Calculates the conditional Akaike Information criterion (cAIC).
Usage
cAIC(object, what = c("cAIC", "EDF"))Arguments
- object
Output from
dsem- what
Whether to return the cAIC or the effective degrees of freedom (EDF) for each group of random effects.
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 crossvalidation.
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 as a byproduct the effective degrees of freedom, i.e., 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 Thorson 2024.
Note that, 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 behavior**
Thorson, J. T. (2024). Measuring complexity for hierarchical models using effective degrees of freedom. Ecology, 105(7), e4327 doi:10.1002/ecy.4327