocal standard deviation. GEV location is not its expectation. link describes the native representation: for example, ziplss() uses an identity link for log rate, while natural rate is the exponential of that predictor. The sinh-arcsinh skewness and tailweight parameters control distribution shape; they are not the response's standardized skewness and kurtosis.

link() and inv_link() retain the fitting package's native conventions and their existing aliases. Use the definitions here to interpret them.

See also

fitted_values(), fitted_samples()

Examples

family_parameters(mgcv::gevlss())
#> # A tibble: 3 x 10
#>   parameter symbol definition   native predictor source link  component returned
#>   <chr>     <chr>  <chr>        <chr>      <int> <chr>  <chr> <chr>     <lgl>   
#> 1 location  mu     Location pa~ locat~         1 predi~ iden~ NA        TRUE    
#> 2 scale     sigma  Positive sc~ log s~         2 predi~ iden~ NA        TRUE    
#> 3 shape     xi     Distributio~ shape          3 predi~ logit NA        TRUE    
#> # i 1 more variable: uncertainty <chr>
family_parameters(mgcv::gaulss())
#> # A tibble: 2 x 10
#>   parameter symbol definition   native predictor source link  component returned
#>   <chr>     <chr>  <chr>        <chr>      <int> <chr>  <chr> <chr>     <lgl>   
#> 1 mean      mu     Mean of the~ mean           1 predi~ iden~ NA        TRUE    
#> 2 sd        sigma  Standard de~ recip~         2 predi~ logb  NA        TRUE    
#> # i 1 more variable: uncertainty <chr>
family_parameters(mgcv::ziplss())
#> # A tibble: 2 x 10
#>   parameter   symbol definition native predictor source link  component returned
#>   <chr>       <chr>  <chr>      <chr>      <int> <chr>  <chr> <chr>     <lgl>   
#> 1 rate        lambda Poisson r~ log r~         1 predi~ iden~ NA        TRUE    
#> 2 presence_p~ p      Probabili~ clogl~         2 predi~ iden~ NA        TRUE    
#> # i 1 more variable: uncertainty <chr>