Skip to contents

Calculate conditional AIC

Source: R/cAIC.R
cAIC.Rd

Calculates the conditional Akaike Information criterion (cAIC).

Usage

cAIC(object, method = c("stable", "fast"))

Arguments

object

Output from tinyVAST().

method

whether to compute effective degrees of freedom using the stable method diag(solve(Hess, Hess_new)) or a faster and experimental method -rowSums(sparseinv::Takahashi_Davis(-Hess) * t(Hess_new)), where the latter avoids constructing a dense matrix prior to extracting its diagonal

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. (2026). A unifying theory for the evaluation of conditional Akaike information for mixed-effects models. Journal of Statistical Computation and Simulation. doi:10.1080/00949655.2026.2736799

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,
                space_term = "logdens <-> logdens, sd_space",
                space_columns = c("Lon",'Lat'),
                spatial_domain = mesh,
                family = tweedie(link="log"),
                variable_column = "var",
                control = tinyVASTcontrol( getsd = FALSE,
                                           profile = "alpha_j" ) )

cAIC(fit) # conditional AIC
#> Error in UseMethod("cAIC", object): no applicable method for 'cAIC' applied to an object of class "tinyVAST"
AIC(fit) # marginal AIC
#> [1] 43073.52