Calculates the conditional Akaike Information criterion (cAIC).
Usage
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.
Value
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.
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. 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 doi:10.1002/ecy.4327
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)
)
#> Detected irregular time spacing with an AR(1) or random walk process.
#> Consider filling in the missing time slices with `extra_time`.
#> `extra_time = c(2005, 2007, 2009, 2011, 2013, 2015, 2017, 2019, 2020)`
cAIC(fit)
#> [1] 12071.43
cAIC(fit, what = "EDF")
#> b_rw_t omega_s s(log(depth))
#> 9.043457 38.730229 6.613376
AIC(fit)
#> [1] 12192.96