cAIC function

Calculate conditional AIC

Calculates the conditional Akaike Information criterion (cAIC).

cAIC(object, what = c("cAIC", "EDF"), ...)

Arguments

• object: Output from sdmTMB().
• what: Whether to return the cAIC or the effective degrees of freedom (EDF) for each group of random effects.
• ...: Other arguments for specific methods. Not used.

Returns

Either the cAIC or the effective degrees of freedom (EDF) by group of random effects depending on the argument what.

Details

cAIC is designed to optimize the expected out-of-sample predictive performance for new data that share the same random effects as the in-sample (fitted) data, e.g., spatial interpolation. In this sense, it should be a fast approximation to optimizing the model structure based on k-fold cross-validation.

By contrast, AIC() calculates the marginal Akaike Information Criterion, which is designed to optimize expected predictive performance for new data that have new random effects, e.g., extrapolation, or inference about generative parameters.

cAIC also calculates the effective degrees of freedom (EDF) as a byproduct. This is the number of fixed effects that would have an equivalent impact on model flexibility as a given random effect.

Both cAIC and EDF are calculated using Eq. 6 of Zheng, Cadigan, and Thorson (2024).

For models that include profiled fixed effects, these profiles are turned off.

Examples

mesh <- make_mesh(dogfish, c("X", "Y"), cutoff = 15)
fit <- sdmTMB(catch_weight ~ s(log(depth)),
  time_varying = ~1,
  time_varying_type = "ar1",
  time = "year",
  spatiotemporal = "off",
  mesh = mesh,
  family = tweedie(),
  data = dogfish,
  offset = log(dogfish$area_swept)
)
cAIC(fit)
cAIC(fit, what = "EDF")
AIC(fit)

References

Deriving the general approximation to cAIC used here:

Zheng, N., Cadigan, N., & Thorson, J. T. (2024). A note on numerical evaluation of conditional Akaike information for nonlinear mixed-effects models (arXiv:2411.14185). arXiv. tools:::Rd_expr_doi("10.48550/arXiv.2411.14185")

The utility of EDF to diagnose hierarchical model behaviour:

Thorson, J. T. (2024). Measuring complexity for hierarchical models using effective degrees of freedom. Ecology, 105(7), e4327 tools:::Rd_expr_doi("10.1002/ecy.4327")