Calculate deviance explained

deviance_explained fits a null model, calculates the deviance relative to a saturated model for both the original and the null model, and uses these to calculate the proportion of deviance explained.

This implementation conditions upon the maximum likelihood estimate of fixed effects and the empirical Bayes ("plug-in") prediction of random effects. It can be described as "conditional deviance explained". A state-space model that estimates measurement error variance approaching zero (i.e., collapses to a process-error-only model) will have a conditional deviance explained that approaches 1.0

For several families (tweedie, negbin1, negbin2, and student), the null model is fitted using the MLE for an overdispersion parameter from the full model. This is done because, e.g., the negbin1 and negbin2 only belong to the exponential family when the overdispersion parameter is fixed, and the deviance relative to a saturated model is only defined for the exponential family.

Usage

deviance_explained(x, null_formula, null_delta_formula = ~1)

Arguments

x

output from \code{tinyVAST()}

null_formula

formula for the null model. If missing, it uses null_formula = response ~ 1. For multivariate models, it might make sense to use null_formula = response ~ category

null_delta_formula

formula for the null model for the delta component. If missing, it uses null_formula = response ~ 1. For multivariate models, it might make sense to use null_delta_formula = response ~ category

Value

the proportion of conditional deviance explained.