A model-specific summary table for GLMs, mgcv GAMs, glmmTMB, brms, lme4, sdmTMB, and tinyVAST. Different criteria occupy different columns; missing or inappropriate criteria are never replaced by another statistic.
Arguments
- fits
One supported fitted model, or a non-empty list of models. A list may mix backends. Complete brms fits are required.
- criterion
Character vector, case-insensitive:
"auto","AIC","BIC","cAIC","logLik","deviance","loo","loo_R2","bayes_R2", or"log_lik"."auto"requests native likelihood-based summaries for frequentist models and LOO/Bayesian R-squared for brms. Add"cAIC"explicitly: native spatial Hessian calculations can be costly."log_lik"is the posterior mean total log likelihood, not ML"logLik".- sort
Preserve input order by default.
TRUEsorts only when every row belongs to one verified comparison group, using LOOIC, AIC, or cAIC in that order. Alternatively specify one of those column names. No sorting combines different criteria, and R-squared is not a ranking rule.- labels
Optional unique, non-empty model labels. Otherwise list names are used, or labels are generated from the list position.
- ...
Arguments passed only to requested brms criterion functions. These arguments cannot select a response or prediction subset: comparison metadata describe the complete fitted response. Refitting options are rejected; this function never launches MCMC or cross-validation refits.
Value
A data frame with model labels, backend/family/likelihood metadata,
sample size, degrees of freedom, convergence flags, requested statistics,
criterion-specific comparison groups and differences, and readable notes.
Inapplicable or unavailable values are NA, with reasons in notes and
the criteria_notes attribute (model, criterion, status, and detail).
No full fits, posterior draws, or pointwise likelihood arrays are retained.
Details
df is the native log-likelihood parameter count or effective penalty
degrees of freedom, not simply the number of regression coefficients.
df_residual is reported separately where provided by the backend.
cAIC_df is the effective penalty used by the conditional criterion, when
available; EDF_random is sdmTMB's summed random-effect EDF.
mgcv's ordinary AIC() already uses a conditional formulation, with its
smoothing-parameter uncertainty correction when available. Its cAIC
column therefore equals native AIC; it is not an independent criterion.
sdmTMB and tinyVAST use their own approximate cAIC() methods. glmmTMB
and lme4 have no supported native conditional-AIC method here. No generic mixed-model
correction, cAIC4 conversion, or refitting workaround is substituted.
For an ordinary model without random effects, cAIC reduces to native AIC.
Profiled spatial fits are not yet validated for conditional penalty
counting; their cAIC is unavailable, while native marginal criteria remain.
Restricted-likelihood and penalised/prior fits are flagged and excluded
from automatic ranking. In particular, REML objective values must not
rank different fixed-effect structures. mgcv's conditional AIC is not its
REML smoothing-selection objective.
AIC/BIC and cAIC comparison groups distinguish conditional observation likelihoods from marginal likelihoods. Ordinary models with no random effects can join either target, but cannot bridge incompatible targets. Groups are formed in input order; compare a subset separately to examine an ordinary model against another target. They require aligned fitted row names, responses, weights, compatible response support, and matching values of shared model-frame columns. Row names must genuinely identify the same observations: these checks cannot establish provenance for independently renumbered datasets. Unsupported or unverifiable cases get separate groups and no differences. Native deviances are descriptive, backend-specific quantities, not a universal scale for ranking families or model classes.
brms LOO comparisons use paired pointwise ELPD differences and their
standard errors through loo::loo_compare(). Pareto-k diagnostics are
reported; unreliable LOO estimates are not ranked. Posterior R-squared
standard deviations retain the earlier se_bayes_R2/se_loo_R2 names,
but are posterior uncertainty, not Monte Carlo standard errors.
Conditional criteria target new observations sharing fitted latent effects; marginal criteria target new random effects. Neither establishes that an abundance index is unbiased or robust to extrapolation. LOO-PIT and refitted cross-validation are separate workflows, not implemented here.
References
Wood, Pya, and Saefken (2016). Smoothing parameter and model selection for general smooth models. doi:10.1080/01621459.2016.1180986 .
Zheng, Cadigan, and Thorson (2024). A note on numerical evaluation of conditional Akaike information for nonlinear mixed-effects models. doi:10.48550/arXiv.2411.14185 .
Examples
a <- glm(mpg ~ wt, data = mtcars, family = gaussian())
b <- glm(mpg ~ wt + hp, data = mtcars, family = gaussian())
result <- table_criterion(list(Weight = a, Weight_and_power = b))
result[c("Model", "df", "AIC", "delta_AIC")]
#> Model df AIC delta_AIC
#> 1 Weight 3 166.0294 9.37709
#> 2 Weight_and_power 4 156.6523 0.00000