Calculate conditional AIC — cAIC • tinyVAST

Calculates the conditional Akaike Information criterion (cAIC).

Usage

cAIC(object)

Arguments

object: Output from tinyVAST().

Value

cAIC value

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.

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

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

Examples

data( red_snapper )
red_snapper = droplevels(subset(red_snapper, Data_type=="Biomass_KG"))

# Define mesh
mesh = fmesher::fm_mesh_2d( red_snapper[,c('Lon','Lat')],
                           cutoff = 1 )

# define formula with a catchability covariate for gear
formula = Response_variable ~ factor(Year) + offset(log(AreaSwept_km2))

# make variable column
red_snapper$var = "logdens"
# fit using tinyVAST
fit = tinyVAST( data = red_snapper,
                formula = formula,
                sem = "logdens <-> logdens, sd_space",
                space_columns = c("Lon",'Lat'),
                spatial_graph = mesh,
                family = tweedie(link="log"),
                variable_column = "var",
                control = tinyVASTcontrol( getsd = FALSE,
                                           profile = "alpha_j" ) )

cAIC(fit)
#> [1] 42912.43